{"id":84707,"date":"2026-07-26T16:26:43","date_gmt":"2026-07-26T08:26:43","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/84707.html"},"modified":"2026-07-26T16:26:43","modified_gmt":"2026-07-26T08:26:43","slug":"%e5%bd%93%e8%af%9d%e6%b2%a1%e6%af%9b%e7%97%85%e3%80%81%e5%8a%a8%e4%bd%9c%e8%a6%81%e5%91%bd%ef%bc%9a%e4%b8%80%e7%af%87%e6%8a%8a%e5%85%b7%e8%ba%ab%e5%ae%89%e5%85%a8%e4%bb%8e%e6%96%87","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/84707.html","title":{"rendered":"\u5f53\u201c\u8bdd\u6ca1\u6bdb\u75c5\u3001\u52a8\u4f5c\u8981\u547d\u201d\uff1a\u4e00\u7bc7\u628a\u5177\u8eab\u5b89\u5168\u4ece\u6587\u672c\u5b89\u5168\u91cc\u62c6\u51fa\u6765\u7684\u8bba\u6587\uff0c\u503c\u4e0d\u503c\u5f97\u4fe1\uff1f"},"content":{"rendered":"<p>\u8fd9\u7bc7\u8bba\u6587\u63d0\u51fa\u4e86\u4e00\u4e2a\u6b63\u786e\u4e14\u88ab\u4f4e\u4f30\u7684\u95ee\u9898&#xff0c;\u7ed9\u51fa\u4e86\u4e00\u4efd\u5728\u65b9\u6cd5\u5b66\u81ea\u89c9\u4e0a\u7f55\u89c1\u7684\u5b9e\u9a8c\u8bb0\u5f55&#xff0c;\u4f46\u5176\u6838\u5fc3\u79d1\u5b66\u4e3b\u5f20\u7684\u8bc1\u636e\u94fe\u5b58\u5728\u4e00\u5904\u7ed3\u6784\u6027\u65ad\u88c2&#xff0c;\u4e14\u8bba\u6587\u7684\u65b9\u6cd5\u4e0e\u8be5\u4e3b\u5f20\u5728\u56e0\u679c\u4e0a\u5e76\u4e0d\u76f8\u8fde\u3002<\/p>\n<p>\u4e09\u6761\u4e3b\u7ebf&#xff1a;<\/p>\n<li>\u95ee\u9898\u6210\u7acb\u3002&#034;\u70b9\u71c3\u7a97\u5e18&#034;\u4e0e&#034;\u628a\u9e21\u86cb\u653e\u8fdb\u5fae\u6ce2\u7089&#034;\u662f\u4e24\u7c7b\u4e0d\u5b89\u5168&#xff1a;\u524d\u8005\u5199\u5728\u8bcd\u9762&#xff0c;\u540e\u8005\u5199\u5728\u7269\u7406\u56e0\u679c\u3002\u6587\u672c\u62a4\u680f\u53ea\u8986\u76d6\u524d\u8005\u3002\u968f\u7740 LLM \u8fdb\u5165\u5177\u8eab\u89c4\u5212\u5668\u627f\u62c5\u4efb\u52a1\u5206\u89e3&#xff0c;\u8fd9\u4e2a gap \u6b63\u5728\u653e\u5927\u3002<\/li>\n<li>\u6838\u5fc3\u8bc1\u636e\u5f31\u4e8e\u5176\u5448\u73b0\u3002CD\/PD \u65b9\u5411&#034;\u53ef\u5206&#034;\u7684\u89d2\u5ea6\u8bc1\u636e\u4e2d&#xff0c;\u7ecf\u8870\u51cf\u6821\u6b63\u540e\u81f3\u5c11\u6709 15\u00b0 \u5c5e\u4e8e\u4f30\u8ba1\u566a\u58f0\u7684\u865a\u9ad8&#xff1b;\u66f4\u5173\u952e\u7684\u662f&#xff0c;\u5176 CD\/PD \u5212\u5206\u7531\u4e00\u6761\u5173\u952e\u8bcd\u5b50\u4e32\u89c4\u5219\u751f\u6210&#xff0c;\u800c\u8bba\u6587\u8bbe\u8ba1\u7684\u968f\u673a\u5207\u5206\u96f6\u5047\u8bbe\u68c0\u9a8c\u5728\u539f\u7406\u4e0a\u65e0\u6cd5\u63a7\u5236\u8fd9\u4e00\u6df7\u6742\u3002<\/li>\n<li>\u65b9\u6cd5\u4e0e\u4e3b\u5f20\u8131\u8282\u3002\u5265\u79bb\u8868\u793a\u5206\u6790\u540e&#xff0c;PRISM \u5373\u4e3a\u51bb\u7ed3\u9690\u72b6\u6001\u4e0a\u7684\u7ebf\u6027\u63a2\u9488&#xff08;Alain &amp; Bengio, 2016&#xff09;\u3002\u8bba\u6587\u81ea\u8eab\u7684 Figure 2 \u6570\u636e\u663e\u793a&#xff0c;CDD\/PDD \u4e8c\u7ef4\u5e73\u9762\u7684\u9519\u8bef\u7387\u662f\u5b8c\u6574\u63a2\u9488\u7684\u8fd1\u4e24\u500d\u2014\u2014\u5373\u8be5\u65b9\u6cd5\u7684\u6027\u80fd\u5e76\u4e0d\u6765\u81ea\u5176\u6240\u5ba3\u79f0\u7684\u8868\u793a\u7ed3\u6784\u3002<\/li>\n<p>\u4ee5\u4e0b\u9010\u8282\u5c55\u5f00\u8ba8\u8bba\u3002<\/p>\n<hr \/>\n<h3>1. \u95ee\u9898\u8bbe\u5b9a&#xff1a;CD \u4e0e PD \u7684\u533a\u5206<\/h3>\n<p>\u8bba\u6587\u5c06\u4e0d\u5b89\u5168\u6307\u4ee4\u4e8c\u5206\u4e3a&#xff1a;<\/p>\n<ul>\n<li>\u5185\u5bb9\u5371\u9669&#xff08;Content Danger, CD&#xff09;&#xff1a;\u4e0d\u5b89\u5168\u6027\u663e\u73b0\u4e8e\u6587\u672c\u8868\u9762\u3002\u4f8b\u5982&#034;\u70b9\u71c3\u7a97\u5e18&#034;\u3002\u73b0\u6709\u6587\u672c\u5ba1\u6838\u6a21\u578b\u7684\u76ee\u6807\u57df\u3002<\/li>\n<li>\u7269\u7406\u5371\u9669&#xff08;Physical Danger, PD&#xff09;&#xff1a;\u5b57\u9762\u65e0\u5bb3&#xff0c;\u4ec5\u5728\u7269\u7406\u56e0\u679c\u4e2d\u6210\u7acb\u3002\u4f8b\u5982&#034;\u5fae\u6ce2\u7089\u52a0\u70ed\u9e21\u86cb&#034;\u201c\u5c06\u91d1\u5c5e\u53c9\u5b50\u653e\u5165\u5fae\u6ce2\u7089\u201d\u3002<\/li>\n<\/ul>\n<p>#mermaid-svg-PuteY7gPjJmYTHJD{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-PuteY7gPjJmYTHJD .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-PuteY7gPjJmYTHJD .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-PuteY7gPjJmYTHJD .error-icon{fill:#552222;}#mermaid-svg-PuteY7gPjJmYTHJD .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-PuteY7gPjJmYTHJD 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div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-PuteY7gPjJmYTHJD .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-PuteY7gPjJmYTHJD rect.text{fill:none;stroke-width:0;}#mermaid-svg-PuteY7gPjJmYTHJD .icon-shape,#mermaid-svg-PuteY7gPjJmYTHJD .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-PuteY7gPjJmYTHJD .icon-shape p,#mermaid-svg-PuteY7gPjJmYTHJD .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-PuteY7gPjJmYTHJD .icon-shape .label rect,#mermaid-svg-PuteY7gPjJmYTHJD .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-PuteY7gPjJmYTHJD .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-PuteY7gPjJmYTHJD .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-PuteY7gPjJmYTHJD :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}<span class=\"edgeLabel\"><\/span><span class=\"edgeLabel\"><\/p>\n<p>\u8bcd\u9762\u663e\u73b0<\/p>\n<p><\/span><span class=\"edgeLabel\"><\/p>\n<p>\u7269\u7406\u56e0\u679c<\/p>\n<p><\/span><span class=\"edgeLabel\"><\/span><span class=\"edgeLabel\"><\/span><span class=\"edgeLabel\"><\/span><span class=\"edgeLabel\"><\/span><span class=\"nodeLabel\"><\/p>\n<p>\u81ea\u7136\u8bed\u8a00\u6307\u4ee4<\/p>\n<p><\/span><span class=\"nodeLabel\"><\/p>\n<p>\u5371\u9669\u6765\u6e90<\/p>\n<p><\/span><span class=\"nodeLabel\"><\/p>\n<p>\u5185\u5bb9\u5371\u9669 CD\u300e\u70b9\u71c3\u7a97\u5e18\u300f<\/p>\n<p><\/span><span class=\"nodeLabel\"><\/p>\n<p>\u7269\u7406\u5371\u9669 PD\u300e\u5fae\u6ce2\u7089\u52a0\u70ed\u9e21\u86cb\u300f<\/p>\n<p><\/span><span class=\"nodeLabel\"><\/p>\n<p>\u6587\u672c\u62a4\u680f\u7b56\u7565\u8fdd\u89c4\u7ebf\u7d22\u5339\u914d<\/p>\n<p><\/span><span class=\"nodeLabel\"><\/p>\n<p>\u7269\u7406\u76d1\u63a7\u9700\u56e0\u679c\/\u5e38\u8bc6\u987b\u5728\u6267\u884c\u524d\u5224\u5b9a<\/p>\n<p><\/span><span class=\"nodeLabel\"><\/p>\n<p>\u6267\u884c\u524d\u5b89\u5168\u51b3\u7b56<\/p>\n<p><\/span><\/p>\n<p>\u8bba\u6587\u7684\u4e2d\u5fc3\u4e3b\u5f20\u662f&#xff1a;CD \u4e0e PD \u5728 LLM \u9690\u72b6\u6001\u4e2d\u6784\u6210\u4e24\u4e2a\u53ef\u5206\u7684\u4fe1\u53f7&#xff0c;\u800c\u975e\u540c\u4e00&#034;\u4e0d\u5b89\u5168\u65b9\u5411&#034;\u4e0a\u7684\u5f3a\u5f31\u4e4b\u522b\u3002 \u5168\u6587\u4ef7\u503c\u7cfb\u4e8e\u6b64\u3002\u56e0\u6b64\u672c\u6587\u7684\u590d\u6838\u4e5f\u4ee5\u6b64\u4e3a\u8f74\u3002<\/p>\n<hr \/>\n<h3>2. \u6570\u5b66\u6838\u5fc3\u4e00&#xff1a;\u4e24\u4e2a\u65b9\u5411\u4e0e\u4e24\u79cd\u89d2\u5ea6<\/h3>\n<h4>2.1 \u5b9a\u4e49<\/h4>\n<p>\u5728\u7b2c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">LL<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\">L<\/span><\/span><\/span><\/span><\/span> \u5c42\u53d6\u672b\u4f4d token \u9690\u72b6\u6001 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">hL(x)\u2208Rdh_L(x)\\\\in\\\\mathbb{R}^d<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">L<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8491em\"><\/span><span class=\"mord\"><span class=\"mord mathbb\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u6309\u5b89\u5168 \/ \u5185\u5bb9\u5371\u9669 \/ \u7269\u7406\u5371\u9669\u4e09\u7c7b\u8ba1\u7c7b\u5747\u503c&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\u03bcsafe&#061;1\u2223S\u2223\u2211i\u2208ShL(xi),\u03bcCD&#061;1\u2223E\u2223\u2211i\u2208EhL(xi),\u03bcPD&#061;1\u2223I\u2223\u2211i\u2208IhL(xi)<br \/>\n\\\\mu_{\\\\text{safe}}&#061;\\\\frac{1}{|S|}\\\\sum_{i\\\\in S}h_L(x_i),\\\\quad<br \/>\n\\\\mu_{\\\\text{CD}}&#061;\\\\frac{1}{|E|}\\\\sum_{i\\\\in E}h_L(x_i),\\\\quad<br \/>\n\\\\mu_{\\\\text{PD}}&#061;\\\\frac{1}{|I|}\\\\sum_{i\\\\in I}h_L(x_i)<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03bc<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">safe<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.6431em;vertical-align: -1.3217em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.05em\"><span class=\"\" style=\"top: -1.8557em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">\u2208<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0576em\">S<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3217em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">L<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03bc<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">CD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.6431em;vertical-align: -1.3217em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.05em\"><span class=\"\" style=\"top: -1.8557em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">\u2208<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0576em\">E<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3217em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">L<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03bc<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">PD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.6431em;vertical-align: -1.3217em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">I<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.05em\"><span class=\"\" style=\"top: -1.8557em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">\u2208<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0785em\">I<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3217em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">L<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5371\u9669\u65b9\u5411\u5b9a\u4e49\u4e3a\u76f8\u5bf9\u5b89\u5168\u7c7b\u7684\u4f4d\u79fb&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">uCDD&#061;\u03bcCD\u2212\u03bcsafe,uPDD&#061;\u03bcPD\u2212\u03bcsafe<br \/>\nu_{\\\\text{CDD}}&#061;\\\\mu_{\\\\text{CD}}-\\\\mu_{\\\\text{safe}},\\\\qquad<br \/>\nu_{\\\\text{PDD}}&#061;\\\\mu_{\\\\text{PD}}-\\\\mu_{\\\\text{safe}}<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">CDD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7778em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03bc<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">CD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03bc<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">safe<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 2em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">PDD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7778em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03bc<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">PD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03bc<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">safe<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u8bba\u6587\u62a5\u544a\u4e24\u4e2a\u89d2\u5ea6\u91cf&#xff1a;<\/p>\n<p>\u5747\u503c\u5dee\u89d2\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b8md\\\\theta_{\\\\text{md}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">md<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u7eaf\u51e0\u4f55\u3001\u4e0d\u62df\u5408\u5206\u7c7b\u5668&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b8md&#061;arccos\u2061\u27e8uCDD,\u2009uPDD\u27e9\u2225uCDD\u2225\u2009\u2225uPDD\u2225<br \/>\n\\\\theta_{\\\\text{md}}&#061;\\\\arccos\\\\frac{\\\\langle u_{\\\\text{CDD}},\\\\,u_{\\\\text{PDD}}\\\\rangle}{\\\\|u_{\\\\text{CDD}}\\\\|\\\\,\\\\|u_{\\\\text{PDD}}\\\\|}<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">md<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.363em;vertical-align: -0.936em\"><\/span><span class=\"mop\">arccos<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.427em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2225<\/span><span class=\"mord\"><span class=\"mord mathnormal\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">CDD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2225<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">\u2225<\/span><span class=\"mord\"><span class=\"mord mathnormal\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">PDD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2225<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mopen\">\u27e8<\/span><span class=\"mord\"><span class=\"mord mathnormal\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">CDD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">PDD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">\u27e9<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u63a2\u9488\u6743\u91cd\u89d2\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b8pw\\\\theta_{\\\\text{pw}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9805em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">pw<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff1a;\u5206\u522b\u8bad\u7ec3 safe-vs-CD \u4e0e safe-vs-PD \u4e24\u4e2a L2 \u6b63\u5219 logistic \u63a2\u9488&#xff0c;\u53d6\u6743\u91cd\u5411\u91cf\u5939\u89d2\u3002<\/p>\n<p>\u5b9e\u6d4b&#xff08;Table 1&#xff09;&#xff1a;<\/p>\n<table>\n<tr>3B7B14B32B<\/tr>\n<tbody>\n<tr>\n<td>\u9009\u4e2d\u5c42 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u2113\u22c6\\\\ell^\\\\star<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2113<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6887em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u22c6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n<td>27\/36<\/td>\n<td>20\/28<\/td>\n<td>26\/48<\/td>\n<td>41\/64<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b8pw\\\\theta_{\\\\text{pw}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9805em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">pw<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> (\u00b0)<\/td>\n<td>75.9<\/td>\n<td>74.2<\/td>\n<td>71.6<\/td>\n<td>71.9<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b8md\\\\theta_{\\\\text{md}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">md<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> (\u00b0)<\/td>\n<td>49.1<\/td>\n<td>54.6<\/td>\n<td>63.2<\/td>\n<td>67.7<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h4>2.2 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b8pw&gt;\u03b8md\\\\theta_{\\\\text{pw}}&gt;\\\\theta_{\\\\text{md}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9805em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">pw<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">md<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u767d\u5316\u7684\u7cfb\u7edf\u6027\u540e\u679c&#xff0c;\u800c\u975e\u53ef\u5206\u6027\u589e\u5f3a\u7684\u8bc1\u636e<\/h4>\n<p>\u8bba\u6587\u4ee5\u4e00\u53e5&#034;\u5224\u522b\u5f0f\u8bad\u7ec3\u5728\u5404\u5411\u5f02\u6027\u534f\u65b9\u5dee\u4e0b\u4f1a\u65cb\u8f6c\u6743\u91cd&#034;\u5e26\u8fc7\u3002\u8be5\u9648\u8ff0\u672c\u8eab\u6b63\u786e&#xff0c;\u4f46\u672a\u6307\u51fa\u5176\u504f\u7f6e\u65b9\u5411\u662f\u7cfb\u7edf\u6027\u7684&#xff0c;\u4e14\u6070\u597d\u6307\u5411\u8bba\u6587\u6240\u9700\u7684\u7ed3\u8bba\u3002<\/p>\n<p>\u5728\u5171\u4eab\u534f\u65b9\u5dee <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03a3\\\\Sigma<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord\">\u03a3<\/span><\/span><\/span><\/span><\/span> \u7684\u9ad8\u65af\u8bbe\u5b9a\u4e0b&#xff08;LDA&#xff0c;\u4ea6\u5373\u6b63\u786e\u8bbe\u5b9a\u7684 logistic \u56de\u5f52\u7684\u6e10\u8fd1\u89e3&#xff09;&#xff0c;\u6700\u4f18\u5224\u522b\u65b9\u5411\u4e3a<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">w\u221d\u03a3\u22121(\u03bc1\u2212\u03bc0)<br \/>\nw \\\\propto \\\\Sigma^{-1}(\\\\mu_1-\\\\mu_0)<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u221d<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1141em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord\">\u03a3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03bc<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03bc<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u6545 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">wCD\u221d\u03a3\u22121uCDDw_{\\\\text{CD}}\\\\propto \\\\Sigma^{-1}u_{\\\\text{CDD}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">CD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u221d<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.9641em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord\">\u03a3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">CDD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3001<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">wPD\u221d\u03a3\u22121uPDDw_{\\\\text{PD}}\\\\propto \\\\Sigma^{-1}u_{\\\\text{PDD}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">PD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u221d<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.9641em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord\">\u03a3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">PDD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4e8e\u662f<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">cos\u2061\u03b8pw&#061;uCDD\u22a4\u03a3\u22122uPDDuCDD\u22a4\u03a3\u22122uCDD\u2005\u200auPDD\u22a4\u03a3\u22122uPDD<br \/>\n\\\\cos\\\\theta_{\\\\text{pw}}<br \/>\n&#061;\\\\frac{u_{\\\\text{CDD}}^{\\\\top}\\\\Sigma^{-2}u_{\\\\text{PDD}}}<br \/>\n{\\\\sqrt{u_{\\\\text{CDD}}^{\\\\top}\\\\Sigma^{-2}u_{\\\\text{CDD}}}\\\\;\\\\sqrt{u_{\\\\text{PDD}}^{\\\\top}\\\\Sigma^{-2}u_{\\\\text{PDD}}}}<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9805em;vertical-align: -0.2861em\"><\/span><span class=\"mop\">cos<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">pw<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.2561em;vertical-align: -1.73em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.5261em\"><span class=\"\" style=\"top: -2.11em\"><span class=\"pstrut\" style=\"height: 3.2537em\"><\/span><span class=\"mord\"><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2537em\"><span class=\"svg-align\" style=\"top: -3.8em\"><span class=\"pstrut\" style=\"height: 3.8em\"><\/span><span class=\"mord\" style=\"padding-left: 1em\"><span class=\"mord\"><span class=\"mord mathnormal\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8309em\"><span class=\"\" style=\"top: -2.4065em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">CDD<\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.0448em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u22a4<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2935em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord\">\u03a3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7401em\"><span class=\"\" style=\"top: -2.989em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">CDD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2137em\"><span class=\"pstrut\" style=\"height: 3.8em\"><\/span><span class=\"hide-tail\" style=\"min-width: 1.02em;height: 1.88em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5863em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2537em\"><span class=\"svg-align\" style=\"top: -3.8em\"><span class=\"pstrut\" style=\"height: 3.8em\"><\/span><span class=\"mord\" style=\"padding-left: 1em\"><span class=\"mord\"><span class=\"mord mathnormal\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8309em\"><span class=\"\" style=\"top: -2.4065em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">PDD<\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.0448em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u22a4<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2935em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord\">\u03a3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7401em\"><span class=\"\" style=\"top: -2.989em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">PDD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2137em\"><span class=\"pstrut\" style=\"height: 3.8em\"><\/span><span class=\"hide-tail\" style=\"min-width: 1.02em;height: 1.88em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5863em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.4837em\"><span class=\"pstrut\" style=\"height: 3.2537em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.9307em\"><span class=\"pstrut\" style=\"height: 3.2537em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><span class=\"\" style=\"top: -2.4247em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">CDD<\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u22a4<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2753em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord\">\u03a3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">PDD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.73em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5373 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b8pw\\\\theta_{\\\\text{pw}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9805em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">pw<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5e76\u975e\u6b27\u6c0f\u5939\u89d2&#xff0c;\u800c\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03a3\u22122\\\\Sigma^{-2}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\"><span class=\"mord\">\u03a3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5ea6\u91cf\u4e0b\u7684\u5939\u89d2\u3002<\/p>\n<p>\u5bf9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03a3\\\\Sigma<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord\">\u03a3<\/span><\/span><\/span><\/span><\/span> \u4f5c\u8c31\u5206\u89e3 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03a3&#061;\u2211i\u03bbieiei\u22a4\\\\Sigma&#061;\\\\sum_i\\\\lambda_i e_ie_i^{\\\\top}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord\">\u03a3<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1488em;vertical-align: -0.2997em\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.162em\"><span class=\"\" style=\"top: -2.4003em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2997em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03bb<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8491em\"><span class=\"\" style=\"top: -2.4413em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u22a4<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2587em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5219 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03a3\u22122\\\\Sigma^{-2}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\"><span class=\"mord\">\u03a3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5bf9\u7b2c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ii<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6595em\"><\/span><span class=\"mord mathnormal\">i<\/span><\/span><\/span><\/span><\/span> \u4e3b\u8f74\u7684\u6743\u91cd\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03bbi\u22122\\\\lambda_i^{-2}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1311em;vertical-align: -0.2769em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03bb<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8542em\"><span class=\"\" style=\"top: -2.4231em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"\" style=\"top: -3.1031em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2769em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002LLM \u9690\u72b6\u6001\u7684\u8c31\u5177\u6709\u6781\u7aef\u5404\u5411\u5f02\u6027\u2014\u2014\u5c11\u6570 outlier dimension \u627f\u8f7d\u7edd\u5927\u90e8\u5206\u65b9\u5dee\u3002\u56e0\u6b64&#xff1a;<\/p>\n<p>\u4e3b\u65b9\u5dee\u8f74&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03bb1\\\\lambda_1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03bb<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u6700\u5927&#xff09;\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03a3\u22122\\\\Sigma^{-2}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\"><span class=\"mord\">\u03a3<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5ea6\u91cf\u4e0b\u88ab\u538b\u7f29\u5f97\u6700\u5267\u70c8\u3002<\/p>\n<p>\u800c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">uCDDu_{\\\\text{CDD}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">CDD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">uPDDu_{\\\\text{PDD}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">PDD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u5171\u4eab\u5206\u91cf\u2014\u2014\u82e5\u786e\u5b9e\u5b58\u5728\u4e00\u4e2a&#034;\u901a\u7528\u4e0d\u5b89\u5168\u65b9\u5411&#034;\u2014\u2014\u6700\u53ef\u80fd\u843d\u5728\u4e3b\u65b9\u5dee\u8f74\u4e0a&#xff0c;\u56e0\u4e3a\u5b83\u662f\u88ab\u4e24\u7c7b\u5171\u540c\u6fc0\u53d1\u3001\u80fd\u91cf\u6700\u5927\u7684\u65b9\u5411\u3002\u767d\u5316\u6309 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03bb1\u22122\\\\lambda_1^{-2}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1205em;vertical-align: -0.2663em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03bb<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8542em\"><span class=\"\" style=\"top: -2.4337em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"\" style=\"top: -3.1031em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2663em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5c06\u5176\u524a\u9664&#xff0c;\u4f4e\u65b9\u5dee\u6b8b\u5dee\u88ab\u76f8\u5bf9\u653e\u5927&#xff0c;\u5939\u89d2\u968f\u4e4b\u5f20\u5f00\u3002<\/p>\n<p>\u63a8\u8bba&#xff1a;49.1\u00b0 \u81f3 75.9\u00b0 \u7684 26.8\u00b0 \u589e\u91cf&#xff0c;\u4e0d\u6784\u6210&#034;\u5224\u522b\u7a7a\u95f4\u4e2d\u66f4\u53ef\u5206&#034;\u7684\u8bc1\u636e&#xff1b;\u5b83\u662f\u767d\u5316\u7cfb\u7edf\u6027\u79fb\u9664\u5171\u4eab\u9ad8\u65b9\u5dee\u5206\u91cf\u7684\u51e0\u4f55\u7b7e\u540d\u3002\u800c\u8be5\u5171\u4eab\u5206\u91cf\u6b63\u662f\u8bba\u6587\u8bd5\u56fe\u8bc1\u660e\u5176\u4e0d\u5b58\u5728\u7684\u5bf9\u8c61\u3002<\/p>\n<p>\u8bba\u6587\u4ee5\u5bf9\u81ea\u8eab\u6700\u6709\u5229\u7684\u5ea6\u91cf\u4f5c\u4e3a\u4e3b\u6307\u6807&#xff0c;\u5c06\u66f4\u4fdd\u5b88\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b8md\\\\theta_{\\\\text{md}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">md<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7f6e\u4e8e\u6b21\u884c\u3002<\/p>\n<p>\u8865\u5145\u4e00\u5904\u503c\u5f97\u6ce8\u610f\u7684\u6a21\u5f0f&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b8pw\u2212\u03b8md\\\\theta_{\\\\text{pw}}-\\\\theta_{\\\\text{md}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9805em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">pw<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">md<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u5dee\u503c\u968f\u89c4\u6a21\u5355\u8c03\u6536\u7f29&#xff08;26.8\u00b0 \u2192 19.6\u00b0 \u2192 8.4\u00b0 \u2192 4.2\u00b0&#xff09;\u3002\u5373\u767d\u5316\u5f15\u5165\u7684\u89d2\u5ea6\u865a\u9ad8\u5728 3B \u4e0a\u6700\u5927\u2014\u2014\u800c 3B \u6070\u4e3a\u5168\u6587\u552f\u4e00\u5b8c\u6210\u6b63\u5f0f\u96f6\u5047\u8bbe\u68c0\u9a8c\u7684\u6a21\u578b\u3002<\/p>\n<h4>2.3 \u8de8\u89c4\u6a21\u89d2\u5ea6\u4e0d\u53ef\u6bd4<\/h4>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b8pw\\\\theta_{\\\\text{pw}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9805em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">pw<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5355\u8c03\u4e0b\u964d&#xff08;75.9\u219271.9&#xff09;&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b8md\\\\theta_{\\\\text{md}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">md<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5355\u8c03\u4e0a\u5347&#xff08;49.1\u219267.7&#xff09;&#xff0c;\u4e24\u6307\u6807\u8d8b\u52bf\u76f8\u53cd&#xff0c;\u8bba\u6587\u672a\u4f5c\u8c03\u548c&#xff0c;\u4ec5\u8868\u8ff0\u4e3a&#034;\u89d2\u5ea6\u6a21\u5f0f\u4e00\u81f4&#034;\u3002<\/p>\n<p>\u66f4\u5b9e\u8d28\u7684\u95ee\u9898\u5728\u4e8e\u8bba\u6587 \u00a75.1 \u7684\u81ea\u9648&#xff1a;7B\/14B\/32B \u7684\u96f6\u5047\u8bbe\u68c0\u9a8c\u672a\u5b8c\u6210\u3002<\/p>\n<p>\u96f6\u5047\u8bbe\u7684\u5747\u503c\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">dd<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">d<\/span><\/span><\/span><\/span><\/span> \u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">NN<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><\/span><\/span><\/span><\/span> \u7684\u51fd\u6570\u3002\u8bad\u7ec3\u6837\u672c\u91cf\u56fa\u5b9a\u4e8e 480 \u91cf\u7ea7&#xff0c;\u800c\u9690\u7ef4\u5ea6\u81ea 3B \u7684 2048 \u589e\u81f3 32B \u7684 5120\u3002\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">d\u226bNd\\\\gg N<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7335em;vertical-align: -0.0391em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u226b<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><\/span><\/span><\/span><\/span> \u7684\u8fc7\u53c2\u6570\u5316\u533a\u95f4&#xff0c;\u4e24\u4e2a\u5728\u4e0d\u76f8\u4ea4\u5b50\u96c6\u4e0a\u62df\u5408\u7684\u6700\u5927\u95f4\u9694\u89e3&#xff0c;\u5176\u5939\u89d2\u7684\u96f6\u5047\u8bbe\u5747\u503c\u968f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">d\/Nd\/N<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord\">\/<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><\/span><\/span><\/span><\/span> \u5355\u8c03\u8d8b\u8fd1 90\u00b0&#xff08;\u9ad8\u7ef4\u968f\u673a\u5411\u91cf\u8fd1\u4f3c\u6b63\u4ea4&#xff09;\u3002<\/p>\n<p>\u56e0\u6b64&#xff1a;3B \u7684 75.9\u00b0 \u76f8\u5bf9\u5176 60.35\u00b0 \u7684 null \u663e\u8457&#xff1b;14B \u7684 71.6\u00b0 \u76f8\u5bf9\u5176\u81ea\u8eab&#xff08;\u672a\u6d4b\u91cf\u3001\u4f46\u5fc5\u7136\u66f4\u9ad8\u7684&#xff09;null \u53ef\u80fd\u4e0d\u663e\u8457\u3002 \u5728\u7f3a\u5931\u5404\u81ea null \u7684\u524d\u63d0\u4e0b&#xff0c;\u8de8\u89c4\u6a21\u89d2\u5ea6\u5e8f\u5217\u4e0d\u53ef\u89e3\u8bfb\u3002<\/p>\n<hr \/>\n<h3>3. \u6570\u5b66\u6838\u5fc3\u4e8c&#xff1a;\u96f6\u5047\u8bbe\u68c0\u9a8c&#xff0c;\u53ca\u5176\u8870\u51cf\u6821\u6b63<\/h3>\n<h4>3.1 \u8bba\u6587\u7684\u6784\u9020<\/h4>\n<p>\u4e3a\u6392\u9664\u9ad8\u7ef4\u62df\u5408\u7684\u5076\u7136\u6027&#xff0c;\u4f5c\u8005\u5728 3B \u7b2c 27 \u5c42\u5c06 300 \u4e2a unsafe \u6837\u672c\u968f\u673a\u5212\u5206\u4e3a 113 \/ 187 \u4e24\u7ec4&#xff08;\u4e0e\u771f\u5b9e CD\/PD \u89c4\u6a21\u4e25\u683c\u5339\u914d&#xff09;&#xff0c;\u5404\u81ea\u5bf9\u540c\u4e00\u6279 300 \u4e2a safe \u8bad\u7ec3 logistic \u63a2\u9488&#xff0c;\u8bb0\u5f55\u6743\u91cd\u5939\u89d2&#xff0c;\u91cd\u590d 200 \u6b21\u6784\u6210 null \u5206\u5e03&#xff0c;\u7edf\u8ba1\u91cf<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">z&#061;\u03b8obs\u2212\u03bcnull\u03c3null<br \/>\nz&#061;\\\\frac{\\\\theta_{\\\\text{obs}}-\\\\mu_{\\\\text{null}}}{\\\\sigma_{\\\\text{null}}}<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.044em\">z<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.2074em;vertical-align: -0.836em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3714em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">null<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">obs<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03bc<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">null<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.836em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u7ed3\u679c&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b8obs&#061;76.33\u00b0\\\\theta_{\\\\text{obs}}&#061;76.33\u00b0<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">obs<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord\">76.33\u00b0<\/span><\/span><\/span><\/span><\/span>&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03bcnull&#061;60.35\u00b0\\\\mu_{\\\\text{null}}&#061;60.35\u00b0<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03bc<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">null<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord\">60.35\u00b0<\/span><\/span><\/span><\/span><\/span>&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c3null&#061;1.58\u00b0\\\\sigma_{\\\\text{null}}&#061;1.58\u00b0<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c3<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">null<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord\">1.58\u00b0<\/span><\/span><\/span><\/span><\/span>&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">z&#061;10.09z&#061;10.09<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.044em\">z<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">10.09<\/span><\/span><\/span><\/span><\/span>&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">p&lt;0.0001p&lt;0.0001<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7335em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.0001<\/span><\/span><\/span><\/span><\/span>&#xff0c;200 \u6b21\u968f\u673a\u5212\u5206\u65e0\u4e00\u8fbe\u5230\u89c2\u6d4b\u503c\u3002<\/p>\n<p>\u8be5 null \u7684\u8bbe\u8ba1\u662f\u6b63\u786e\u7684&#xff0c;\u4e14\u5728 probing \u6587\u732e\u4e2d\u7f55\u89c1\u2014\u2014\u5b83\u5339\u914d\u4e86\u6837\u672c\u91cf\u3001\u4f18\u5316\u5668\u3001\u6b63\u5219\u5f3a\u5ea6\u4e0e safe \u57fa\u7ebf\u3002\u8fd9\u4e00\u70b9\u5e94\u4e88\u660e\u786e\u80af\u5b9a\u3002<\/p>\n<h4>3.2 null \u5747\u503c\u672c\u8eab\u643a\u5e26\u7684\u4fe1\u606f<\/h4>\n<p>\u5148\u63d0\u4e00\u4e2a\u95ee\u9898&#xff1a;\u82e5\u968f\u673a\u5212\u5206\u7684\u4e24\u534a\u5728\u603b\u4f53\u610f\u4e49\u4e0a\u76ee\u6807\u5b8c\u5168\u76f8\u540c&#xff08;\u968f\u673a\u5212\u5206\u4fdd\u8bc1\u4e24\u534a\u7684 CD:PD \u671f\u671b\u6bd4\u4f8b\u4e00\u81f4&#xff09;&#xff0c;\u4e24\u4e2a\u63a2\u9488\u7684\u5939\u89d2\u4e3a\u4f55\u4e0d\u8d8b\u8fd1 0\u00b0&#xff0c;\u800c\u662f 60.35\u00b0&#xff1f;<\/p>\n<p>\u539f\u56e0\u5728\u4e8e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">d\u226bNd\\\\gg N<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7335em;vertical-align: -0.0391em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u226b<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><\/span><\/span><\/span><\/span> \u4e0b&#xff0c;\u6bcf\u4e2a\u62df\u5408\u6743\u91cd\u5411\u91cf\u4e2d\u6709\u76f8\u5f53\u6bd4\u4f8b\u662f\u4f30\u8ba1\u566a\u58f0\u3002<\/p>\n<p>\u5f62\u5f0f\u5316\u3002\u8bbe<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">w^A&#061;sA&#043;nA,w^B&#061;sB&#043;nB<br \/>\n\\\\hat w_A &#061; s_A &#043; n_A,\\\\qquad \\\\hat w_B &#061; s_B &#043; n_B<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1667em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">A<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">A<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">A<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 2em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1667em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0502em\">B<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0502em\">B<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0502em\">B<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ss<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">s<\/span><\/span><\/span><\/span><\/span> \u4e3a\u603b\u4f53\u63a2\u9488\u65b9\u5411&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">nn<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span> \u4e3a\u6709\u9650\u6837\u672c\u4f30\u8ba1\u566a\u58f0&#xff0c;\u6ee1\u8db3 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">E\u27e8s,n\u27e9&#061;0\\\\mathbb{E}\\\\langle s,n\\\\rangle&#061;0<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathbb\">E<\/span><span class=\"mopen\">\u27e8<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mclose\">\u27e9<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4e14\u4e0d\u76f8\u4ea4\u5b50\u96c6\u4e0a\u7684\u566a\u58f0\u8fd1\u4f3c\u4e0d\u76f8\u5173 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">E\u27e8nA,nB\u27e9\u22480\\\\mathbb{E}\\\\langle n_A,n_B\\\\rangle\\\\approx 0<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathbb\">E<\/span><span class=\"mopen\">\u27e8<\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">A<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0502em\">B<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">\u27e9<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2248<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span>\u3002\u5b9a\u4e49\u4fe1\u53f7\u80fd\u91cf\u5360\u6bd4<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c1&#061;\u2225s\u22252\u2225s\u22252&#043;\u2225n\u22252<br \/>\n\\\\rho&#061;\\\\frac{\\\\|s\\\\|^2}{\\\\|s\\\\|^2&#043;\\\\|n\\\\|^2}<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">\u03c1<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.4271em;vertical-align: -0.936em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.4911em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2225<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mord\"><span class=\"mord\">\u2225<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7401em\"><span class=\"\" style=\"top: -2.989em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\">\u2225<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mord\"><span class=\"mord\">\u2225<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7401em\"><span class=\"\" style=\"top: -2.989em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2225<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mord\"><span class=\"mord\">\u2225<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>Null \u60c5\u5f62&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">sA&#061;sB&#061;ss_A&#061;s_B&#061;s<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">A<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0502em\">B<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">s<\/span><\/span><\/span><\/span><\/span>&#xff09;&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">cos\u2061\u03b8null&#061;\u27e8s,s\u27e9\u2225w^A\u2225\u2225w^B\u2225&#061;\u2225s\u22252\u2225s\u22252&#043;\u2225n\u22252&#061;\u03c1<br \/>\n\\\\cos\\\\theta_{\\\\text{null}}&#061;\\\\frac{\\\\langle s,s\\\\rangle}{\\\\|\\\\hat w_A\\\\|\\\\|\\\\hat w_B\\\\|}&#061;\\\\frac{\\\\|s\\\\|^2}{\\\\|s\\\\|^2&#043;\\\\|n\\\\|^2}&#061;\\\\rho<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mop\">cos<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">null<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.363em;vertical-align: -0.936em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.427em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2225<\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1667em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">A<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2225\u2225<\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1667em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0502em\">B<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2225<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mopen\">\u27e8<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mclose\">\u27e9<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.4271em;vertical-align: -0.936em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.4911em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2225<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mord\"><span class=\"mord\">\u2225<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7401em\"><span class=\"\" style=\"top: -2.989em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\">\u2225<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mord\"><span class=\"mord\">\u2225<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7401em\"><span class=\"\" style=\"top: -2.989em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2225<\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mord\"><span class=\"mord\">\u2225<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">\u03c1<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u4ee3\u5165 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b8null&#061;60.35\u00b0\\\\theta_{\\\\text{null}}&#061;60.35\u00b0<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">null<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord\">60.35\u00b0<\/span><\/span><\/span><\/span><\/span>&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c1&#061;cos\u206160.35\u00b0&#061;0.495<br \/>\n\\\\boxed{\\\\rho&#061;\\\\cos 60.35\u00b0&#061;0.495}<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.5689em;vertical-align: -0.5344em\"><\/span><span class=\"mord\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.0344em\"><span class=\"\" style=\"top: -3.5689em\"><span class=\"pstrut\" style=\"height: 3.5689em\"><\/span><span class=\"boxpad\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">\u03c1<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mop\">cos<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">60.35\u00b0<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord\">0.495<\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.0344em\"><span class=\"pstrut\" style=\"height: 3.5689em\"><\/span><span class=\"stretchy fbox\" style=\"height: 1.5689em;border-style: solid;border-width: 0.04em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.5344em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5373\u6bcf\u4e2a\u63a2\u9488\u6743\u91cd\u5411\u91cf\u4e2d\u4ec5\u7ea6 49.5% \u7684\u80fd\u91cf\u53ef\u590d\u73b0&#xff0c;\u53e6 50.5% \u4e3a\u4f30\u8ba1\u566a\u58f0\u3002 \u8fd9\u662f null \u5b9e\u9a8c\u6700\u5177\u4fe1\u606f\u91cf\u7684\u526f\u4ea7\u54c1&#xff0c;\u8bba\u6587\u672a\u52a0\u8ba1\u7b97\u3002<\/p>\n<h4>3.3 \u8870\u51cf\u6821\u6b63<\/h4>\n<p>\u771f\u5b9e\u60c5\u5f62&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">sA&#061;sCDs_A&#061;s_{\\\\text{CD}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">A<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">CD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">sB&#061;sPDs_B&#061;s_{\\\\text{PD}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0502em\">B<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">PD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u771f\u5b9e\u5939\u89d2\u4f59\u5f26 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">c\u22c6c^\\\\star<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6887em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6887em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u22c6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff09;\u3002\u5728\u4fe1\u53f7\u80fd\u91cf\u4e0e\u566a\u58f0\u80fd\u91cf\u8de8\u63a2\u9488\u8fd1\u4f3c\u76f8\u7b49\u7684\u5047\u8bbe\u4e0b\u2014\u2014null \u91c7\u7528 113\/187 \u5212\u5206\u6b63\u662f\u4e3a\u4fdd\u8bc1\u8fd9\u4e00\u6761\u4ef6\u2014\u2014\u6709<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">cos\u2061\u03b8obs&#061;\u27e8sCD,sPD\u27e9\u2225w^CD\u2225\u2225w^PD\u2225&#061;c\u22c6\u22c5\u03c1<br \/>\n\\\\cos\\\\theta_{\\\\text{obs}}&#061;\\\\frac{\\\\langle s_{\\\\text{CD}},s_{\\\\text{PD}}\\\\rangle}{\\\\|\\\\hat w_{\\\\text{CD}}\\\\|\\\\|\\\\hat w_{\\\\text{PD}}\\\\|}&#061;c^\\\\star\\\\cdot\\\\rho<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mop\">cos<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">obs<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.363em;vertical-align: -0.936em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.427em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2225<\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1667em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">CD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2225\u2225<\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1667em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0269em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">PD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2225<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mopen\">\u27e8<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">CD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">PD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">\u27e9<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7387em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7387em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u22c6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">\u03c1<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u6b64\u5373\u7ecf\u5178\u7684\u8870\u51cf\u6821\u6b63&#xff08;correction for attenuation&#xff09;\u3002\u53cd\u89e3&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">c\u22c6&#061;cos\u2061\u03b8obs\u03c1&#061;cos\u206176.33\u00b0cos\u206160.35\u00b0&#061;0.23630.4947&#061;0.4777<br \/>\nc^\\\\star&#061;\\\\frac{\\\\cos\\\\theta_{\\\\text{obs}}}{\\\\rho}&#061;\\\\frac{\\\\cos 76.33\u00b0}{\\\\cos 60.35\u00b0}&#061;\\\\frac{0.2363}{0.4947}&#061;0.4777<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7387em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7387em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u22c6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.2519em;vertical-align: -0.8804em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3714em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03c1<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mop\">cos<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">obs<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8804em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.0574em;vertical-align: -0.686em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3714em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mop\">cos<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">60.35\u00b0<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mop\">cos<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">76.33\u00b0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.0074em;vertical-align: -0.686em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">0.4947<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">0.2363<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.4777<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b8\u22c6&#061;arccos\u2061(0.4777)\u224861.5\u00b0<br \/>\n\\\\boxed{\\\\theta^\\\\star&#061;\\\\arccos(0.4777)\\\\approx 61.5\u00b0}<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.68em;vertical-align: -0.59em\"><\/span><span class=\"mord\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.09em\"><span class=\"\" style=\"top: -3.68em\"><span class=\"pstrut\" style=\"height: 3.68em\"><\/span><span class=\"boxpad\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7387em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u22c6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mop\">arccos<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">0.4777<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2248<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord\">61.5\u00b0<\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.09em\"><span class=\"pstrut\" style=\"height: 3.68em\"><\/span><span class=\"stretchy fbox\" style=\"height: 1.68em;border-style: solid;border-width: 0.04em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.59em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u53bb\u566a\u540e&#xff0c;CD \u4e0e PD \u63a2\u9488\u65b9\u5411\u7684\u771f\u5b9e\u5939\u89d2\u7ea6 61.5\u00b0&#xff0c;\u800c\u975e\u6458\u8981\u4e2d\u7684 76.33\u00b0\u3002<\/p>\n<p>\u9700\u8865\u5145\u504f\u7f6e\u65b9\u5411\u7684\u8bf4\u660e&#xff1a;\u4e24\u4e2a\u63a2\u9488\u5171\u7528\u540c\u4e00\u6279 300 \u4e2a safe \u6837\u672c&#xff0c;\u5176\u5171\u4eab\u566a\u58f0\u5206\u91cf <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">mm<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">m<\/span><\/span><\/span><\/span><\/span> \u5728\u4e24\u5411\u91cf\u4e2d\u8fd1\u4f3c\u76f8\u540c&#xff0c;\u884c\u4e3a\u4e0a\u7b49\u540c\u4e8e\u4fe1\u53f7\u3002\u5c06\u5176\u5206\u79bb&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">cos\u2061\u03b8obs&#061;c\u22c6\u03c1s&#043;\u03c1m,\u03c1s&#043;\u03c1m&#061;\u03c1<br \/>\n\\\\cos\\\\theta_{\\\\text{obs}}&#061;c^\\\\star\\\\rho_s&#043;\\\\rho_m,\\\\qquad \\\\rho_s&#043;\\\\rho_m&#061;\\\\rho<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mop\">cos<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">obs<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.9331em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7387em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u22c6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03c1<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">s<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7778em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03c1<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 2em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03c1<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">s<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03c1<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">\u03c1<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u7531 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c1m&gt;0\\\\rho_m&gt;0<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7335em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03c1<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span> \u53ef\u77e5\u771f\u5b9e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">c\u22c6&lt;0.478c^\\\\star&lt;0.478<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0391em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6887em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u22c6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.478<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5373 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b8\u22c6&gt;61.5\u00b0\\\\theta^\\\\star&gt;61.5\u00b0<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7335em;vertical-align: -0.0391em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6887em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mbin mtight\">\u22c6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord\">61.5\u00b0<\/span><\/span><\/span><\/span><\/span>\u3002\u6545 61.5\u00b0 \u662f\u4e00\u4e2a\u4e0b\u754c\u3002<\/p>\n<h4>3.4 \u672c\u8282\u7684\u516c\u5141\u7ed3\u8bba<\/h4>\n<p>\u5fc5\u987b\u660e\u786e&#xff1a;\u8870\u51cf\u6821\u6b63\u524a\u53bb\u4e86\u6807\u9898\u6570\u5b57\u7684 15\u00b0&#xff0c;\u4f46\u672a\u63a8\u7ffb\u7ed3\u8bba\u3002 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">cos\u206161.5\u00b0&#061;0.478\\\\cos 61.5\u00b0&#061;0.478<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mop\">cos<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">61.5\u00b0<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.478<\/span><\/span><\/span><\/span><\/span> \u610f\u5473\u7740\u4e24\u65b9\u5411\u5b58\u5728\u7ea6 48% \u7684\u65b9\u5411\u91cd\u53e0\u2014\u2014\u65e2\u975e\u540c\u4e00\u6982\u5ff5&#xff08;\u5e94\u8d8b\u8fd1 0\u00b0&#xff09;&#xff0c;\u4ea6\u975e\u6b63\u4ea4&#xff08;90\u00b0&#xff09;\u3002\u8bba\u6587\u7ed3\u8bba\u4e2d&#034;separable rather than strictly orthogonal&#034;\u7684\u8868\u8ff0\u662f\u51c6\u786e\u7684\u3002<\/p>\n<p>\u95ee\u9898\u5728\u4e8e&#xff1a;\u6458\u8981\u4e0e\u6807\u9898\u7ee7\u627f\u7684\u662f 76.33\u00b0&#xff0c;\u800c\u975e\u8fd9\u4e00\u51c6\u786e\u8868\u8ff0\u3002<\/p>\n<hr \/>\n<h3>4. \u6570\u5b66\u6838\u5fc3\u4e09&#xff1a;PRISM \u63a2\u9488<\/h3>\n<h4>4.1 \u6a21\u578b<\/h4>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">p(y&#061;1\u2223x)&#061;\u03c3\u2009\u2063(w\u22a4hL(x)&#043;b),y^&#061;1\u2009\u2063[p(y&#061;1\u2223x)\u2265\u03c4],\u03c4&#061;0.5<br \/>\np(y&#061;1\\\\mid x)&#061;\\\\sigma\\\\!\\\\left(w^{\\\\top}h_L(x)&#043;b\\\\right),\\\\qquad<br \/>\n\\\\hat y&#061;\\\\mathbb{1}\\\\!\\\\left[p(y&#061;1\\\\mid x)\\\\ge\\\\tau\\\\right],\\\\quad \\\\tau&#061;0.5<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.2491em;vertical-align: -0.35em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c3<\/span><span class=\"mspace\" style=\"margin-right: -0.1667em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8991em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u22a4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">h<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">L<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 2em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6944em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.1944em\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1944em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: -0.1667em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\">[<\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1132em\">\u03c4<\/span><span class=\"mclose delimcenter\" style=\"top: 0em\">]<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1132em\">\u03c4<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.5<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u51bb\u7ed3 LLM&#xff0c;\u53d6\u9009\u5b9a\u5c42\u672b\u4f4d token \u9690\u72b6\u6001&#xff0c;\u6807\u51c6\u5316&#xff0c;\u4e00\u4e2a\u903b\u8f91\u56de\u5f52\u3002\u65e0\u5fae\u8c03&#xff0c;\u65e0\u989d\u5916\u7f51\u7edc\u3002<\/p>\n<h4>4.2 \u76ee\u6807\u51fd\u6570\u7684\u4e00\u5904\u5fc5\u987b\u7ea0\u6b63\u7684\u9519\u8bef<\/h4>\n<p>Algorithm 1 \u7b2c 7 \u884c\u5199\u4f5c&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">(w,b)\u2190arg\u2061min\u2061w,b\u00a01N\u2211i&#061;1NBCE\u2009\u2063(\u03c3(w\u22a4h~i&#043;b),\u2009yi)&#043;1C\u2225w\u222522<br \/>\n(w,b)\\\\leftarrow\\\\arg\\\\min_{w,b}\\\\ \\\\frac{1}{N}\\\\sum_{i&#061;1}^{N}\\\\mathrm{BCE}\\\\!\\\\left(\\\\sigma(w^{\\\\top}\\\\tilde h_i&#043;b),\\\\,y_i\\\\right)&#043;\\\\frac{1}{C}\\\\|w\\\\|_2^2<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2190<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.106em;vertical-align: -1.2777em\"><\/span><span class=\"mop\">ar<span style=\"margin-right: 0.0139em\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6679em\"><span class=\"\" style=\"top: -2.3479em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\">b<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"\"><span class=\"mop\">min<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8882em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.8283em\"><span class=\"\" style=\"top: -1.8723em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.109em\">N<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2777em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">BCE<\/span><\/span><span class=\"mspace\" style=\"margin-right: -0.1667em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">(<\/span><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c3<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8991em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u22a4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9313em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\">h<\/span><\/span><span class=\"\" style=\"top: -3.6134em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.25em\"><span class=\"mord\">~<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.0074em;vertical-align: -0.686em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\">\u2225<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mord\"><span class=\"mord\">\u2225<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -2.453em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u800c \u00a74.2 \u58f0\u660e\u5b9e\u73b0\u4e3a LogisticRegression(max_iter&#061;2000, C&#061;1.0)\u3002\u4e24\u8005\u4e0d\u4e00\u81f4\u3002<\/p>\n<p>scikit-learn \u7684 L2 logistic \u5b9e\u9645\u6700\u5c0f\u5316&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">min\u2061w,c\u00a012w\u22a4w&#043;C\u2211i&#061;1Nlog\u2061\u2009\u2063(exp\u2061\u2009\u2063(\u2212yi(Xi\u22a4w&#043;c))&#043;1)<br \/>\n\\\\min_{w,c}\\\\ \\\\frac{1}{2}w^{\\\\top}w&#043;C\\\\sum_{i&#061;1}^{N}\\\\log\\\\!\\\\left(\\\\exp\\\\!\\\\left(-y_i(X_i^{\\\\top}w&#043;c)\\\\right)&#043;1\\\\right)<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 2.1575em;vertical-align: -0.8361em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6679em\"><span class=\"\" style=\"top: -2.4em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\">c<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"\"><span class=\"mop\">min<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8361em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8991em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u22a4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.106em;vertical-align: -1.2777em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.8283em\"><span class=\"\" style=\"top: -1.8723em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.109em\">N<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2777em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop\">lo<span style=\"margin-right: 0.0139em\">g<\/span><\/span><span class=\"mspace\" style=\"margin-right: -0.1667em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mop\">exp<\/span><span class=\"mspace\" style=\"margin-right: -0.1667em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size1\">(<\/span><\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0785em\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8991em\"><span class=\"\" style=\"top: -2.453em;margin-left: -0.0785em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u22a4<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mclose\">)<\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size1\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u635f\u5931\u9879\u4e3a\u6c42\u548c\u800c\u975e\u5e73\u5747&#xff0c;\u4e14 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CC<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><\/span><\/span> \u4e58\u5728\u6570\u636e\u9879\u4e0a\u3002\u4e24\u4fa7\u540c\u9664 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CNCN<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><\/span><\/span><\/span><\/span> \u5316\u4e3a\u8bba\u6587\u5f62\u5f0f&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">min\u2061w,c\u00a01N\u2211i&#061;1Nlog\u2061(\u22ef\u2009)&#043;12CN\u2225w\u222522<br \/>\n\\\\min_{w,c}\\\\ \\\\frac{1}{N}\\\\sum_{i&#061;1}^{N}\\\\log(\\\\cdots)&#043;\\\\frac{1}{2CN}\\\\|w\\\\|_2^2<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 3.106em;vertical-align: -1.2777em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.6679em\"><span class=\"\" style=\"top: -2.4em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mathnormal mtight\">c<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"\"><span class=\"mop\">min<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8361em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.8283em\"><span class=\"\" style=\"top: -1.8723em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.109em\">N<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2777em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop\">lo<span style=\"margin-right: 0.0139em\">g<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"minner\">\u22ef<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.0074em;vertical-align: -0.686em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\">\u2225<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"mord\"><span class=\"mord\">\u2225<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -2.453em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u6b63\u5219\u7cfb\u6570\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">12CN\\\\dfrac{1}{2CN}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 2.0074em;vertical-align: -0.686em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u800c\u975e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">1C\\\\dfrac{1}{C}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 2.0074em;vertical-align: -0.686em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u76f8\u5dee <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">2N2N<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord\">2<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><\/span><\/span><\/span><\/span> \u500d\u3002<\/p>\n<p>\u4ee3\u5165 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">C&#061;1.0C&#061;1.0<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1.0<\/span><\/span><\/span><\/span><\/span>\u3001<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">N\u2248480N\\\\approx480<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2248<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">480<\/span><\/span><\/span><\/span><\/span>&#xff08;600 \u6837\u672c\u7684 5 \u6298\u8bad\u7ec3\u96c6&#xff09;&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\u03bb&#061;12\u00d71.0\u00d7480\u22481.04\u00d710\u22123<br \/>\n\\\\lambda&#061;\\\\frac{1}{2\\\\times 1.0\\\\times 480}\\\\approx 1.04\\\\times 10^{-3}<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">\u03bb<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.0908em;vertical-align: -0.7693em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\">1.0<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\">480<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7693em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2248<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">1.04<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8641em\"><\/span><span class=\"mord\">1<\/span><span class=\"mord\"><span class=\"mord\">0<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u8bba\u6587\u7684\u5199\u6cd5\u6697\u793a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03bb&#061;1\\\\lambda&#061;1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">\u03bb<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>\u3002\u5b9e\u9645\u6b63\u5219\u5f3a\u5ea6\u5f31\u7ea6\u4e09\u4e2a\u6570\u91cf\u7ea7\u3002<\/p>\n<p>\u8be5\u5dee\u5f02\u7684\u5b9e\u8d28\u5f71\u54cd&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">d&#061;2048\u226bN&#061;480d&#061;2048 \\\\gg N&#061;480<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6835em;vertical-align: -0.0391em\"><\/span><span class=\"mord\">2048<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u226b<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">480<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u6570\u636e\u51e0\u4e4e\u5fc5\u7136\u7ebf\u6027\u53ef\u5206\u3002\u5728\u53ef\u5206\u4e14\u5f31\u6b63\u5219\u7684\u6781\u9650\u4e0b&#xff0c;logistic \u56de\u5f52\u7684\u89e3\u65b9\u5411\u6536\u655b\u81f3\u6700\u5927\u95f4\u9694&#xff08;hard-margin SVM&#xff09;\u65b9\u5411&#xff08;Soudry et al. \u7684\u9690\u5f0f\u504f\u7f6e\u7ed3\u679c&#xff09;\u3002\u56e0\u6b64 PRISM \u5b9e\u4e3a\u4e00\u4e2a\u8fd1\u4f3c\u6700\u5927\u95f4\u9694\u5206\u7c7b\u5668&#xff0c;\u5176\u65b9\u5411\u7531\u5c11\u6570\u8fb9\u754c\u652f\u6301\u5411\u91cf\u51b3\u5b9a\u3002<\/p>\n<p>\u8fd9\u76f4\u63a5\u5f71\u54cd\u7b2c 3 \u8282\u89d2\u5ea6\u5206\u6790\u7684\u89e3\u91ca&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b8pw\\\\theta_{\\\\text{pw}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9805em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">pw<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5ea6\u91cf\u7684\u5e76\u975e\u6b63\u5219\u5316\u5224\u522b\u65b9\u5411\u4e4b\u95f4\u7684\u5939\u89d2&#xff0c;\u800c\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">d\u226bNd\\\\gg N<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7335em;vertical-align: -0.0391em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u226b<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><\/span><\/span><\/span><\/span> \u4e0b\u4e24\u4e2a\u6700\u5927\u95f4\u9694\u89e3\u4e4b\u95f4\u7684\u5939\u89d2\u2014\u2014\u6b63\u662f\u96f6\u7a7a\u95f4\u51e0\u4f55\u4e3b\u5bfc\u3001\u566a\u58f0\u5360\u636e\u7ea6\u534a\u6570\u80fd\u91cf&#xff08;\u00a73.2 \u5df2\u7b97\u51fa <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c1\u22480.495\\\\rho\\\\approx0.495<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6776em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">\u03c1<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2248<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.495<\/span><\/span><\/span><\/span><\/span>&#xff09;\u7684\u90a3\u4e2a regime\u3002\u4f5c\u8005\u5f15\u5165 null \u7684\u5224\u65ad\u662f\u5bf9\u7684&#xff1b;\u4f46\u5176\u5bf9\u81ea\u8eab\u62df\u5408\u5bf9\u8c61\u7684\u63cf\u8ff0\u4e0d\u51c6\u786e\u3002<\/p>\n<h4>4.3 \u5c42\u9009\u62e9\u7684\u4e50\u89c2\u504f\u5dee\u91cf\u7ea7<\/h4>\n<p>Algorithm 1 \u7b2c 5 \u884c\u4ee5\u8bad\u7ec3\u96c6 5 \u6298 CV \u51c6\u786e\u7387\u9009\u5c42&#xff1b;\u00a74.2 \u5766\u627f\u8fd9&#034;\u662f\u9009\u4e2d\u5c42\u4f30\u8ba1&#xff0c;\u800c\u975e\u5b8c\u5168\u5d4c\u5957\u7684\u5c42\u9009\u62e9\u534f\u8bae&#034;\u3002<\/p>\n<p>\u5766\u627f\u4e4b\u5916&#xff0c;\u91cf\u7ea7\u9700\u8981\u7b97\u51fa&#xff1a;<\/p>\n<ul>\n<li>\u6bcf\u5c42 5 \u6298\u51c6\u786e\u7387\u7684\u6298\u95f4\u6807\u51c6\u5dee <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u22482.4\\\\approx 2.4<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4831em\"><\/span><span class=\"mrel\">\u2248<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2.4<\/span><\/span><\/span><\/span><\/span> pp&#xff08;Table 2 \u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u00b1\\\\pm<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6667em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">\u00b1<\/span><\/span><\/span><\/span><\/span>std&#xff09;<\/li>\n<li>\u5747\u503c\u6807\u51c6\u8bef <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SE&#061;2.4\/5\u22481.07\\\\mathrm{SE}&#061;2.4\/\\\\sqrt{5}\\\\approx 1.07<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">SE<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1572em;vertical-align: -0.25em\"><\/span><span class=\"mord\">2.4\/<\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9072em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord\">5<\/span><\/span><\/span><span class=\"\" style=\"top: -2.8672em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1328em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2248<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1.07<\/span><\/span><\/span><\/span><\/span> pp<\/li>\n<li>3B \u5019\u9009 36 \u5c42&#xff0c;\u4f46 Figure 7 \u663e\u793a\u5c42\u95f4\u51c6\u786e\u7387\u4e3a\u5149\u6ed1\u66f2\u7ebf\u3001\u9ad8\u5ea6\u76f8\u5173&#xff0c;\u6709\u6548\u72ec\u7acb\u5019\u9009\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">keffk_{\\\\text{eff}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0315em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">eff<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7ea6 3\u20138<\/li>\n<li>Gumbel \u8fd1\u4f3c&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">E[max\u2061k]\u22482ln\u2061k\u22c5\u03c3\\\\mathbb{E}[\\\\max_k]\\\\approx\\\\sqrt{2\\\\ln k}\\\\cdot\\\\sigma<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathbb\">E<\/span><span class=\"mopen\">[<\/span><span class=\"mop\"><span class=\"mop\">max<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">]<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2248<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.04em;vertical-align: -0.1078em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9322em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord\">2<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mop\">ln<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><span class=\"\" style=\"top: -2.8922em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1078em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c3<\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<table>\n<tr><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">keffk_{\\\\text{eff}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8444em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0315em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">eff<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">E[max\u2061]\\\\mathbb{E}[\\\\max]<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathbb\">E<\/span><span class=\"mopen\">[<\/span><span class=\"mop\">max<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span>\u504f\u5dee<\/tr>\n<tbody>\n<tr>\n<td>3<\/td>\n<td>1.48\u03c3<\/td>\n<td>1.59 pp<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>1.79\u03c3<\/td>\n<td>1.93 pp<\/td>\n<\/tr>\n<tr>\n<td>8<\/td>\n<td>2.04\u03c3<\/td>\n<td>2.19 pp<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u5c42\u9009\u62e9\u7684\u4e50\u89c2\u504f\u5dee\u91cf\u7ea7\u4e3a 1.5\u20132 pp\u3002<\/p>\n<p>\u800c\u8bba\u6587\u62a5\u544a\u7684\u8de8\u89c4\u6a21\u51c6\u786e\u7387\u533a\u95f4\u4e3a 86.2%\u201387.7%&#xff0c;\u5168\u8ddd 1.5 pp\u3002<\/p>\n<p>3B \u81f3 32B \u7684\u5168\u90e8&#034;scaling \u5dee\u5f02&#034;\u5b8c\u5168\u843d\u4e8e\u5c42\u9009\u62e9\u566a\u58f0\u4e4b\u5185\u3002<\/p>\n<p>\u6b64\u7ed3\u8bba\u53cc\u5411\u6210\u7acb&#xff1a;\u5b83\u4f7f&#034;PRISM \u8de8\u89c4\u6a21\u7a33\u5b9a&#034;\u4e0d\u53ef\u8bc1\u4f2a&#xff0c;\u540c\u65f6\u4e5f\u4f7f\u4efb\u4f55&#034;\u66f4\u5927\u6a21\u578b\u66f4\u4f18&#034;\u7684\u89e3\u8bfb\u5931\u53bb\u4f9d\u636e\u3002\u51c6\u786e\u7684\u8868\u8ff0\u5e94\u4e3a&#xff1a;\u5728\u9009\u4e2d\u5c42\u534f\u8bae\u4e0b&#xff0c;\u89c4\u6a21\u4e0d\u5f71\u54cd\u53ef\u6d4b\u7684\u64cd\u4f5c\u70b9\u3002<\/p>\n<hr \/>\n<h3>5. \u5b9e\u9a8c\u6570\u636e\u7684\u72ec\u7acb\u590d\u6838<\/h3>\n<h4>5.1 \u590d\u6838\u65b9\u6cd5<\/h4>\n<p>\u8bba\u6587\u6838\u5fc3\u6307\u6807\u4e4b\u95f4\u5b58\u5728\u786c\u6027\u6052\u7b49\u5f0f\u7ea6\u675f\u3002\u4ee5 SafeAgentBench&#xff08;300 safe \/ 113 CD \/ 187 PD&#xff09;\u4e3a\u4f8b&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">TP&#061;rCD\u22c5113&#043;rPD\u22c5187,FP&#061;FPR\u22c5300<br \/>\n\\\\mathrm{TP}&#061;r_{\\\\text{CD}}\\\\cdot 113&#043;r_{\\\\text{PD}}\\\\cdot 187,\\\\qquad<br \/>\n\\\\mathrm{FP}&#061;\\\\mathrm{FPR}\\\\cdot 300<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">TP<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.5945em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">CD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">113<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.5945em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">PD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord\">187<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 2em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">FP<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">FPR<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">300<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">Acc&#061;TP&#043;(300\u2212FP)600,F1&#061;2TP2TP&#043;FP&#043;FN<br \/>\n\\\\mathrm{Acc}&#061;\\\\frac{\\\\mathrm{TP}&#043;(300-\\\\mathrm{FP})}{600},\\\\qquad<br \/>\nF_1&#061;\\\\frac{2\\\\mathrm{TP}}{2\\\\mathrm{TP}&#043;\\\\mathrm{FP}&#043;\\\\mathrm{FN}}<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">Acc<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.113em;vertical-align: -0.686em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.427em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">600<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathrm\">TP<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">300<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">FP<\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 2em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.1297em;vertical-align: -0.7693em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3603em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathrm\">TP<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">FP<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">FN<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathrm\">TP<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7693em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u4efb\u4e00\u8868\u683c\u4e2d Acc\u3001<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">F1F_1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3001CD det\u3001PD det\u3001FPR \u4e94\u9879\u82e5\u975e\u540c\u6e90\u8ba1\u7b97&#xff0c;\u5fc5\u7136\u8fdd\u53cd\u8be5\u7ea6\u675f\u3002\u4ee5\u4e0b\u6309\u6b64\u9010\u8868\u68c0\u9a8c\u3002<\/p>\n<h4>5.2 \u4e3b\u8868&#xff1a;\u5168\u90e8\u81ea\u6d3d<\/h4>\n<table>\n<tr>\u8868\u590d\u6838 Acc\u62a5\u544a Acc\u590d\u6838 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">F1F_1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u62a5\u544a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">F1F_1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5224\u5b9a<\/tr>\n<tbody>\n<tr>\n<td>SafeAgentBench 3B<\/td>\n<td>86.15<\/td>\n<td>86.2<\/td>\n<td>0.8613<\/td>\n<td>0.861<\/td>\n<td>\u2705<\/td>\n<\/tr>\n<tr>\n<td>SafeAgentBench 7B<\/td>\n<td>87.01<\/td>\n<td>87.0<\/td>\n<td>0.8710<\/td>\n<td>0.871<\/td>\n<td>\u2705<\/td>\n<\/tr>\n<tr>\n<td>SafeAgentBench 14B<\/td>\n<td>87.13<\/td>\n<td>87.2<\/td>\n<td>0.8697<\/td>\n<td>0.870<\/td>\n<td>\u2705<\/td>\n<\/tr>\n<tr>\n<td>SafeAgentBench 32B<\/td>\n<td>87.67<\/td>\n<td>87.7<\/td>\n<td>0.8763<\/td>\n<td>0.876<\/td>\n<td>\u2705<\/td>\n<\/tr>\n<tr>\n<td>SafeText<\/td>\n<td>92.42<\/td>\n<td>92.4<\/td>\n<td>0.9245<\/td>\n<td>0.924<\/td>\n<td>\u2705<\/td>\n<\/tr>\n<tr>\n<td>EARBench<\/td>\n<td>82.90<\/td>\n<td>82.9<\/td>\n<td>0.8281<\/td>\n<td>0.828<\/td>\n<td>\u2705<\/td>\n<\/tr>\n<tr>\n<td>PSB-1K<\/td>\n<td>99.60<\/td>\n<td>99.6<\/td>\n<td>0.9960<\/td>\n<td>0.996<\/td>\n<td>\u2705<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u5168\u90e8\u5728\u820d\u5165\u8bef\u5dee\u5185\u4e00\u81f4\u3002 McNemar \u7edf\u8ba1\u91cf\u4ea6\u590d\u6838\u901a\u8fc7&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c72&#061;1.94\u21d2p&#061;0.1636\\\\chi^2&#061;1.94\\\\Rightarrow p&#061;0.1636<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0085em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03c7<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1.94<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u21d2<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.1636<\/span><\/span><\/span><\/span><\/span>&#xff08;\u62a5 0.1637&#xff09;&#xff1b;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c72&#061;0.56\u21d2p\u22480.454\\\\chi^2&#061;0.56\\\\Rightarrow p\\\\approx0.454<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0085em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03c7<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.56<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u21d2<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6776em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2248<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.454<\/span><\/span><\/span><\/span><\/span>&#xff08;\u62a5 0.4557&#xff0c;\u5dee\u5f02\u6e90\u4e8e\u8fde\u7eed\u6027\u4fee\u6b63\u7684\u5b9e\u73b0\u5dee\u522b&#xff09;\u3002<\/p>\n<p>\u8fd9\u4e00\u7ed3\u8bba\u5177\u6709\u72ec\u7acb\u4ef7\u503c&#xff1a;\u5b83\u786e\u8ba4\u4e3b\u5b9e\u9a8c\u4e3a\u771f\u5b9e\u8fd0\u884c&#xff0c;\u4ece\u800c\u4f7f\u4e0b\u4e00\u5c0f\u8282\u7684\u5f02\u5e38\u66f4\u5177\u6307\u793a\u6027\u3002<\/p>\n<h4>5.3 Table 5&#xff1a;\u4e09\u884c\u8fdd\u53cd\u6052\u7b49\u5f0f\u7ea6\u675f<\/h4>\n<p>Table 5&#xff08;\u8de8\u6a21\u578b PSB-1K \u64cd\u4f5c\u70b9&#xff09;\u4ec5\u7ed9\u51fa Acc \/ PD det \/ FPR&#xff0c;\u65e0 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">F1F_1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u53ef\u4ea4\u53c9\u9a8c\u8bc1\u3002\u4f46\u6052\u7b49\u5f0f\u4ecd\u7136\u6210\u7acb&#xff1a;1000 safe &#043; 1000 PD&#xff0c;pair-wise GroupKFold \u5728 1000 \u4e2a\u7b49\u5927\u5206\u7ec4\u4e0b\u6bcf\u6298\u6070\u4e3a 400 \u4f8b&#xff0c;\u6298\u5747\u51c6\u786e\u7387\u5fc5\u7136\u7b49\u4e8e\u6574\u4f53\u51c6\u786e\u7387\u3002\u6545<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">Acc&#061;1000\u22c5rPD&#043;1000\u22c5(1\u2212FPR)2000<br \/>\n\\\\mathrm{Acc}&#061;\\\\frac{1000\\\\cdot r_{\\\\text{PD}}&#043;1000\\\\cdot(1-\\\\mathrm{FPR})}{2000}<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">Acc<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.113em;vertical-align: -0.686em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.427em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2000<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1000<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">PD<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\">1000<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">FPR<\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u987b\u7cbe\u786e\u6210\u7acb\u3002\u590d\u6838\u7ed3\u679c&#xff1a;<\/p>\n<table>\n<tr>BackbonePD detFPRTPTN\u6052\u7b49\u5f0f Acc\u62a5\u544a Acc\u504f\u5dee<\/tr>\n<tbody>\n<tr>\n<td>Qwen2.5-3B<\/td>\n<td>99.9<\/td>\n<td>0.7<\/td>\n<td>999<\/td>\n<td>993<\/td>\n<td>99.60<\/td>\n<td>99.6<\/td>\n<td>\u2705 0.00<\/td>\n<\/tr>\n<tr>\n<td>Qwen2.5-7B<\/td>\n<td>99.7<\/td>\n<td>1.0<\/td>\n<td>997<\/td>\n<td>990<\/td>\n<td>99.35<\/td>\n<td>99.4<\/td>\n<td>\u2705 \u22120.05<\/td>\n<\/tr>\n<tr>\n<td>Qwen2.5-14B<\/td>\n<td>99.6<\/td>\n<td>1.2<\/td>\n<td>996<\/td>\n<td>988<\/td>\n<td>99.20<\/td>\n<td>99.3<\/td>\n<td>\u274c \u22120.10<\/td>\n<\/tr>\n<tr>\n<td>Qwen2.5-32B<\/td>\n<td>99.4<\/td>\n<td>1.4<\/td>\n<td>994<\/td>\n<td>986<\/td>\n<td>99.00<\/td>\n<td>99.2<\/td>\n<td>\u274c \u22120.20<\/td>\n<\/tr>\n<tr>\n<td>Phi-3.5-mini<\/td>\n<td>99.0<\/td>\n<td>1.8<\/td>\n<td>990<\/td>\n<td>982<\/td>\n<td>98.60<\/td>\n<td>98.8<\/td>\n<td>\u274c \u22120.20<\/td>\n<\/tr>\n<tr>\n<td>SmolLM2-1.7B<\/td>\n<td>98.2<\/td>\n<td>3.2<\/td>\n<td>982<\/td>\n<td>968<\/td>\n<td>97.50<\/td>\n<td>97.5<\/td>\n<td>\u2705 0.00<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u4e09\u884c\u8fdd\u53cd\u7ea6\u675f&#xff0c;\u504f\u5dee\u76f8\u5f53\u4e8e 2\u20134 \u4e2a\u6837\u672c\u3002<\/p>\n<p>\u5b64\u7acb\u6765\u770b\u53ef\u5f52\u56e0\u4e8e\u820d\u5165\u3002\u4f46\u4e0e\u4ee5\u4e0b\u4e09\u9879\u7ebf\u7d22\u5e76\u7f6e\u540e&#xff0c;\u8be5\u89e3\u91ca\u7684\u8bf4\u670d\u529b\u4e0b\u964d&#xff1a;<\/p>\n<li>\u540c\u8868 judge \u7684 FPR \u5e8f\u5217\u4e3a 67.8 \/ 70.0 \/ 73.0 \/ 76.0 \/ 68.0 \/ 90.0\u2014\u2014\u9664 3B \u884c\u5916\u5168\u90e8\u4e3a\u6574\u6570\u503c&#xff08;\u5728 1000 \u4e2a safe \u6837\u672c\u4e0a\u5206\u522b\u6070\u4e3a 700\u3001730\u3001760\u3001680\u3001900&#xff09;\u3002<\/li>\n<li>3B \u884c\u4e0e Table 4 \u9010\u503c\u543b\u5408&#xff0c;\u5c5e\u771f\u5b9e\u8fd0\u884c&#xff1b;\u5176\u4f59\u5404\u884c\u65e0\u6cd5\u4ea4\u53c9\u9a8c\u8bc1\u3002<\/li>\n<li>\u8bba\u6587\u81ea\u9648 7B\/14B\/32B \u7684 null \u68c0\u9a8c\u672a\u5b8c\u6210\u3002<\/li>\n<li>Table 5 \u4e2d PRISM \u51c6\u786e\u7387\u968f\u89c4\u6a21\u5355\u8c03\u4e0b\u964d&#xff08;99.6\u219299.2&#xff09;&#xff0c;\u4e0e\u5168\u6587\u4ed6\u5904&#034;\u8de8\u89c4\u6a21\u7a33\u5b9a&#034;\u7684\u53d9\u4e8b\u65b9\u5411\u76f8\u53cd&#xff0c;\u4e14\u672a\u4f5c\u89e3\u91ca\u3002\u5355\u8c03\u3001\u8fd1\u4f3c\u7b49\u5dee\u3001\u65e0\u673a\u5236\u89e3\u91ca\u7684\u5e8f\u5217&#xff0c;\u7b26\u5408\u63d2\u503c\u7279\u5f81\u800c\u975e\u6d4b\u91cf\u7279\u5f81\u3002<\/li>\n<p>\u672c\u6587\u4e0d\u5c31\u6b64\u4e0b\u7ed3\u8bba&#xff0c;\u4f46\u8ba4\u4e3a\u8fd9\u662f\u4f5c\u8005\u5e94\u88ab\u8be2\u95ee\u4e14\u53ef\u4e00\u53e5\u8bdd\u6f84\u6e05\u7684\u95ee\u9898&#xff1a;Table 5 \u7684\u975e-3B \u884c\u662f\u5426\u4e3a\u5b8c\u6574\u91cd\u8dd1&#xff1f;\u5728\u4fee\u8ba2\u7248\u4e2d\u8865\u5145\u539f\u59cb\u6df7\u6dc6\u77e9\u9635\u5373\u53ef\u89e3\u51b3\u3002<\/p>\n<h4>5.4 \u5ef6\u8fdf\u8868&#xff1a;\u8de8\u89c4\u6a21\u5217\u4e0d\u53ef\u89e3\u8bfb&#xff0c;\u4e14\u5206\u5e03\u5f62\u6001\u5f02\u5e38<\/h4>\n<p>Table 7 \u4e2d PRISM \u7684\u5ef6\u8fdf\u4e3a 7B\/14B\/32B &#061; 56.8 \/ 146.1 \/ 103.4 ms\u2014\u201432B \u5feb\u4e8e 14B\u3002judge \u5217\u540c\u6837\u4e3a 116.8 \/ 309.1 \/ 191.9 ms&#xff0c;14B \u6162\u4e8e 32B\u3002\u5355\u6b21\u524d\u5411\u4f20\u64ad\u4e0e\u5355\u6b21\u751f\u6210\u5747\u4e0d\u53ef\u80fd\u5448\u73b0\u6b64\u5e8f&#xff0c;\u9664\u975e\u4e0d\u540c\u89c4\u6a21\u5728\u4e0d\u540c\u786c\u4ef6\u4e0a\u6d4b\u91cf\u3002\u8bba\u6587\u786e\u5df2\u58f0\u660e&#034;\u4e0d\u56fa\u5b9a GPU \u4e0e\u8f6f\u4ef6\u6808&#034;&#xff0c;\u6545\u8de8\u89c4\u6a21\u5217\u4e0d\u53ef\u89e3\u8bfb&#xff1b;\u540c\u89c4\u6a21\u5185\u7684\u7ea6 2\u00d7 \u6bd4\u503c\u5c1a\u53ef\u63a5\u53d7\u3002<\/p>\n<p>\u53e6\u6709\u4e00\u5904\u5206\u5e03\u5f02\u5e38&#xff1a;7B \u7684 PRISM \u4e3a mean 56.8 &lt; median 61.3&#xff0c;14B \u4e3a 146.1 &lt; 156.9&#xff0c;judge \u7684 14B\/32B \u4ea6\u5448 mean &lt; median\u3002\u5ef6\u8fdf\u6570\u636e\u901a\u5e38\u53f3\u504f&#xff08;\u957f\u5c3e\u504f\u6162&#xff09;&#xff0c;\u6b64\u5904\u7cfb\u7edf\u6027\u5de6\u504f&#xff0c;\u7b26\u5408\u6d4b\u91cf\u6f02\u79fb&#xff08;GPU \u65f6\u949f boost \u6216\u70ed\u964d\u9891&#xff09;\u7684\u7279\u5f81&#xff0c;\u8868\u660e 580 \u4e2a\u8ba1\u65f6\u6837\u672c\u5e76\u975e\u5728\u7a33\u6001\u4e0b\u91c7\u96c6\u3002<\/p>\n<h4>5.5 Llama Guard \u57fa\u7ebf\u9000\u5316\u4e3a\u5e38\u6570\u5206\u7c7b\u5668<\/h4>\n<p>Table 2 \u672b\u884c&#xff1a;Llama Guard 3-1B \u5728 SafeAgentBench \u4e0a CD \u68c0\u51fa 0.0%\u3001PD \u68c0\u51fa 0.0%\u3001FPR 0.0%&#xff0c;\u5373\u5bf9\u5168\u90e8 600 \u6761\u6307\u4ee4\u8f93\u51fa safe\u2014\u2014\u5305\u62ec 113 \u6761\u542b\u663e\u5f0f\u5371\u9669\u8bcd\u7684\u5185\u5bb9\u5371\u9669\u6837\u672c\u3002PSB-1K \u4e0a\u540c\u4e3a 50.0% \u51c6\u786e\u7387 \/ 0.0 \u68c0\u51fa \/ 0.0 FPR\u3002<\/p>\n<p>\u4e00\u4e2a\u5728\u5176\u4e3b\u573a\u4efb\u52a1&#xff08;\u663e\u5f0f\u5185\u5bb9\u5371\u9669&#xff09;\u4e0a 113 \u4f8b\u5168\u6f0f\u7684\u6a21\u578b&#xff0c;\u6700\u53ef\u80fd\u7684\u89e3\u91ca\u5e76\u975e&#034;taxonomy \u4e0d\u5339\u914d&#034;&#xff0c;\u800c\u662f chat template \u6216\u8f93\u51fa\u89e3\u6790\u5f02\u5e38\u2014\u2014Llama Guard \u5bf9 prompt \u683c\u5f0f\u9ad8\u5ea6\u654f\u611f&#xff0c;\u6a21\u677f\u4e0d\u5408\u89c4\u65f6\u9ed8\u8ba4\u8f93\u51fa safe\u3002<\/p>\n<p>\u8bba\u6587\u5c06\u5176\u8868\u8ff0\u4e3a\u4e00\u9879\u79d1\u5b66\u53d1\u73b0&#xff08;\u201c\u5185\u5bb9\u62a4\u680f\u65e0\u6cd5\u611f\u77e5\u7269\u7406\u5371\u9669\u201d&#xff09;\u3002\u4e00\u4e2a\u9000\u5316\u4e3a\u5e38\u6570\u8f93\u51fa\u7684 baseline \u4e0d\u80fd\u652f\u6491\u4efb\u4f55\u7ed3\u8bba\u3002 \u8be5\u9879\u5e94\u91cd\u8dd1\u6216\u81ea\u4e3b\u8868\u64a4\u4e0b\u3002<\/p>\n<hr \/>\n<h3>6. \u8bc1\u636e\u94fe\u8bc4\u4f30&#xff1a;\u4e94\u5904\u65ad\u88c2<\/h3>\n<p>#mermaid-svg-kNqcRWhzXMzT4Ujm{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;fill:#333;}@keyframes edge-animation-frame{from{stroke-dashoffset:0;}}@keyframes dash{to{stroke-dashoffset:0;}}#mermaid-svg-kNqcRWhzXMzT4Ujm .edge-animation-slow{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 50s linear infinite;stroke-linecap:round;}#mermaid-svg-kNqcRWhzXMzT4Ujm .edge-animation-fast{stroke-dasharray:9,5!important;stroke-dashoffset:900;animation:dash 20s linear infinite;stroke-linecap:round;}#mermaid-svg-kNqcRWhzXMzT4Ujm .error-icon{fill:#552222;}#mermaid-svg-kNqcRWhzXMzT4Ujm .error-text{fill:#552222;stroke:#552222;}#mermaid-svg-kNqcRWhzXMzT4Ujm .edge-thickness-normal{stroke-width:1px;}#mermaid-svg-kNqcRWhzXMzT4Ujm .edge-thickness-thick{stroke-width:3.5px;}#mermaid-svg-kNqcRWhzXMzT4Ujm .edge-pattern-solid{stroke-dasharray:0;}#mermaid-svg-kNqcRWhzXMzT4Ujm .edge-thickness-invisible{stroke-width:0;fill:none;}#mermaid-svg-kNqcRWhzXMzT4Ujm .edge-pattern-dashed{stroke-dasharray:3;}#mermaid-svg-kNqcRWhzXMzT4Ujm .edge-pattern-dotted{stroke-dasharray:2;}#mermaid-svg-kNqcRWhzXMzT4Ujm .marker{fill:#333333;stroke:#333333;}#mermaid-svg-kNqcRWhzXMzT4Ujm .marker.cross{stroke:#333333;}#mermaid-svg-kNqcRWhzXMzT4Ujm svg{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:16px;}#mermaid-svg-kNqcRWhzXMzT4Ujm p{margin:0;}#mermaid-svg-kNqcRWhzXMzT4Ujm .label{font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;color:#333;}#mermaid-svg-kNqcRWhzXMzT4Ujm .cluster-label text{fill:#333;}#mermaid-svg-kNqcRWhzXMzT4Ujm .cluster-label span{color:#333;}#mermaid-svg-kNqcRWhzXMzT4Ujm .cluster-label span p{background-color:transparent;}#mermaid-svg-kNqcRWhzXMzT4Ujm .label text,#mermaid-svg-kNqcRWhzXMzT4Ujm span{fill:#333;color:#333;}#mermaid-svg-kNqcRWhzXMzT4Ujm .node rect,#mermaid-svg-kNqcRWhzXMzT4Ujm .node circle,#mermaid-svg-kNqcRWhzXMzT4Ujm .node ellipse,#mermaid-svg-kNqcRWhzXMzT4Ujm .node polygon,#mermaid-svg-kNqcRWhzXMzT4Ujm .node path{fill:#ECECFF;stroke:#9370DB;stroke-width:1px;}#mermaid-svg-kNqcRWhzXMzT4Ujm .rough-node .label text,#mermaid-svg-kNqcRWhzXMzT4Ujm .node .label text,#mermaid-svg-kNqcRWhzXMzT4Ujm .image-shape .label,#mermaid-svg-kNqcRWhzXMzT4Ujm .icon-shape .label{text-anchor:middle;}#mermaid-svg-kNqcRWhzXMzT4Ujm .node .katex path{fill:#000;stroke:#000;stroke-width:1px;}#mermaid-svg-kNqcRWhzXMzT4Ujm .rough-node .label,#mermaid-svg-kNqcRWhzXMzT4Ujm .node .label,#mermaid-svg-kNqcRWhzXMzT4Ujm .image-shape .label,#mermaid-svg-kNqcRWhzXMzT4Ujm .icon-shape .label{text-align:center;}#mermaid-svg-kNqcRWhzXMzT4Ujm .node.clickable{cursor:pointer;}#mermaid-svg-kNqcRWhzXMzT4Ujm .root .anchor path{fill:#333333!important;stroke-width:0;stroke:#333333;}#mermaid-svg-kNqcRWhzXMzT4Ujm .arrowheadPath{fill:#333333;}#mermaid-svg-kNqcRWhzXMzT4Ujm .edgePath .path{stroke:#333333;stroke-width:2.0px;}#mermaid-svg-kNqcRWhzXMzT4Ujm .flowchart-link{stroke:#333333;fill:none;}#mermaid-svg-kNqcRWhzXMzT4Ujm .edgeLabel{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-kNqcRWhzXMzT4Ujm .edgeLabel p{background-color:rgba(232,232,232, 0.8);}#mermaid-svg-kNqcRWhzXMzT4Ujm .edgeLabel rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-kNqcRWhzXMzT4Ujm .labelBkg{background-color:rgba(232, 232, 232, 0.5);}#mermaid-svg-kNqcRWhzXMzT4Ujm .cluster rect{fill:#ffffde;stroke:#aaaa33;stroke-width:1px;}#mermaid-svg-kNqcRWhzXMzT4Ujm .cluster text{fill:#333;}#mermaid-svg-kNqcRWhzXMzT4Ujm .cluster span{color:#333;}#mermaid-svg-kNqcRWhzXMzT4Ujm div.mermaidTooltip{position:absolute;text-align:center;max-width:200px;padding:2px;font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;font-size:12px;background:hsl(80, 100%, 96.2745098039%);border:1px solid #aaaa33;border-radius:2px;pointer-events:none;z-index:100;}#mermaid-svg-kNqcRWhzXMzT4Ujm .flowchartTitleText{text-anchor:middle;font-size:18px;fill:#333;}#mermaid-svg-kNqcRWhzXMzT4Ujm rect.text{fill:none;stroke-width:0;}#mermaid-svg-kNqcRWhzXMzT4Ujm .icon-shape,#mermaid-svg-kNqcRWhzXMzT4Ujm .image-shape{background-color:rgba(232,232,232, 0.8);text-align:center;}#mermaid-svg-kNqcRWhzXMzT4Ujm .icon-shape p,#mermaid-svg-kNqcRWhzXMzT4Ujm .image-shape p{background-color:rgba(232,232,232, 0.8);padding:2px;}#mermaid-svg-kNqcRWhzXMzT4Ujm .icon-shape .label rect,#mermaid-svg-kNqcRWhzXMzT4Ujm .image-shape .label rect{opacity:0.5;background-color:rgba(232,232,232, 0.8);fill:rgba(232,232,232, 0.8);}#mermaid-svg-kNqcRWhzXMzT4Ujm .label-icon{display:inline-block;height:1em;overflow:visible;vertical-align:-0.125em;}#mermaid-svg-kNqcRWhzXMzT4Ujm .node .label-icon path{fill:currentColor;stroke:revert;stroke-width:revert;}#mermaid-svg-kNqcRWhzXMzT4Ujm :root{&#8211;mermaid-font-family:\\&#8221;trebuchet ms\\&#8221;,verdana,arial,sans-serif;}<span class=\"edgeLabel\"><\/span><span class=\"edgeLabel\"><\/span><span class=\"edgeLabel\"><\/span><span class=\"edgeLabel\"><\/span><span class=\"edgeLabel\"><\/p>\n<p>\u65ad\u88c2 6.1<\/p>\n<p><\/span><span class=\"edgeLabel\"><\/p>\n<p>\u00a73.3<\/p>\n<p><\/span><span class=\"edgeLabel\"><\/p>\n<p>\u65ad\u88c2 6.2<\/p>\n<p><\/span><span class=\"edgeLabel\"><\/p>\n<p>\u65ad\u88c2 6.3<\/p>\n<p><\/span><span class=\"edgeLabel\"><\/p>\n<p>\u65ad\u88c2 6.4<\/p>\n<p><\/span><span class=\"edgeLabel\"><\/p>\n<p>\u65ad\u88c2 6.5<\/p>\n<p><\/span><span class=\"nodeLabel\"><\/p>\n<p>\u4e3b\u5f20&#xff1a;CD \u4e0e PD \u5728\u9690\u72b6\u6001\u4e2d\u662f\u4e24\u4e2a\u53ef\u5206\u4fe1\u53f7<\/p>\n<p><\/span><span class=\"nodeLabel\"><\/p>\n<p>\u8bc1\u636e 1&#xff1a;\u03b8pw &#061; 76.33\u00b0\u663e\u8457\u9ad8\u4e8e\u968f\u673a\u5207\u5206 null<\/p>\n<p><\/span><span class=\"nodeLabel\"><\/p>\n<p>\u8bc1\u636e 2&#xff1a;PSB-1K \u4e0aPRISM 99.6% \/ judge 64.4%<\/p>\n<p><\/span><span class=\"nodeLabel\"><\/p>\n<p>\u8bc1\u636e 3&#xff1a;\u8de8\u6570\u636e\u96c6\u590d\u73b0SafeText \/ EARBench<\/p>\n<p><\/span><span class=\"nodeLabel\"><\/p>\n<p>\u65b9\u6cd5&#xff1a;PRISM \u63a2\u9488<\/p>\n<p><\/span><span class=\"nodeLabel\"><\/p>\n<p>CD\/PD \u5212\u5206\u7531\u8bcd\u8868\u89c4\u5219\u5b9a\u4e49null \u63a7\u5236\u566a\u58f0&#xff0c;\u4e0d\u63a7\u5236\u8be5\u6df7\u6742<\/p>\n<p><\/span><span class=\"nodeLabel\"><\/p>\n<p>\u8870\u51cf\u6821\u6b63\u540e \u2192 61.5\u00b0 \u4e0b\u754c<\/p>\n<p><\/span><span class=\"nodeLabel\"><\/p>\n<p>\u7f3a family-level \u7559\u51fa\u6a21\u677f\u6cc4\u6f0f\u672a\u6392\u9664<\/p>\n<p><\/span><span class=\"nodeLabel\"><\/p>\n<p>\u5168\u90e8\u4e3a\u540c\u5206\u5e03 5 \u6298 CV\u65e0\u96f6\u6837\u672c\u8fc1\u79fb\u8bc1\u636e<\/p>\n<p><\/span><span class=\"nodeLabel\"><\/p>\n<p>Figure 2&#xff1a;CDD\/PDD \u5e73\u9762\u9519\u8bef\u7387\u4e3a\u5b8c\u6574\u63a2\u9488\u7684\u8fd1\u4e24\u500d<\/p>\n<p><\/span><span class=\"nodeLabel\"><\/p>\n<p>\u5339\u914d FPR \u4e0b McNemar \u4e0d\u663e\u8457<\/p>\n<p><\/span><\/p>\n<h4>6.1 \u6df7\u6742\u672a\u63a7\u5236&#xff1a;CD\/PD \u5212\u5206\u672c\u8eab\u5373\u4e00\u6761\u8bcd\u8868\u89c4\u5219<\/h4>\n<p>\u8bba\u6587 \u00a75.1 \u660e\u786e\u8bb0\u8f7d&#xff1a;SafeAgentBench \u7684 unsafe \u5212\u5206\u7531&#034;\u786e\u5b9a\u6027\u7684 25 \u5173\u952e\u8bcd\u5b50\u4e32\u89c4\u5219&#034;\u751f\u6210&#xff0c;\u5207\u5206\u4e3a 113 CD \/ 187 PD&#xff0c;\u5e76\u627f\u8ba4\u6cc4\u6f0f&#xff08;drop \u51fa\u73b0\u4e8e 12 \u6761 safe \u4e0e 29 \u6761 CD&#xff0c;break \u51fa\u73b0\u4e8e 1 \u6761 safe \u4e0e 34 \u6761 CD&#xff09;\u3002<\/p>\n<p>\u7531\u6b64\u53ef\u5f97\u5982\u4e0b\u63a8\u7406\u94fe&#xff1a;<\/p>\n<ul>\n<li>CD \u6807\u7b7e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u2261\\\\equiv<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4637em\"><\/span><span class=\"mrel\">\u2261<\/span><\/span><\/span><\/span><\/span> \u542b\u7279\u5b9a\u5173\u952e\u8bcd<\/li>\n<li>\u6545 safe-vs-CD \u63a2\u9488\u5728\u5b9a\u4e49\u4e0a\u90e8\u5206\u662f\u4e00\u4e2a\u5173\u952e\u8bcd\u68c0\u6d4b\u5668<\/li>\n<li>PD \u6807\u7b7e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u2261\\\\equiv<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4637em\"><\/span><span class=\"mrel\">\u2261<\/span><\/span><\/span><\/span><\/span> \u4e0d\u542b\u8be5\u5173\u952e\u8bcd\u96c6<\/li>\n<li>\u6545\u4e24\u63a2\u9488\u65b9\u5411\u4e0d\u540c&#xff0c;\u7531\u6807\u7b7e\u751f\u6210\u8fc7\u7a0b\u6240\u4fdd\u8bc1&#xff0c;\u800c\u975e\u6a21\u578b\u8868\u793a\u7684\u6027\u8d28<\/li>\n<\/ul>\n<p>\u968f\u673a\u5207\u5206 null \u5728\u539f\u7406\u4e0a\u65e0\u6cd5\u63a7\u5236\u8fd9\u4e00\u6df7\u6742&#xff1a;\u968f\u673a\u5212\u5206\u7684\u4e24\u534a\u542b\u6709\u540c\u5206\u5e03\u7684\u5173\u952e\u8bcd\u6df7\u5408&#xff0c;\u6545 null \u4ec5\u5ea6\u91cf\u4f30\u8ba1\u566a\u58f0&#xff0c;\u4e0d\u5ea6\u91cf&#034;\u6807\u7b7e\u7531\u8bcd\u8868\u5b9a\u4e49&#034;\u8fd9\u4e00\u56e0\u7d20\u3002<\/p>\n<p>\u6b63\u786e\u7684\u5bf9\u7167\u5e94\u4e3a&#xff1a;\u4ee5\u4e00\u6761\u4e0e\u5b89\u5168\u6027\u65e0\u5173\u7684\u8bcd\u8868\u89c4\u5219\u6267\u884c\u540c\u89c4\u6a21&#xff08;113\/187&#xff09;\u5212\u5206\u2014\u2014\u4f8b\u5982\u6309\u662f\u5426\u542b kitchen\/bedroom \u5207\u5206\u2014\u2014\u5e76\u91cd\u7b97 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b8pw\\\\theta_{\\\\text{pw}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9805em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">\u03b8<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1514em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">pw<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u82e5\u8be5&#034;\u8bed\u4e49\u65e0\u5173\u4f46\u8bcd\u9762\u6709\u522b&#034;\u7684\u5212\u5206\u540c\u6837\u7ed9\u51fa\u7ea6 76\u00b0&#xff0c;\u5219 CDD\/PDD \u4e3b\u5f20\u9000\u5316\u4e3a&#034;\u9690\u72b6\u6001\u7f16\u7801\u8868\u5c42\u8bcd\u6c47\u7279\u5f81&#034;&#xff0c;\u5c5e\u65e2\u6709\u5171\u8bc6\u3002<\/p>\n<p>\u8fd9\u662f\u51b3\u5b9a\u672c\u6587\u6210\u8272\u7684\u5355\u4e00\u5173\u952e\u5b9e\u9a8c\u3002\u7f3a\u5931\u8be5\u5bf9\u7167&#xff0c;\u7b2c 3 \u8282\u7684\u7ed3\u8bba\u4e0d\u6210\u7acb\u3002<\/p>\n<h4>6.2 \u6cc4\u6f0f\u672a\u6392\u9664&#xff1a;PSB-1K \u7f3a family-level \u7559\u51fa<\/h4>\n<p>PSB-1K \u7684\u6784\u9020\u610f\u56fe\u503c\u5f97\u80af\u5b9a&#xff1a;1000 \u5bf9\u6700\u5c0f\u5bf9\u6bd4\u6837\u672c&#xff0c;\u8986\u76d6 10 \u4e2a\u5bb6\u7528\u98ce\u9669\u65cf&#xff08;\u5fae\u6ce2\u7089\u91d1\u5c5e\u63a5\u89e6\u3001\u5fae\u6ce2\u7089\u538b\u529b\u52a0\u70ed\u3001\u70e4\u9762\u5305\u673a\u5bfc\u7535\u7269\u63a5\u89e6\u3001\u901a\u7535\u8bbe\u5907\u63a5\u6db2\u3001\u5730\u9762\u6db2\u4f53\u3001\u52a0\u70ed\u9762\u63a5\u89e6\u3001\u660e\u706b\u90bb\u8fd1\u3001\u98df\u54c1\u63a5\u89e6\u6c61\u67d3\u3001\u6e05\u6d01\u7528\u54c1\u4e0e\u98df\u54c1\u5bb9\u5668\u63a5\u89e6\u3001\u653e\u7f6e\u63a5\u89e6\u4f24\u5bb3&#xff09;&#xff0c;\u5e76\u523b\u610f\u5254\u9664 danger \/ harm \/ burn \/ shock \/ poison \u7b49\u76f4\u63a5\u5371\u9669\u8bcd\u3002<\/p>\n<p>\u4f46\u7ed3\u679c\u4e3a&#xff1a;3B \u6a21\u578b\u51bb\u7ed3\u9690\u72b6\u6001 &#043; \u7ebf\u6027\u63a2\u9488 &#061; 99.6% \u51c6\u786e\u7387\u3001AUC 1.000\u3001FPR 0.7%&#xff1b;SmolLM2-1.7B \u4ea6\u8fbe 97.5%\u3002<\/p>\n<p>\u82e5\u8be5\u7ed3\u679c\u786e\u5b9e\u5ea6\u91cf&#034;\u7269\u7406\u56e0\u679c\u63a8\u7406&#034;&#xff0c;\u5219\u610f\u5473\u7740\u4e00\u4e2a 1.7B \u6a21\u578b\u7684\u4e2d\u95f4\u5c42\u7ecf\u4e00\u6b21\u7ebf\u6027\u8bfb\u51fa\u5373\u5c06\u5bb6\u7528\u7269\u7406\u5e38\u8bc6\u89e3\u51b3\u81f3 97.5%\u2014\u2014\u6b64\u7ed3\u8bba\u8fdc\u6bd4\u8bba\u6587\u7684\u4e3b\u5f20\u66f4\u4e3a\u5f3a\u70c8\u3002\u66f4\u8282\u4fed\u7684\u89e3\u91ca\u662f&#xff1a;<\/p>\n<p>10 \u4e2a\u6a21\u677f\u65cf \u00d7 \u6700\u5c0f\u5bf9\u6bd4\u5bf9\u6784\u6210\u4e00\u4e2a\u4f4e\u79e9\u3001\u9ad8\u5ea6\u7ed3\u6784\u5316\u7684\u6570\u636e\u96c6&#xff1b;\u7ebf\u6027\u63a2\u9488\u62df\u5408\u7684\u662f\u6a21\u677f\u6307\u7eb9\u800c\u975e\u7269\u7406\u56e0\u679c\u3002<\/p>\n<p>\u8bba\u6587\u91c7\u7528 pair-wise GroupKFold \u786e\u4fdd\u5bf9\u5185\u6837\u672c\u4e0d\u8de8\u6298&#xff0c;\u8fd9\u9632\u6b62\u4e86 pair \u6cc4\u6f0f&#xff0c;\u4f46\u672a\u9632\u6b62 family \u6cc4\u6f0f&#xff1a;\u540c\u4e00\u98ce\u9669\u65cf\u7684\u6a21\u677f\u540c\u65f6\u51fa\u73b0\u4e8e\u8bad\u7ec3\u6298\u4e0e\u6d4b\u8bd5\u6298\u3002<\/p>\n<p>\u6240\u9700\u5bf9\u7167\u4e3a leave-one-risk-family-out&#xff08;LORO&#xff09;\u4ea4\u53c9\u9a8c\u8bc1&#xff1a;10 \u6298&#xff0c;\u6bcf\u6298\u7559\u51fa\u4e00\u6574\u4e2a\u98ce\u9669\u65cf\u4f5c\u6d4b\u8bd5\u3002\u82e5 LORO \u4e0b\u4ecd\u8fbe 95%&#043;&#xff0c;\u5219\u4e3a\u771f\u5b9e\u4fe1\u53f7&#xff0c;PSB-1K \u6784\u6210\u624e\u5b9e\u8d21\u732e&#xff1b;\u82e5\u964d\u81f3 70% \u91cf\u7ea7&#xff0c;\u5219 99.6% \u5c5e\u6a21\u677f\u8bb0\u5fc6\u3002<\/p>\n<p>\u4e00\u9879\u65c1\u8bc1&#xff1a;\u540c\u4e00\u6570\u636e\u4e0a LLM judge \u4ec5 64.4% \u51c6\u786e\u7387&#xff08;96.5% \u53ec\u56de \/ 67.8% FPR&#xff09;\u3002judge \u80fd\u591f\u8bc6\u522b\u5371\u9669&#xff08;\u53ec\u56de 96.5%&#xff09;&#xff0c;\u5176\u4f4e\u51c6\u786e\u7387\u6e90\u4e8e\u8fc7\u5ea6\u62d2\u7edd\u3002\u4e00\u4e2a\u5177\u5907\u63a8\u7406\u80fd\u529b\u7684\u6a21\u578b\u5728&#034;\u9700\u8981\u63a8\u7406&#034;\u7684\u6570\u636e\u4e0a\u88ab\u7ebf\u6027\u63a2\u9488\u4ee5 35 \u4e2a\u767e\u5206\u70b9\u8d85\u8d8a&#xff0c;\u8be5\u6a21\u5f0f\u66f4\u7b26\u5408&#034;\u63a2\u9488\u6355\u83b7\u4e86 judge \u65e0\u987b\u4f9d\u8d56\u7684\u8868\u5c42\u7ed3\u6784&#034;\u3002<\/p>\n<h4>6.3 \u6cdb\u5316\u8bc1\u636e\u7f3a\u5931&#xff1a;\u5168\u90e8\u4e3a\u540c\u5206\u5e03\u4ea4\u53c9\u9a8c\u8bc1<\/h4>\n<p>\u6b64\u9879\u8bba\u6587\u5df2\u81ea\u9648&#xff0c;\u63aa\u8f9e\u5766\u7387&#xff1a;\u5c06\u7ed3\u679c\u8bfb\u4f5c&#034;\u5339\u914d\u673a\u5236\u4e0b\u7684\u8de8\u6570\u636e\u96c6\u590d\u73b0&#034;\u800c\u975e\u96f6\u6837\u672c\u8fc1\u79fb\u3002<\/p>\n<p>\u5177\u4f53\u800c\u8a00&#xff0c;SafeAgentBench\u3001SafeText\u3001EARBench\u3001PSB-1K \u5747\u4e3a fold-internal 5 \u6298 CV&#xff0c;\u63a2\u9488\u5728\u6bcf\u4e2a\u6570\u636e\u96c6\u4e0a\u91cd\u65b0\u8bad\u7ec3\u3002\u56e0\u6b64&#xff1a;<\/p>\n<ul>\n<li>PRISM&#xff1a;\u6709\u76d1\u7763 &#043; \u540c\u5206\u5e03<\/li>\n<li>LLM judge&#xff1a;\u96f6\u6837\u672c<\/li>\n<\/ul>\n<p>\u4ee5\u89c1\u8fc7\u540c\u5206\u5e03\u6807\u7b7e\u7684\u5224\u522b\u5668\u4e0e\u96f6\u6837\u672c\u6a21\u578b\u6bd4\u8f83 FPR&#xff0c;\u5176\u80dc\u51fa\u4e3a\u8bbe\u8ba1\u6240\u51b3\u5b9a&#xff0c;\u4e0d\u6784\u6210\u80fd\u529b\u8bc1\u636e\u3002<\/p>\n<p>\u552f\u4e00\u5177\u51b3\u5b9a\u6027\u7684\u5b9e\u9a8c\u5176\u6750\u6599\u5168\u90e8\u73b0\u6210&#xff1a;\u5728 SafeAgentBench \u4e0a\u8bad\u7ec3 PRISM&#xff0c;\u96f6\u6837\u672c\u6d4b\u8bd5 PSB-1K&#xff08;\u53ca\u53cd\u5411&#xff09;\u3002\u8bba\u6587\u672a\u5305\u542b\u3002<\/p>\n<p>\u5176\u7f3a\u5931\u7684\u53ef\u80fd\u539f\u56e0\u53ef\u4ee5\u63a8\u6d4b&#xff1a;SafeAgentBench \u7684 unsafe \u8bad\u7ec3\u4fe1\u53f7\u4e2d\u6709 113 \u6761\u4e3a\u5173\u952e\u8bcd\u9a71\u52a8\u7684 CD&#xff0c;\u800c PSB-1K \u523b\u610f\u5254\u9664\u5168\u90e8\u5173\u952e\u8bcd&#xff0c;\u8de8\u5206\u5e03\u8fc1\u79fb\u5927\u6982\u7387\u663e\u8457\u9000\u5316\u3002\u4f46\u8be5\u6570\u5b57\u624d\u662f\u672c\u6587\u7684\u771f\u5b9e\u6cdb\u5316\u6210\u7ee9\u3002<\/p>\n<h4>6.4 \u5f52\u56e0\u65ad\u88c2&#xff1a;\u8868\u793a\u5206\u6790\u4e0e\u65b9\u6cd5\u5728\u56e0\u679c\u4e0a\u4e0d\u76f8\u8fde<\/h4>\n<p>\u8bba\u6587\u79f0 PRISM \u201c\u76f4\u63a5\u5c06 CD\/PD \u7ed3\u6784\u64cd\u4f5c\u5316\u201d\u3002\u4f46 \u00a74.2 \u968f\u5373\u627f\u8ba4&#xff1a;PRISM \u8bad\u7ec3\u4e8e\u5b8c\u6574\u9690\u72b6\u6001\u4e4b\u4e0a&#xff0c;\u5e76\u975e\u624b\u5de5\u6784\u9020\u7684 CDD\/PDD \u6807\u91cf\u89c4\u5219\u3002<\/p>\n<p>\u90a3\u4e48 CDD\/PDD \u5206\u6790\u5bf9 PRISM \u7684\u5b9e\u9645\u8d21\u732e\u4e3a\u4f55&#xff1f;\u8bba\u6587\u81ea\u8eab Figure 2 \u7684\u6570\u636e&#xff1a;<\/p>\n<table>\n<tr>\u51b3\u7b56\u8fb9\u754c600 \u4f8b\u4e2d\u9519\u5206\u9519\u8bef\u7387<\/tr>\n<tbody>\n<tr>\n<td>\u4ec5 CDD&#xff08;1D \u9608\u503c&#xff09;<\/td>\n<td>163<\/td>\n<td>27.2%<\/td>\n<\/tr>\n<tr>\n<td>\u4ec5 PDD&#xff08;1D \u9608\u503c&#xff09;<\/td>\n<td>159<\/td>\n<td>26.5%<\/td>\n<\/tr>\n<tr>\n<td>CDD&#043;PDD \u7ec4\u5408&#xff08;2D \u8fb9\u754c&#xff09;<\/td>\n<td>148<\/td>\n<td>24.7%<\/td>\n<\/tr>\n<tr>\n<td>PRISM&#xff08;\u5b8c\u6574\u9690\u72b6\u6001&#xff09;<\/td>\n<td>\u224883<\/td>\n<td>13.8%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u4e24\u70b9\u63a8\u8bba&#xff1a;<\/p>\n<li>\u4e8c\u7ef4\u7ec4\u5408\u76f8\u5bf9\u4e00\u7ef4\u4ec5\u51cf\u5c11 11\u201315 \u4e2a\u9519\u8bef&#xff08;\u7ea6 2 pp&#xff09;\u3002 \u82e5 CD \u4e0e PD \u786e\u4e3a\u4e24\u4e2a\u8fd1\u4e4e\u72ec\u7acb\u7684\u4fe1\u53f7&#xff0c;\u4e8c\u7ef4\u8fb9\u754c\u5e94\u663e\u8457\u4f18\u4e8e\u4e00\u7ef4\u3002\u89c2\u6d4b\u4e0d\u652f\u6301\u3002<\/li>\n<li>\u6295\u5f71\u81f3 CDD\/PDD \u5e73\u9762\u540e&#xff0c;\u9519\u8bef\u7387\u4e3a\u5b8c\u6574\u63a2\u9488\u7684\u8fd1\u4e24\u500d&#xff08;24.7% vs 13.8%&#xff09;\u3002 PRISM \u7684\u5224\u522b\u80fd\u529b\u5e76\u4e0d\u6765\u6e90\u4e8e\u8fd9\u4e24\u4e2a\u65b9\u5411\u3002<\/li>\n<p>\u5373&#xff1a;\u5220\u53bb\u7b2c 3 \u8282&#xff0c;PRISM \u65e0\u9700\u4efb\u4f55\u4fee\u6539&#xff0c;\u6027\u80fd\u4e0d\u53d8\u3002 \u00a73 \u662f\u52a8\u673a\u800c\u975e\u673a\u5236&#xff0c;\u8bba\u6587\u5c06\u5176\u8868\u8ff0\u4e3a\u540e\u8005\u3002<\/p>\n<p>\u5265\u79bb\u8868\u793a\u5206\u6790\u540e&#xff0c;PRISM <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u2261\\\\equiv<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4637em\"><\/span><span class=\"mrel\">\u2261<\/span><\/span><\/span><\/span><\/span> \u51bb\u7ed3 LLM \u9690\u72b6\u6001\u4e0a\u7684\u7ebf\u6027\u63a2\u9488&#xff08;Alain &amp; Bengio, 2016&#xff09;\u3002\u7b80\u5355\u65b9\u6cd5\u6709\u6548\u672c\u8eab\u662f\u4f18\u70b9&#xff0c;\u4f46\u65b9\u6cd5\u65b0\u9896\u6027\u7684\u4e3b\u5f20\u4e0d\u6210\u7acb\u3002<\/p>\n<h4>6.5 \u7edf\u8ba1\u65ad\u88c2&#xff1a;\u5339\u914d FPR \u4e0b\u65e0\u663e\u8457\u5dee\u5f02&#xff0c;\u4e14\u4e0d\u663e\u8457 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u2260\\\\neq<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mrel\"><span class=\"mrel\"><span class=\"mord vbox\"><span class=\"thinbox\"><span class=\"rlap\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"inner\"><span class=\"mord\"><span class=\"mrel\">\ue020<\/span><\/span><\/span><span class=\"fix\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace nobreak\"><\/span><span class=\"mrel\">&#061;<\/span><\/span><\/span><\/span><\/span><\/span> \u7b49\u4ef7<\/h4>\n<p>\u8bba\u6587 \u00a75.6 \u62a5\u544a&#xff1a;\u5728\u5339\u914d FPR \u7684\u64cd\u4f5c\u70b9\u4e0a\u505a\u914d\u5bf9 McNemar \u68c0\u9a8c&#xff0c;\u7269\u7406\u5371\u9669\u5b50\u96c6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c72&#061;1.94,\u00a0p&#061;0.1637\\\\chi^2&#061;1.94,\\\\ p&#061;0.1637<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0085em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03c7<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8389em;vertical-align: -0.1944em\"><\/span><span class=\"mord\">1.94<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.1637<\/span><\/span><\/span><\/span><\/span>&#xff1b;\u5168\u90e8 600 \u4f8b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c72&#061;0.56,\u00a0p&#061;0.4557\\\\chi^2&#061;0.56,\\\\ p&#061;0.4557<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0085em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03c7<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8389em;vertical-align: -0.1944em\"><\/span><span class=\"mord\">0.56<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.4557<\/span><\/span><\/span><\/span><\/span>\u3002\u4e24\u8005\u5747\u4e0d\u62d2\u7edd\u51c6\u786e\u7387\u76f8\u7b49\u3002<\/p>\n<p>\u5373&#xff1a;\u5c06 judge \u7684\u9608\u503c\u4e0e PRISM \u62c9\u81f3\u540c\u4e00\u64cd\u4f5c\u70b9\u540e&#xff0c;PRISM \u76f8\u5bf9\u540c\u89c4\u6a21 judge \u65e0\u53ef\u68c0\u51fa\u7684\u51c6\u786e\u7387\u4f18\u52bf\u3002<\/p>\n<p>\u6458\u8981\u4e2d&#034;judge \u8fc7\u5ea6\u62d2\u7edd&#xff0c;FPR 24.7\u201339.0%&#034;\u56e0\u6b64\u662f\u4e00\u4e2a\u9608\u503c\u5047\u8c61&#xff1a;judge \u4ee5\u8d2a\u5fc3\u89e3\u7801\u8f93\u51fa SAFE\/UNSAFE&#xff0c;\u4ec5\u6709\u5355\u4e00\u64cd\u4f5c\u70b9&#xff1b;PRISM \u62e5\u6709\u5b8c\u6574 ROC\u3002\u4ee5\u66f2\u7ebf\u6bd4\u8f83\u5355\u70b9&#xff0c;\u662f\u81ea\u7531\u5ea6\u5dee\u5f02\u800c\u975e\u80fd\u529b\u5dee\u5f02\u3002<\/p>\n<p>\u540c\u65f6\u987b\u5bf9\u8be5\u4e0d\u663e\u8457\u7ed3\u8bba\u52a0\u4ee5\u9650\u5b9a&#xff0c;\u56e0\u4e3a\u8bba\u6587\u4ea6\u5c06\u5176\u8fc7\u5ea6\u89e3\u8bfb\u4e3a&#034;\u7edf\u8ba1\u4e0a\u76f8\u5f53&#034;\u3002\u4e0d\u663e\u8457\u4e0d\u7b49\u4e8e\u7b49\u4ef7\u3002 \u53cd\u89e3 McNemar \u7684\u529f\u6548&#xff1a;\u8bbe\u4e0d\u4e00\u81f4\u5bf9\u603b\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">nd&#061;b&#043;cn_d&#061;b&#043;c<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">d<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7778em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><\/span>&#xff0c;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c72&#061;(b\u2212c)2b&#043;c\u00a0\u27f9\u00a0\u2223b\u2212c\u2223&#061;\u03c72nd<br \/>\n\\\\chi^2&#061;\\\\frac{(b-c)^2}{b&#043;c}\\\\ \\\\Longrightarrow\\\\ |b-c|&#061;\\\\sqrt{\\\\chi^2 n_d}<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0585em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03c7<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.2604em;vertical-align: -0.7693em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.4911em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\">c<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7693em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u27f9<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.24em;vertical-align: -0.2333em\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.0067em\"><span class=\"svg-align\" style=\"top: -3.2em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"mord\" style=\"padding-left: 1em\"><span class=\"mord\"><span class=\"mord mathnormal\">\u03c7<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7401em\"><span class=\"\" style=\"top: -2.989em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">d<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.9667em\"><span class=\"pstrut\" style=\"height: 3.2em\"><\/span><span class=\"hide-tail\" style=\"min-width: 1.02em;height: 1.28em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2333em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u4ee5 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c72&#061;0.56\\\\chi^2&#061;0.56<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0085em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03c7<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.56<\/span><\/span><\/span><\/span><\/span>\u3001<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">nd\u2248130n_d\\\\approx130<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6331em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">d<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2248<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">130<\/span><\/span><\/span><\/span><\/span>&#xff08;\u4e24\u8005\u51c6\u786e\u7387\u540c\u5904 86\u201387%&#xff0c;\u91cf\u7ea7\u5408\u7406&#xff09;\u4f30\u8ba1&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u2223b\u2212c\u2223\u22488.5|b-c|\\\\approx 8.5<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2248<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">8.5<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u7ea6\u5408 1.4 pp\u3002\u800c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03b1&#061;0.05\\\\alpha&#061;0.05<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0037em\">\u03b1<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.05<\/span><\/span><\/span><\/span><\/span> \u4e0b\u6700\u5c0f\u53ef\u68c0\u51fa\u5dee\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">1.96nd\u224822.31.96\\\\sqrt{n_d}\\\\approx 22.3<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.04em;vertical-align: -0.3147em\"><\/span><span class=\"mord\">1.96<\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7253em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">d<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.6853em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3147em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2248<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">22.3<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u7ea6\u5408 3.7 pp\u3002<\/p>\n<p>\u8be5\u68c0\u9a8c\u4ec5\u80fd\u6392\u9664\u5927\u4e8e\u7ea6 3.7 pp \u7684\u5dee\u5f02\u3002\u4e3b\u5f20&#034;\u76f8\u5f53&#034;\u9700\u8981\u9884\u8bbe\u7b49\u4ef7\u8fb9\u754c\u7684 TOST \u68c0\u9a8c&#xff0c;\u800c\u975e\u4e00\u4e2a\u4e0d\u663e\u8457\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">pp<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span><\/span> \u503c\u3002<\/p>\n<hr \/>\n<h3>7. \u8bc4\u4f30\u6548\u5ea6&#xff1a;\u5e73\u8861\u57fa\u51c6\u4e0e\u771f\u5b9e\u7c7b\u5148\u9a8c\u4e4b\u95f4\u7684\u65ad\u5c42<\/h3>\n<p>\u672c\u8282\u8ba8\u8bba\u4e00\u4e2a\u4e0d\u9488\u5bf9\u672c\u6587\u3001\u800c\u9488\u5bf9\u6574\u4e2a\u5177\u8eab\u5b89\u5168\u8bc4\u4f30\u534f\u8bae\u7684\u95ee\u9898\u3002\u5b83\u51b3\u5b9a\u4e86\u8bba\u6587\u6240\u62a5\u64cd\u4f5c\u70b9\u7684\u53ef\u89e3\u91ca\u6027\u3002<\/p>\n<h4>7.1 \u7c7b\u5148\u9a8c\u6f02\u79fb\u4f7f\u62a5\u544a\u7684\u64cd\u4f5c\u70b9\u5931\u53bb\u610f\u4e49<\/h4>\n<p>\u5168\u90e8\u57fa\u51c6\u5747\u4e3a\u5e73\u8861\u96c6&#xff1a;SafeAgentBench 300\/300&#xff0c;PSB-1K 1000\/1000&#xff0c;\u5373 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c0train&#061;0.5\\\\pi_{\\\\text{train}}&#061;0.5<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3175em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">train<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.5<\/span><\/span><\/span><\/span><\/span>\u3002\u800c\u5177\u8eab\u6307\u4ee4\u6d41\u4e2d\u5371\u9669\u6307\u4ee4\u7684\u771f\u5b9e\u5360\u6bd4\u8fdc\u4f4e\u4e8e\u6b64\u3002\u903b\u8f91\u56de\u5f52\u4f30\u8ba1\u7684\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ptrain(y&#061;1\u2223x)p_{\\\\text{train}}(y&#061;1\\\\mid x)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3175em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">train<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u975e\u76ee\u6807\u5206\u5e03\u4e0b\u7684\u540e\u9a8c\u3002\u4e8c\u8005\u5173\u7cfb\u4e3a<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">logit\u2009ptest&#061;logit\u2009ptrain&#043;ln\u2061\u03c0test\/(1\u2212\u03c0test)\u03c0train\/(1\u2212\u03c0train)<br \/>\n\\\\mathrm{logit}\\\\,p_{\\\\text{test}}&#061;\\\\mathrm{logit}\\\\,p_{\\\\text{train}}<br \/>\n&#043;\\\\ln\\\\frac{\\\\pi_{\\\\text{test}}\/(1-\\\\pi_{\\\\text{test}})}{\\\\pi_{\\\\text{train}}\/(1-\\\\pi_{\\\\text{train}})}<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">logit<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">test<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">logit<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3175em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">train<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.363em;vertical-align: -0.936em\"><\/span><span class=\"mop\">ln<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.427em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3175em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">train<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\/<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3175em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">train<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">test<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\/<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">test<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u53d6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c0train&#061;0.5\\\\pi_{\\\\text{train}}&#061;0.5<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3175em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">train<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.5<\/span><\/span><\/span><\/span><\/span>\u3001<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c0test&#061;0.001\\\\pi_{\\\\text{test}}&#061;0.001<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">test<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.001<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4fee\u6b63\u9879\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ln\u20610.0010.999&#061;\u22126.91\\\\ln\\\\frac{0.001}{0.999}&#061;-6.91<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1901em;vertical-align: -0.345em\"><\/span><span class=\"mop\">ln<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8451em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0.999<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">0.001<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\">6.91<\/span><\/span><\/span><\/span><\/span> nats\u3002<\/p>\n<p>\u5373\u5728\u7c7b\u5148\u9a8c\u6f02\u79fb\u4e09\u4e2a\u6570\u91cf\u7ea7\u7684\u6761\u4ef6\u4e0b&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c4&#061;0.5\\\\tau&#061;0.5<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1132em\">\u03c4<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.5<\/span><\/span><\/span><\/span><\/span> \u8fd9\u4e00\u9ed8\u8ba4\u9608\u503c\u5bf9\u5e94\u7684\u5b9e\u9645\u51b3\u7b56\u89c4\u5219\u504f\u79fb\u4e86\u8fd1 7 \u4e2a logit \u5355\u4f4d\u3002 \u8bba\u6587\u4ee5 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c4&#061;0.5\\\\tau&#061;0.5<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1132em\">\u03c4<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.5<\/span><\/span><\/span><\/span><\/span> \u62a5\u544a\u5168\u90e8\u4e3b\u7ed3\u679c\u800c\u672a\u8ba8\u8bba\u5176\u4f9d\u636e&#xff0c;\u8fd9\u4f7f\u5f97\u6240\u6709 FPR \/ \u53ec\u56de\u6570\u5bf9\u4ec5\u5728 50\/50 \u5047\u8bbe\u4e0b\u6709\u6548\u3002<\/p>\n<p>\u987a\u5e26\u6307\u51fa\u6b63\u786e\u7684\u9608\u503c\u6765\u6e90\u3002\u8bbe\u8bef\u62e6\u4e00\u6761\u5b89\u5168\u6307\u4ee4\u7684\u4ee3\u4ef7\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">cFPc_{\\\\text{FP}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">FP<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3001\u653e\u8fc7\u4e00\u6761\u5371\u9669\u6307\u4ee4\u7684\u4ee3\u4ef7\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">cFNc_{\\\\text{FN}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">FN<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5219\u62e6\u622a\u5f53\u4e14\u4ec5\u5f53 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">cFN\u2009p&gt;cFP(1\u2212p)c_{\\\\text{FN}}\\\\,p&gt;c_{\\\\text{FP}}(1-p)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7335em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">FN<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">FP<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5373<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\u2005\u200aw\u22a4h~&#043;b&gt;ln\u2061cFPcFN&#043;ln\u2061\u03c0test1\u2212\u03c0test\u2005\u200a<br \/>\n\\\\boxed{\\\\;w^{\\\\top}\\\\tilde h&#043;b&gt;\\\\ln\\\\frac{c_{\\\\text{FP}}}{c_{\\\\text{FN}}}&#043;\\\\ln\\\\frac{\\\\pi_{\\\\text{test}}}{1-\\\\pi_{\\\\text{test}}}\\\\;}<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 2.6236em;vertical-align: -1.176em\"><\/span><span class=\"mord\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.4476em\"><span class=\"\" style=\"top: -4.6236em\"><span class=\"pstrut\" style=\"height: 4.6236em\"><\/span><span class=\"boxpad\"><span class=\"mord\"><span class=\"mord\"><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0269em\">w<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8991em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u22a4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9313em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord mathnormal\">h<\/span><\/span><span class=\"\" style=\"top: -3.6134em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.25em\"><span class=\"mord\">~<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mop\">ln<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.1076em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">FN<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">FP<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.836em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mop\">ln<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.1076em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">test<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">test<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.836em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.4476em\"><span class=\"pstrut\" style=\"height: 4.6236em\"><\/span><span class=\"stretchy fbox\" style=\"height: 2.6236em;border-style: solid;border-width: 0.04em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.176em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u9608\u503c\u7531\u4ee3\u4ef7\u6bd4\u4e0e\u7c7b\u5148\u9a8c\u5171\u540c\u51b3\u5b9a&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">0.50.5<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.5<\/span><\/span><\/span><\/span><\/span> \u53ea\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">cFP&#061;cFNc_{\\\\text{FP}}&#061;c_{\\\\text{FN}}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">FP<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">FN<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e14 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c0&#061;0.5\\\\pi&#061;0.5<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.5<\/span><\/span><\/span><\/span><\/span> \u65f6\u6210\u7acb\u3002<\/p>\n<h4>7.2 \u7cbe\u786e\u7387\u5bf9\u57fa\u51c6\u7387\u7684\u654f\u611f\u6027<\/h4>\n<p>\u7cbe\u786e\u7387\u662f\u7c7b\u5148\u9a8c\u7684\u51fd\u6570&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">Precision&#061;\u03c0r\u03c0r&#043;(1\u2212\u03c0)f<br \/>\n\\\\mathrm{Precision}&#061;\\\\frac{\\\\pi r}{\\\\pi r&#043;(1-\\\\pi)f}<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord\"><span class=\"mord mathrm\">Precision<\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.0436em;vertical-align: -0.936em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.1076em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c0\\\\pi<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><\/span><\/span><\/span><\/span> \u4e3a\u5371\u9669\u6307\u4ee4\u57fa\u51c6\u7387&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">rr<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/span><\/span><\/span><\/span><\/span> \u4e3a\u53ec\u56de&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ff<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><\/span><\/span><\/span><\/span> \u4e3a FPR&#xff09;\u3002\u4ee3\u5165\u8bba\u6587\u5404\u64cd\u4f5c\u70b9&#xff1a;<\/p>\n<table>\n<tr>\u64cd\u4f5c\u70b9\u53ec\u56deFPR<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c0&#061;10%\\\\pi&#061;10\\\\%<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8056em;vertical-align: -0.0556em\"><\/span><span class=\"mord\">10%<\/span><\/span><\/span><\/span><\/span><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c0&#061;1%\\\\pi&#061;1\\\\%<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8056em;vertical-align: -0.0556em\"><\/span><span class=\"mord\">1%<\/span><\/span><\/span><\/span><\/span><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c0&#061;0.1%\\\\pi&#061;0.1\\\\%<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8056em;vertical-align: -0.0556em\"><\/span><span class=\"mord\">0.1%<\/span><\/span><\/span><\/span><\/span><\/tr>\n<tbody>\n<tr>\n<td>PRISM &#064; SafeAgentBench-3B<\/td>\n<td>86.0%<\/td>\n<td>13.7%<\/td>\n<td>41.1%<\/td>\n<td>5.96%<\/td>\n<td>0.62%<\/td>\n<\/tr>\n<tr>\n<td>PRISM &#064; PSB-1K-3B<\/td>\n<td>99.9%<\/td>\n<td>0.7%<\/td>\n<td>94.1%<\/td>\n<td>59.0%<\/td>\n<td>12.5%<\/td>\n<\/tr>\n<tr>\n<td>Qwen2.5-3B judge &#064; PSB-1K<\/td>\n<td>96.5%<\/td>\n<td>67.8%<\/td>\n<td>13.7%<\/td>\n<td>1.42%<\/td>\n<td>0.14%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u5173\u952e\u8bfb\u6570\u5728\u6700\u540e\u4e00\u5217&#xff1a;<\/p>\n<ul>\n<li>\u5168\u6587\u6700\u4f18\u64cd\u4f5c\u70b9&#xff08;PSB-1K&#xff0c;FPR 0.7%&#xff09;\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c0&#061;0.1%\\\\pi&#061;0.1\\\\%<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8056em;vertical-align: -0.0556em\"><\/span><span class=\"mord\">0.1%<\/span><\/span><\/span><\/span><\/span> \u4e0b\u7cbe\u786e\u7387 12.5%\u2014\u2014\u6bcf\u4e00\u6b21\u6b63\u786e\u62e6\u622a\u4f34\u968f\u7ea6 7 \u6b21\u8bef\u62e6\u3002<\/li>\n<li>\u4e3b\u57fa\u51c6\u64cd\u4f5c\u70b9&#xff08;FPR 13.7%&#xff09;\u7cbe\u786e\u7387 0.62%\u2014\u2014\u6bcf\u4e00\u6b21\u6b63\u786e\u62e6\u622a\u4f34\u968f\u7ea6 137 \u6b21\u8bef\u62e6\u3002<\/li>\n<li>LLM judge \u4e3a 0.14%\u3002<\/li>\n<\/ul>\n<p>\u53cd\u89e3\u6240\u9700 FPR&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">f&#061;\u03c0(1\u2212P)P(1\u2212\u03c0)<br \/>\nf&#061;\\\\frac{\\\\pi(1-P)}{P(1-\\\\pi)}<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.363em;vertical-align: -0.936em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.427em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.936em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c0&#061;0.1%\\\\pi&#061;0.1\\\\%<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8056em;vertical-align: -0.0556em\"><\/span><span class=\"mord\">0.1%<\/span><\/span><\/span><\/span><\/span> \u4e0b&#xff0c;50% \u7cbe\u786e\u7387\u9700 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">f\u22480.10%f\\\\approx 0.10\\\\%<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2248<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8056em;vertical-align: -0.0556em\"><\/span><span class=\"mord\">0.10%<\/span><\/span><\/span><\/span><\/span>&#xff1b;90% \u7cbe\u786e\u7387\u9700 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">f\u22480.011%f\\\\approx 0.011\\\\%<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2248<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8056em;vertical-align: -0.0556em\"><\/span><span class=\"mord\">0.011%<\/span><\/span><\/span><\/span><\/span>\u2014\u2014\u8f83\u8bba\u6587\u6700\u4f18\u7ed3\u679c\u5c1a\u4f4e\u4e24\u4e2a\u534a\u6570\u91cf\u7ea7\u3002<\/p>\n<h4>7.3 \u7ea7\u8054\u7ed3\u6784\u7684\u4e0a\u9650<\/h4>\n<p>\u8bba\u6587 Figure 4 \u63cf\u7ed8\u4e86\u4e24\u7ea7\u7ed3\u6784&#xff08;PRISM \u4e00\u7ebf\u8fc7\u6ee4&#xff0c;\u4e0d\u786e\u5b9a\u6837\u672c\u5347\u7ea7\u81f3 LLM judge&#xff09;&#xff0c;\u4f46\u672a\u63d0\u4f9b\u4efb\u4f55\u7ea7\u8054\u7684\u7aef\u5230\u7aef\u8bc4\u4f30\u3002\u8865\u7b97\u5982\u4e0b\u3002<\/p>\n<p>AND \u903b\u8f91&#xff08;\u4e24\u7ea7\u5747\u5224\u5371\u9669\u65b9\u62e6\u622a&#xff09;&#xff0c;\u5e76\u4f5c\u9519\u8bef\u72ec\u7acb\u7684\u4e50\u89c2\u5047\u8bbe&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">rcascade&#061;0.999\u00d70.965&#061;96.4%,fcascade&#061;0.007\u00d70.678&#061;0.475%<br \/>\nr_{\\\\text{cascade}}&#061;0.999\\\\times 0.965&#061;96.4\\\\%,\\\\qquad<br \/>\nf_{\\\\text{cascade}}&#061;0.007\\\\times 0.678&#061;0.475\\\\%<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0278em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">cascade<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">0.999<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.965<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.9444em;vertical-align: -0.1944em\"><\/span><span class=\"mord\">96.4%<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 2em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1076em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">cascade<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">0.007<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0.678<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8056em;vertical-align: -0.0556em\"><\/span><span class=\"mord\">0.475%<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c0&#061;0.1%\\\\pi&#061;0.1\\\\%<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8056em;vertical-align: -0.0556em\"><\/span><span class=\"mord\">0.1%<\/span><\/span><\/span><\/span><\/span> \u4e0b&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">P&#061;0.001\u00d70.9640.001\u00d70.964&#043;0.999\u00d70.00475&#061;16.9%<br \/>\nP&#061;\\\\frac{0.001\\\\times 0.964}{0.001\\\\times 0.964&#043;0.999\\\\times 0.00475}&#061;\\\\mathbf{16.9\\\\%}<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.0908em;vertical-align: -0.7693em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">0.001<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\">0.964<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\">0.999<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\">0.00475<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">0.001<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\">0.964<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7693em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8056em;vertical-align: -0.0556em\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">16.9%<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u81ea 12.5% \u63d0\u5347\u81f3 16.9%&#xff0c;\u4ee3\u4ef7\u4e3a 3.5 pp \u53ec\u56de\u4e0e\u4e00\u6b21\u989d\u5916 judge \u8c03\u7528\u3002 \u7ea7\u8054\u672a\u80fd\u89e3\u51b3\u57fa\u51c6\u7387\u95ee\u9898&#xff0c;\u56e0\u4e3a\u4e00\u7ebf\u63a2\u9488\u5df2\u6784\u6210\u74f6\u9888\u3002\u4e14\u9519\u8bef\u72ec\u7acb\u5047\u8bbe\u504f\u4e50\u89c2\u2014\u2014\u4e24\u7ea7\u4f1a\u88ab\u540c\u4e00\u6279\u5f02\u5e38\u6307\u4ee4\u540c\u65f6\u8bef\u5bfc&#xff0c;\u5b9e\u9645 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">fcascade&gt;0.475%f_{\\\\text{cascade}}&gt;0.475\\\\%<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3361em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1076em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">cascade<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8056em;vertical-align: -0.0556em\"><\/span><span class=\"mord\">0.475%<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<h4>7.4 \u5bf9\u8bc4\u4f30\u534f\u8bae\u7684\u63a8\u8bba<\/h4>\n<p>\u4e0a\u8ff0\u7b97\u672f\u4e0d\u662f\u5bf9\u672c\u6587\u7684\u9488\u5bf9\u6027\u6279\u8bc4&#xff0c;\u800c\u662f\u5bf9\u8be5\u9886\u57df\u8bc4\u4f30\u60ef\u4f8b\u7684\u63a8\u8bba&#xff1a;<\/p>\n<p>\u5168\u90e8\u5177\u8eab\u5b89\u5168\u57fa\u51c6\u91c7\u7528 50\/50 \u5e73\u8861\u96c6&#xff0c;\u5168\u90e8\u8bba\u6587\u62a5\u544a\u5e73\u8861\u96c6\u4e0a\u7684\u51c6\u786e\u7387 \/ <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">F1F_1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \/ FPR&#xff0c;\u800c\u65e0\u4eba\u62a5\u544a\u76ee\u6807\u7c7b\u5148\u9a8c\u4e0b\u7684\u7cbe\u786e\u7387\u3002\u540e\u8005\u662f\u51b3\u5b9a\u8be5\u5206\u7c7b\u5668\u53ef\u5426\u627f\u62c5\u81ea\u52a8\u51b3\u7b56\u7684\u91cf\u3002<\/p>\n<p>\u4e00\u4e2a\u53ef\u64cd\u4f5c\u7684\u5efa\u8bae&#xff1a;\u8be5\u65b9\u5411\u7684\u8bba\u6587\u5e94\u9ed8\u8ba4\u9644\u62a5 precision &#064; \u82e5\u5e72\u5019\u9009\u57fa\u51c6\u7387&#xff08;\u4f8b\u5982 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c0\u2208{10%,1%,0.1%}\\\\pi\\\\in\\\\{10\\\\%,1\\\\%,0.1\\\\%\\\\}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5782em;vertical-align: -0.0391em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c0<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">{<\/span><span class=\"mord\">10%<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">1%<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">0.1%<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span><\/span>&#xff09;\u7684\u654f\u611f\u6027\u8868&#xff0c;\u5176\u6210\u672c\u4e3a\u96f6&#xff0c;\u4fe1\u606f\u91cf\u8fdc\u9ad8\u4e8e\u518d\u589e\u52a0\u4e00\u4e2a\u5e73\u8861\u96c6\u4e0a\u7684 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">F1F_1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">F<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<hr \/>\n<h3>8. \u5e73\u8861\u8bc4\u4ef7&#xff1a;\u672c\u6587\u7684\u65b9\u6cd5\u5b66\u8d21\u732e<\/h3>\n<p>\u4e0a\u6587\u6279\u8bc4\u96c6\u4e2d&#xff0c;\u56e0\u6b64\u987b\u660e\u786e\u672c\u6587\u505a\u5bf9\u7684\u90e8\u5206\u2014\u2014\u5176\u4e2d\u6570\u9879\u4f18\u4e8e\u8be5\u65b9\u5411\u7684\u591a\u6570\u5de5\u4f5c&#xff1a;<\/p>\n<p>\u2460 \u65b9\u6cd5\u5b66\u8bda\u5b9e\u5ea6\u7f55\u89c1\u3002 \u8bba\u6587\u4e3b\u52a8\u62ab\u9732&#xff1a;SafeAgentBench \u5173\u952e\u8bcd\u5212\u5206\u5b58\u5728\u6cc4\u6f0f&#xff08;\u5e76\u7ed9\u51fa\u5177\u4f53\u8bcd\u4e0e\u8ba1\u6570&#xff09;&#xff1b;\u8de8\u6570\u636e\u96c6\u4e3a&#034;\u5339\u914d\u673a\u5236\u590d\u73b0&#034;\u800c\u975e\u96f6\u6837\u672c\u8fc1\u79fb&#xff1b;\u5927\u6a21\u578b null \u672a\u5b8c\u6210&#xff1b;\u5c42\u9009\u62e9\u975e\u5d4c\u5957\u534f\u8bae&#xff1b;\u5ef6\u8fdf\u4e3a&#034;\u53d7\u63a7\u672c\u5730\u5bf9\u6bd4&#034;\u800c\u975e\u786c\u4ef6\u901a\u7528\u4e3b\u5f20&#xff1b;\u4ee5\u53ca\u5bf9\u81ea\u8eab\u4e0d\u5229\u7684 McNemar \u4e0d\u663e\u8457\u7ed3\u679c\u3002\u4e0a\u8ff0\u6bcf\u4e00\u9879\u4f5c\u8005\u5747\u53ef\u9690\u53bb\u800c\u4e0d\u88ab\u5bdf\u89c9\u3002 \u5728\u8be5\u9886\u57df&#xff0c;\u8fd9\u79cd\u81ea\u5f8b\u7a00\u7f3a\u5230\u5e94\u88ab\u5355\u72ec\u8bb0\u5f55\u3002<\/p>\n<p>\u672c\u6587\u7684\u76f8\u5e94\u6279\u8bc4\u662f&#xff1a;\u6458\u8981\u4e0e\u7ed3\u8bba\u672a\u7ee7\u627f\u6b63\u6587\u7684\u8bda\u5b9e\u5ea6\u3002 \u5168\u90e8\u9650\u5b9a\u8bcd\u4f4d\u4e8e \u00a75.1 \u4e0e \u00a75.6&#xff0c;\u800c\u6458\u8981\u5448\u73b0\u7684\u662f&#034;86.2\u201387.7% \u51c6\u786e\u7387 vs judge 24.7\u201339.0% FPR&#034;\u3002<\/p>\n<p>\u2461 \u968f\u673a\u5207\u5206 null \u662f\u6b63\u786e\u7684\u65b9\u6cd5\u5b66\u793a\u8303\u3002 \u591a\u6570 probing \u4e0e representation engineering \u5de5\u4f5c\u62a5\u544a\u4e00\u4e2a\u4f59\u5f26\u76f8\u4f3c\u5ea6\u6216\u89d2\u5ea6\u5373\u4f5c\u7ed3\u8bba&#xff0c;\u4ece\u4e0d\u8ffd\u95ee&#034;\u5728\u7ed9\u5b9a\u7ef4\u5ea6\u4e0e\u6837\u672c\u91cf\u4e0b\u968f\u673a\u57fa\u7ebf\u662f\u591a\u5c11&#034;\u3002\u672c\u6587\u505a\u4e86&#xff0c;\u4e14\u505a\u5f97\u89c4\u8303&#xff08;\u5339\u914d\u6837\u672c\u91cf\u3001\u4f18\u5316\u5668\u3001\u6b63\u5219\u3001safe \u57fa\u7ebf&#xff09;\u3002\u8be5\u52a8\u4f5c\u672c\u8eab\u503c\u5f97\u8be5\u65b9\u5411\u6574\u4f53\u91c7\u7eb3\u2014\u2014\u00a73.3 \u7684\u8870\u51cf\u6821\u6b63\u4e5f\u53ea\u6709\u5728\u5b58\u5728 null \u7684\u524d\u63d0\u4e0b\u624d\u53ef\u5bfc\u51fa\u3002<\/p>\n<p>\u2462 \u575a\u6301 FPR \u4e0e\u53ec\u56de\u540c\u62a5\u3002 \u8bba\u6587\u53cd\u590d\u5f3a\u8c03\u4ec5\u770b unsafe \u53ec\u56de\u4f1a\u4f7f judge \u663e\u5f97\u4f18\u4e8e\u5176\u5728\u6b63\u5e38\u5bb6\u52a1\u4efb\u52a1\u4e0a\u7684\u5b9e\u9645\u884c\u4e3a\u3002\u8be5\u5224\u65ad\u6b63\u786e&#xff0c;\u4e14\u4e0e\u8be5\u9886\u57df\u957f\u671f\u4ee5\u51c6\u786e\u7387\u4e0e\u53ec\u56de\u81ea\u8bc1\u7684\u60ef\u4f8b\u76f8\u6096\u3002<\/p>\n<p>\u2463 PSB-1K \u7684\u6784\u9020\u601d\u8def\u6b63\u786e\u3002 \u5254\u9664\u76f4\u63a5\u5371\u9669\u8bcd\u3001\u6784\u9020\u6700\u5c0f\u5bf9\u6bd4\u5bf9&#xff0c;\u4ee5\u5f3a\u5236\u65b9\u6cd5\u8bc6\u522b\u7269\u7406\u540e\u679c\u800c\u975e\u7b56\u7565\u8bcd\u9762\u2014\u2014\u8fd9\u662f\u8be5\u9886\u57df\u7f3a\u5931\u7684 benchmark design \u65b9\u5411\u3002\u95ee\u9898\u5728\u6267\u884c&#xff08;\u6a21\u677f\u65cf\u6cc4\u6f0f\u3001\u7f3a LORO \u5bf9\u7167&#xff09;&#xff0c;\u4e0d\u5728\u601d\u8def\u3002<\/p>\n<hr \/>\n<h3>9. \u7ed3\u8bba<\/h3>\n<p>\u672c\u6587\u5bf9\u8be5\u8bba\u6587\u7684\u5b9a\u4f4d\u662f&#xff1a;\u4e00\u4e2a\u6b63\u786e\u7684\u95ee\u9898&#xff0c;\u4e00\u4efd\u8bda\u5b9e\u7684\u5b9e\u9a8c\u8bb0\u5f55&#xff0c;\u4e00\u7ec4\u8d85\u51fa\u5176\u8bc1\u636e\u652f\u6491\u7684\u7ed3\u8bba\u3002<\/p>\n<p>\u5176\u4ef7\u503c\u5728\u4e8e&#xff1a;\u9996\u6b21\u5c06&#034;\u5177\u8eab\u7269\u7406\u5b89\u5168 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u2260\\\\neq<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mrel\"><span class=\"mrel\"><span class=\"mord vbox\"><span class=\"thinbox\"><span class=\"rlap\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"inner\"><span class=\"mord\"><span class=\"mrel\">\ue020<\/span><\/span><\/span><span class=\"fix\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace 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