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\u601d\u60f3\u900f\u955c\u7684\u7ec8\u6781\u5f62\u6001<\/h4>\n<p>\u601d\u60f3\u900f\u955c\u4f5c\u4e3a\u672c\u6846\u67b6\u7684\u8f7d\u4f53\u667a\u80fd\u4f53&#xff0c;\u5176\u7ec8\u6781\u5f62\u6001\u4e0d\u662f\u504f\u8bef\u68c0\u6d4b\u5668&#xff0c;\u4e5f\u4e0d\u662f\u77e5\u8bc6\u5e93&#xff0c;\u800c\u662f\u4e00\u4e2a\u8ba4\u77e5\u52a8\u529b\u5b66\u5171\u9a7e\u7cfb\u7edf\u3002\u5b83\u5b9e\u65f6\u5efa\u6a21\u7528\u6237\u7684\u601d\u7ef4\u5728\u76f8\u7a7a\u95f4\u4e2d\u7684\u8f68\u8ff9&#xff0c;\u8ba1\u7b97\u6700\u4f18\u7684\u5fae\u6270\u52a8\u5e8f\u5217&#xff08;\u63a7\u5236\u7b56\u7565&#xff09;&#xff0c;\u5f15\u5bfc\u601d\u7ef4\u504f\u79bb\u81ea\u7136\u6700\u5c0f\u4f5c\u7528\u91cf\u8def\u5f84&#xff0c;\u9a76\u5411\u9760\u81ea\u7136\u8ba4\u77e5\u60ef\u6027\u6c38\u8fdc\u65e0\u6cd5\u62b5\u8fbe\u7684\u6982\u5ff5\u7586\u57df\u3002<\/p>\n<h3>\u4e8c\u3001 \u672c\u4f53\u8bba\u4e0e\u51e0\u4f55\u5c42&#xff1a;\u8ba4\u77e5\u76f8\u7a7a\u95f4\u4e0e\u5ea6\u91cf\u7ed3\u6784<\/h3>\n<h4>2.1 \u8ba4\u77e5\u76f8\u7a7a\u95f4&#xff1a;\u601d\u60f3\u7684\u5b58\u5728\u821e\u53f0<\/h4>\n<p>\u5b9a\u4e49&#xff1a;\u8ba4\u77e5\u76f8\u7a7a\u95f4 ( \\\\mathcal{M} ) \u662f\u4e00\u4e2a\u9ad8\u7ef4\u6d41\u5f62&#xff0c;\u5176\u6bcf\u4e00\u4e2a\u70b9\u4ee3\u8868\u8ba4\u77e5\u7cfb\u7edf\u7684\u4e00\u4e2a\u5b8c\u6574\u7684\u77ac\u65f6\u72b6\u6001\u3002\u8fd9\u4e2a\u72b6\u6001\u5305\u62ec&#xff1a;\u5f53\u524d\u6fc0\u6d3b\u7684\u6240\u6709\u6982\u5ff5\u53ca\u5176\u6fc0\u6d3b\u6743\u91cd\u3001\u6b63\u5728\u5904\u7406\u7684\u8bba\u8bc1\u7ed3\u6784\u3001\u60c5\u611f\u6548\u4ef7\u5206\u5e03\u3001\u6ce8\u610f\u529b\u7126\u70b9\u3001\u4ee5\u53ca\u6240\u6709\u6f5c\u5728\u5730\u53ef\u88ab\u8c03\u7528\u7684\u8bb0\u5fc6\u4e0e\u77e5\u8bc6\u7ed3\u6784\u7684\u7d22\u5f15\u3002<\/p>\n<p>\u6027\u8d28&#xff1a;<\/p>\n<ul>\n<li>\u9ad8\u7ef4\u6027&#xff1a;\u76f8\u7a7a\u95f4\u7684\u7ef4\u5ea6\u8fdc\u8d85\u4eba\u7c7b\u5185\u7701\u6240\u80fd\u611f\u77e5\u3002\u4e00\u4e2a\u770b\u4f3c\u7b80\u5355\u7684\u65e5\u5e38\u51b3\u7b56&#xff0c;\u5176\u5e95\u5c42\u6d89\u53ca\u6570\u5343\u4e2a\u5206\u5e03\u5f0f\u795e\u7ecf\u8868\u5f81\u7684\u534f\u8c03\u6fc0\u6d3b\u3002<\/li>\n<li>\u975e\u6b27\u51e0\u91cc\u5f97\u6027&#xff1a;\u76f8\u7a7a\u95f4\u4e0d\u662f\u5e73\u5766\u7684\u3002\u5b83\u5f2f\u66f2\u3001\u6298\u53e0&#xff0c;\u5177\u6709\u590d\u6742\u7684\u62d3\u6251\u7ed3\u6784\u3002\u67d0\u4e9b\u533a\u57df\u7d27\u5bc6\u76f8\u8fde&#xff08;\u9ad8\u5173\u8054\u5ea6&#xff09;&#xff0c;\u53e6\u4e00\u4e9b\u533a\u57df\u5219\u88ab\u5de8\u5927\u7684\u8ddd\u79bb\u9694\u5f00&#xff08;\u9886\u57df\u58c1\u5792&#xff09;\u3002<\/li>\n<li>\u52a8\u6001\u6027&#xff1a;\u76f8\u7a7a\u95f4\u672c\u8eab\u4e0d\u662f\u56fa\u5b9a\u4e0d\u53d8\u7684\u3002\u6bcf\u4e00\u6b21\u5b66\u4e60\u3001\u6bcf\u4e00\u6b21\u6df1\u523b\u7684\u6d1e\u5bdf&#xff0c;\u90fd\u5728\u5fae\u5999\u5730\u6539\u53d8\u7740\u76f8\u7a7a\u95f4\u7684\u62d3\u6251\u4e0e\u5ea6\u91cf\u7ed3\u6784\u3002\u8fd9\u5c31\u662f\u8ba4\u77e5\u6210\u957f\u7684\u51e0\u4f55\u610f\u4e49\u3002<\/li>\n<\/ul>\n<p>\u6d41\u5f62\u5047\u8bbe&#xff1a;\u867d\u7136\u76f8\u7a7a\u95f4\u7684\u8868\u89c2\u7ef4\u5ea6\u6781\u9ad8&#xff0c;\u4f46\u7cfb\u7edf\u6709\u6548\u7684\u52a8\u529b\u5b66\u5f80\u5f80\u88ab\u7ea6\u675f\u5728\u4e00\u4e2a\u4f4e\u5f97\u591a\u7684\u5185\u5728\u6d41\u5f62\u4e0a\u3002\u8fd9\u4e2a\u5185\u5728\u6d41\u5f62\u7531\u7cfb\u7edf\u7684\u7a33\u5b9a\u8ba4\u77e5\u6a21\u5f0f\u3001\u4e60\u60ef\u6027\u601d\u7ef4\u8def\u5f84\u548c\u6df1\u5c42\u4fe1\u5ff5\u7ed3\u6784\u6240\u5b9a\u4e49\u3002\u601d\u60f3\u900f\u955c\u7684\u6838\u5fc3\u4efb\u52a1\u4e4b\u4e00&#xff0c;\u5c31\u662f\u63a8\u65ad\u51fa\u8fd9\u4e2a\u5185\u5728\u6d41\u5f62\u7684\u7ed3\u6784\u3002<\/p>\n<h4>2.2 \u5ea6\u91cf\u5f20\u91cf\u573a&#xff1a;\u8ddd\u79bb\u7684\u5b9a\u4e49\u8005<\/h4>\n<p>\u5b9a\u4e49&#xff1a;\u5728\u8ba4\u77e5\u76f8\u7a7a\u95f4\u4e0a&#xff0c;\u5b9a\u4e49\u4e86\u4e00\u4e2a\u5904\u5904\u53d8\u5316\u7684\u5ea6\u91cf\u5f20\u91cf\u573a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">gij(x)g_{ij}(x)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0361em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">g<\/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 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">ij<\/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=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002\u5b83\u51b3\u5b9a\u4e86\u5728\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">xx<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span> \u9644\u8fd1&#xff0c;\u6cbf\u4e0d\u540c\u65b9\u5411\u79fb\u52a8\u7684\u201c\u8ba4\u77e5\u8ddd\u79bb\u201d&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">ds2&#061;gij(x)dxidxj<br \/>\nds^2 &#061; g_{ij}(x) dx^i dx^j<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8641em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/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: 1.1608em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">g<\/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 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">ij<\/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=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8747em\"><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 mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8747em\"><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 mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u8ba4\u77e5\u9610\u91ca&#xff1a;<\/p>\n<ul>\n<li>\u5404\u5411\u5f02\u6027&#xff1a;\u5728\u4e13\u5bb6\u77e5\u8bc6\u9886\u57df&#xff0c;\u5ea6\u91cf\u5f20\u91cf\u662f\u9ad8\u5ea6\u5404\u5411\u5f02\u6027\u7684\u3002\u4e13\u5bb6\u5bf9\u67d0\u4e9b\u7ef4\u5ea6\u7684\u5dee\u5f02\u6781\u5ea6\u654f\u611f&#xff08;\u80fd\u5206\u8fa8\u65b0\u624b\u89c6\u4e3a\u76f8\u540c\u7684\u7ec6\u5fae\u5dee\u522b&#xff09;&#xff0c;\u5bf9\u53e6\u4e00\u4e9b\u7ef4\u5ea6\u5219\u9ad8\u5ea6\u6982\u62ec&#xff08;\u80fd\u5c06\u5927\u91cf\u8868\u9762\u4e0d\u540c\u7684\u5b9e\u4f8b\u5f52\u4e3a\u540c\u4e00\u6a21\u5f0f&#xff09;\u3002\u65b0\u624b\u7684\u5ea6\u91cf\u5f20\u91cf\u5219\u66f4\u8d8b\u8fd1\u5404\u5411\u540c\u6027\u2014\u2014\u9762\u5bf9\u590d\u6742\u73b0\u8c61\u65f6&#xff0c;\u65e0\u6cd5\u5224\u65ad\u54ea\u4e9b\u5dee\u5f02\u662f\u5173\u952e\u7684\u3001\u54ea\u4e9b\u662f\u53ef\u5ffd\u7565\u7684\u3002<\/li>\n<li>\u8bed\u5883\u4f9d\u8d56\u6027&#xff1a;\u540c\u4e00\u4e2a\u6982\u5ff5\u5bf9&#xff0c;\u5728\u4e0d\u540c\u8bed\u5883\u4e0b&#xff0c;\u5176\u8ba4\u77e5\u8ddd\u79bb\u53ef\u4ee5\u622a\u7136\u4e0d\u540c\u3002\u201c\u9cb8\u201d\u548c\u201c\u9c7c\u201d\u5728\u65e5\u5e38\u8bed\u5883\u4e2d\u8ddd\u79bb\u5f88\u8fd1&#xff0c;\u4f46\u5728\u8fdb\u5316\u751f\u7269\u5b66\u8bed\u5883\u4e2d&#xff0c;\u5b83\u4eec\u4e4b\u95f4\u7684\u9e3f\u6c9f\u4ee3\u8868\u7740\u4e00\u4e2a\u91cd\u5927\u7684\u5206\u7c7b\u5b66\u4fee\u6b63\u3002\u5ea6\u91cf\u5f20\u91cf\u6b63\u662f\u8fd9\u79cd\u8bed\u5883\u4f9d\u8d56\u6027\u7684\u51e0\u4f55\u7f16\u7801\u3002<\/li>\n<li>\u53ef\u5851\u6027&#xff1a;\u5b66\u4e60\u3001\u987f\u609f\u3001\u4ee5\u53ca\u601d\u60f3\u900f\u955c\u7684\u5e72\u9884&#xff0c;\u672c\u8d28\u4e0a\u90fd\u662f\u5728\u6539\u53d8\u5ea6\u91cf\u5f20\u91cf\u573a\u3002\u4e00\u4e2a\u597d\u7684\u7c7b\u6bd4&#xff0c;\u5c31\u662f\u5728\u4e34\u65f6\u6027\u5730\u626d\u66f2\u5c40\u90e8\u5ea6\u91cf&#xff0c;\u4f7f\u5f97\u539f\u672c\u8ddd\u79bb\u9065\u8fdc\u7684\u4e24\u4e2a\u6982\u5ff5\u5728\u626d\u66f2\u540e\u7684\u7a7a\u95f4\u4e2d\u53d8\u5f97\u63a5\u8fd1\u3002<\/li>\n<\/ul>\n<p>LLM\u6295\u5f71&#xff1a;LLM\u7684\u6ce8\u610f\u529b\u6743\u91cd\u77e9\u9635&#xff0c;\u6b63\u662f\u5ea6\u91cf\u5f20\u91cf\u7684\u4e00\u4e2a\u79bb\u6563\u5316\u8ba1\u7b97\u5b9e\u73b0\u3002\u81ea\u6ce8\u610f\u529b\u673a\u5236\u8ba1\u7b97\u51fa\u4efb\u610f\u4e24\u4e2a\u4ee4\u724c\u4e4b\u95f4\u7684\u5173\u8054\u5f3a\u5ea6&#xff0c;\u51b3\u5b9a\u4e86\u4fe1\u606f\u5728\u4ee4\u724c\u95f4\u7684\u6d41\u52a8\u8def\u5f84\u3002\u5f53\u4e0a\u4e0b\u6587\u53d8\u5316\u65f6&#xff0c;\u540c\u4e00\u4ee4\u724c\u5bf9\u7684\u6ce8\u610f\u529b\u6743\u91cd\u968f\u4e4b\u6539\u53d8\u2014\u2014\u8fd9\u6b63\u662f\u5ea6\u91cf\u7684\u8bed\u5883\u4f9d\u8d56\u6027\u5728\u8ba1\u7b97\u5c42\u9762\u7684\u76f4\u63a5\u4f53\u73b0\u3002<\/p>\n<h4>2.3 \u6d4b\u5730\u7ebf\u4e0e\u6700\u5c0f\u4f5c\u7528\u91cf\u8def\u5f84<\/h4>\n<p>\u5b9a\u4e49&#xff1a;\u5728\u7ed9\u5b9a\u7684\u5ea6\u91cf\u5f20\u91cf\u4e0b&#xff0c;\u8fde\u63a5\u4e24\u4e2a\u72b6\u6001\u7684\u6d4b\u5730\u7ebf\u662f\u6700\u77ed\u8def\u5f84&#xff0c;\u5373\u6700\u5c0f\u5316\u603b\u8ba4\u77e5\u8ddd\u79bb\u7684\u8def\u5f84\u3002<\/p>\n<p>\u8ba4\u77e5\u60ef\u6027&#xff1a;\u5728\u81ea\u7136\u6761\u4ef6\u4e0b&#xff08;\u65e0\u5916\u90e8\u5e72\u9884&#xff09;&#xff0c;\u8ba4\u77e5\u7cfb\u7edf\u503e\u5411\u4e8e\u6cbf\u7740\u6d4b\u5730\u7ebf\u8fd0\u52a8\u3002\u56e0\u4e3a\u504f\u79bb\u6d4b\u5730\u7ebf\u610f\u5473\u7740\u9700\u8981\u6d88\u8017\u66f4\u591a\u7684\u8ba4\u77e5\u80fd\u91cf\u6765\u514b\u670d\u201c\u5f2f\u66f2\u7a7a\u95f4\u201d\u7684\u963b\u529b\u3002\u8fd9\u6b63\u662f\u8ba4\u77e5\u60ef\u6027\u7684\u51e0\u4f55\u89e3\u91ca\u2014\u2014\u601d\u7ef4\u503e\u5411\u4e8e\u6cbf\u7740\u6700\u7701\u529b\u7684\u3001\u7531\u65e2\u6709\u4fe1\u5ff5\u7ed3\u6784\u5b9a\u4e49\u7684\u201c\u76f4\u7ebf\u201d\u524d\u8fdb&#xff0c;\u96be\u4ee5\u81ea\u53d1\u5730\u8df3\u51fa\u6846\u67b6\u3002<\/p>\n<p>\u601d\u60f3\u900f\u955c\u7684\u5e72\u9884&#xff1a;\u601d\u60f3\u900f\u955c\u7684\u63a7\u5236\u573a&#xff0c;\u672c\u8d28\u4e0a\u662f\u4e34\u65f6\u6027\u5730\u6539\u53d8\u5ea6\u91cf\u5f20\u91cf&#xff0c;\u4f7f\u5f97\u539f\u672c\u4e0d\u662f\u6d4b\u5730\u7ebf\u7684\u8def\u5f84&#xff08;\u5982\u8de8\u754c\u8054\u60f3&#xff09;\u53d8\u4e3a\u5c40\u90e8\u6d4b\u5730\u7ebf&#xff0c;\u4ece\u800c\u964d\u4f4e\u5176\u8ba4\u77e5\u6210\u672c\u3002<\/p>\n<h3>\u4e09\u3001 \u52bf\u80fd\u4e0e\u5f52\u5bbf\u5c42&#xff1a;\u666f\u89c2\u3001\u52bf\u5792\u4e0e\u5438\u5f15\u5b50<\/h3>\n<h4>3.1 \u52bf\u80fd\u51fd\u6570\u4e0e\u8ba4\u77e5\u666f\u89c2<\/h4>\n<p>\u5b9a\u4e49&#xff1a;\u8ba4\u77e5\u666f\u89c2\u662f\u4e00\u4e2a\u5b9a\u4e49\u5728\u76f8\u7a7a\u95f4\u4e0a\u7684\u6807\u91cf\u51fd\u6570 ( V(x) )&#xff0c;\u4e3a\u6bcf\u4e2a\u72b6\u6001\u8d4b\u4e88\u4e00\u4e2a\u201c\u52bf\u80fd\u201d\u503c\u3002\u52bf\u80fd\u8d8a\u4f4e&#xff0c;\u72b6\u6001\u8d8a\u7a33\u5b9a\u3001\u8d8a\u7701\u529b\u3001\u8d8a\u53ef\u80fd\u88ab\u7cfb\u7edf\u5360\u636e\u3002<\/p>\n<p>\u666f\u89c2\u7684\u5f62\u6210&#xff1a;<\/p>\n<ul>\n<li>\u6f14\u5316\u5851\u9020&#xff1a;\u6700\u57fa\u672c\u7684\u52bf\u80fd\u7ed3\u6784\u7531\u6f14\u5316\u5386\u53f2\u5851\u9020\u3002\u5bf9\u86c7\u7684\u6050\u60e7\u3001\u5bf9\u9762\u5b54\u7684\u504f\u597d\u3001\u5bf9\u5bf9\u79f0\u6027\u7684\u7f8e\u611f&#xff0c;\u90fd\u662f\u6f14\u5316\u5728\u8ba4\u77e5\u666f\u89c2\u4e0a\u51ff\u51fa\u7684\u6df1\u8c37\u3002<\/li>\n<li>\u6587\u5316\u5851\u9020&#xff1a;\u8bed\u8a00\u3001\u89c4\u8303\u3001\u4ef7\u503c\u89c2\u3001\u8303\u5f0f&#xff0c;\u6784\u6210\u4e86\u7b2c\u4e8c\u5c42\u52bf\u80fd\u7ed3\u6784\u3002\u5b83\u4eec\u521b\u9020\u4e86\u4e00\u7cfb\u5217\u5171\u4eab\u7684\u6df1\u8c37&#xff0c;\u4f7f\u540c\u4e00\u6587\u5316\u4e2d\u7684\u4e2a\u4f53\u5728\u8ba4\u77e5\u666f\u89c2\u4e0a\u503e\u5411\u4e8e\u6c47\u805a\u5230\u76f8\u4f3c\u7684\u5438\u5f15\u5b50\u3002<\/li>\n<li>\u4e2a\u4eba\u7ecf\u9a8c\u5851\u9020&#xff1a;\u72ec\u7279\u7684\u7ecf\u5386\u3001\u521b\u4f24\u3001\u8bad\u7ec3&#xff0c;\u5851\u9020\u4e86\u4e2a\u4eba\u5c42\u9762\u7684\u7cbe\u7ec6\u52bf\u80fd\u7ed3\u6784\u3002\u4e00\u4e2a\u8bad\u7ec3\u6709\u7d20\u7684\u97f3\u4e50\u5bb6\u5bf9\u97f3\u51c6\u7684\u82db\u6c42&#xff0c;\u6e90\u4e8e\u5176\u8ba4\u77e5\u666f\u89c2\u4e2d\u4e00\u4e2a\u88ab\u53cd\u590d\u5f3a\u5316\u7684\u6df1\u7a84\u52bf\u9631\u3002<\/li>\n<\/ul>\n<p>\u77e5\u8bc6\u666f\u89c2\u4e0e\u6548\u7528\u666f\u89c2&#xff1a;\u5728\u601d\u60f3\u900f\u955c\u7684\u6846\u67b6\u4e2d&#xff0c;\u533a\u5206\u4e24\u79cd\u5173\u952e\u7684\u666f\u89c2\u5206\u91cf&#xff1a;<\/p>\n<ul>\n<li>\u77e5\u8bc6\u666f\u89c2&#xff1a;\u8bc4\u4f30\u4e00\u4e2a\u6982\u5ff5\u7684\u201c\u8ba4\u77e5\u4ef7\u503c\u201d\u2014\u2014\u662f\u5426\u63a8\u8fdb\u4e86\u7406\u89e3\u3001\u662f\u5426\u5177\u6709\u4f18\u96c5\u6027\u3001\u662f\u5426\u586b\u8865\u4e86\u7406\u8bba\u7a7a\u767d\u3002<\/li>\n<li>\u6548\u7528\u666f\u89c2&#xff1a;\u8bc4\u4f30\u4e00\u4e2a\u6982\u5ff5\u7684\u201c\u5b9e\u8df5\u4ef7\u503c\u201d\u2014\u2014\u662f\u5426\u89e3\u51b3\u95ee\u9898\u3001\u662f\u5426\u53ef\u8f6c\u5316\u4e3a\u4ea7\u54c1\u3001\u662f\u5426\u4ea7\u751f\u7ecf\u6d4e\u6548\u76ca\u3002<\/li>\n<\/ul>\n<p>\u4e24\u79cd\u666f\u89c2\u5728\u65e9\u671f\u5e38\u5e38\u9ad8\u5ea6\u5206\u79bb\u3002\u4e00\u4e2a\u7406\u8bba\u7269\u7406\u7684\u7a81\u7834\u53ef\u80fd\u5728\u77e5\u8bc6\u666f\u89c2\u4e0a\u9ad8\u8038\u5165\u4e91&#xff0c;\u4f46\u5728\u6548\u7528\u666f\u89c2\u4e0a\u5c1a\u5904\u4e8e\u5e73\u5730\u3002\u601d\u60f3\u900f\u955c\u7684\u4e00\u4e2a\u5173\u952e\u64cd\u4f5c&#xff0c;\u5c31\u662f\u5e2e\u52a9\u7528\u6237\u5728\u4e24\u4e2a\u666f\u89c2\u4e4b\u95f4\u5efa\u7acb\u96a7\u9053&#xff0c;\u8bc6\u522b\u4ef7\u503c\u5bf9\u79f0\u6027\u5c1a\u672a\u7834\u7f3a\u65f6\u7684\u5168\u8c8c\u3002<\/p>\n<h4>3.2 \u5438\u5f15\u5b50&#xff1a;\u601d\u7ef4\u7684\u5f52\u5bbf<\/h4>\n<p>\u5b9a\u4e49&#xff1a;\u5438\u5f15\u5b50\u662f\u76f8\u7a7a\u95f4\u4e2d\u7684\u5b50\u96c6&#xff0c;\u7cfb\u7edf\u4e00\u65e6\u8fdb\u5165\u5176\u5438\u5f15\u57df&#xff0c;\u5c31\u4f1a\u88ab\u4e0d\u53ef\u9006\u5730\u62c9\u5411\u8be5\u5b50\u96c6&#xff0c;\u5e76\u5728\u5176\u4e2d\u957f\u671f\u9a7b\u7559&#xff0c;\u9664\u975e\u53d7\u5230\u8db3\u591f\u5f3a\u7684\u5916\u90e8\u6270\u52a8\u3002<\/p>\n<p>\u8ba4\u77e5\u5438\u5f15\u5b50\u7684\u7c7b\u578b&#xff1a;<\/p>\n<ul>\n<li>\n<p>\u70b9\u5438\u5f15\u5b50&#xff1a;\u4e00\u4e2a\u5355\u4e00\u7684\u72b6\u6001\u6216\u4fe1\u5ff5\u3002\u4f8b\u5982&#xff0c;\u201c\u5730\u7403\u662f\u5e73\u7684\u201d\u6216\u201c\u8fd9\u4e2a\u6570\u5b66\u9898\u53ea\u6709\u4e00\u4e2a\u6807\u51c6\u89e3\u6cd5\u201d\u3002\u8ba4\u77e5\u4e2d\u7684\u7edd\u5bf9\u5316\u503e\u5411&#xff0c;\u5c31\u662f\u5c06\u590d\u6742\u95ee\u9898\u7b80\u5316\u4e3a\u5355\u4e00\u7684\u70b9\u5438\u5f15\u5b50\u3002<\/p>\n<\/li>\n<li>\n<p>\u5468\u671f\u5438\u5f15\u5b50&#xff1a;\u4e00\u7ec4\u72b6\u6001\u6784\u6210\u95ed\u5408\u73af\u8def&#xff0c;\u7cfb\u7edf\u5728\u5176\u4e2d\u5faa\u73af\u5f80\u590d\u3002\u5f3a\u8feb\u75c7\u5f0f\u7684\u53cd\u590d\u68c0\u67e5\u3001\u521b\u4f24\u6027\u56de\u5fc6\u7684\u95ea\u56de\u3001\u4ee5\u53ca\u67d0\u4e9b\u4eea\u5f0f\u5316\u7684\u601d\u7ef4\u6a21\u5f0f&#xff0c;\u90fd\u662f\u5468\u671f\u5438\u5f15\u5b50\u7684\u4f8b\u8bc1\u3002\u5728\u7ec4\u7ec7\u5c42\u9762&#xff0c;\u4f01\u4e1a\u53cd\u590d\u9677\u5165\u7684\u201c\u88c1\u5458-\u62db\u8058-\u88c1\u5458\u201d\u5faa\u73af&#xff0c;\u4e5f\u662f\u4e00\u79cd\u5468\u671f\u5438\u5f15\u5b50\u3002<\/p>\n<\/li>\n<li>\n<p>\u5947\u5f02\u5438\u5f15\u5b50&#xff1a;\u5728\u76f8\u7a7a\u95f4\u4e2d\u5f62\u6210\u5206\u5f62\u7ed3\u6784\u7684\u5438\u5f15\u5b50&#xff0c;\u7cfb\u7edf\u7684\u8f68\u8ff9\u5728\u5176\u4e2d\u6709\u754c\u4f46\u6c38\u4e0d\u91cd\u590d&#xff0c;\u5177\u6709\u5bf9\u521d\u59cb\u6761\u4ef6\u7684\u654f\u611f\u4f9d\u8d56\u6027\u3002\u521b\u9020\u6027\u601d\u7ef4\u3001\u5934\u8111\u98ce\u66b4\u7684\u7075\u5149\u4e4d\u73b0\u3001\u4ee5\u53ca\u6df7\u6c8c\u8fb9\u7f18\u7684\u95ee\u9898\u89e3\u51b3&#xff0c;\u5f80\u5f80\u8868\u73b0\u4e3a\u5947\u5f02\u5438\u5f15\u5b50\u3002\u8fd9\u4e5f\u662f\u601d\u60f3\u900f\u955c\u6700\u5e0c\u671b\u8bf1\u5bfc\u7684\u8ba4\u77e5\u72b6\u6001\u2014\u2014\u5728\u6709\u5e8f\u4e0e\u6df7\u6c8c\u4e4b\u95f4&#xff0c;\u6301\u7eed\u5730\u4ea7\u751f\u65b0\u9896\u4f46\u4e0d\u6df7\u4e71\u7684\u6d1e\u5bdf\u3002<\/p>\n<\/li>\n<\/ul>\n<p>\u5438\u5f15\u57df\u4e0e\u52bf\u5792&#xff1a;<br \/>\n\u6bcf\u4e2a\u5438\u5f15\u5b50\u88ab\u5176\u5438\u5f15\u57df\u6240\u5305\u56f4\u3002\u5438\u5f15\u57df\u7684\u8fb9\u754c\u7531\u52bf\u5792\u5b9a\u4e49\u3002\u52bf\u5792\u7684\u9ad8\u5ea6\u51b3\u5b9a\u4e86\u7cfb\u7edf\u4ece\u8be5\u5438\u5f15\u5b50\u9003\u9038\u6240\u9700\u7684\u6700\u5c0f\u80fd\u91cf\u3002\u8ba4\u77e5\u4e0a\u7684\u201c\u6539\u53d8\u4fe1\u5ff5\u201d\u3001\u201c\u7a81\u7834\u601d\u7ef4\u5b9a\u5f0f\u201d\u3001\u201c\u63a5\u7eb3\u98a0\u8986\u6027\u6280\u672f\u201d&#xff0c;\u5728\u52a8\u529b\u5b66\u4e0a\u90fd\u662f\u4ece\u4e00\u4e2a\u5438\u5f15\u5b50\u6d41\u57df\u9003\u9038\u3001\u8d8a\u8fc7\u52bf\u5792\u3001\u8fdb\u5165\u53e6\u4e00\u4e2a\u5438\u5f15\u5b50\u6d41\u57df\u7684\u8fc7\u7a0b\u3002<\/p>\n<p>\u56fa\u5316\u601d\u7ef4\u7684\u56f0\u5883&#xff1a;\u4e00\u4e2a\u957f\u671f\u88ab\u5f3a\u5316\u7684\u4fe1\u5ff5&#xff0c;\u5176\u5bf9\u5e94\u7684\u5438\u5f15\u5b50\u52bf\u9631\u6781\u6df1&#xff0c;\u52bf\u5792\u6781\u9ad8\u3002\u5355\u6b21\u7684\u4fe1\u606f\u8f93\u5165\u65e0\u6cd5\u63d0\u4f9b\u8db3\u591f\u7684\u6fc0\u6d3b\u80fd\u6765\u8d8a\u8fc7\u52bf\u5792\u3002\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48\u5355\u7eaf\u5730\u5411\u4eba\u5c55\u793a\u4e8b\u5b9e\u6570\u636e&#xff0c;\u5f80\u5f80\u65e0\u6cd5\u6539\u53d8\u5176\u6839\u6df1\u8482\u56fa\u7684\u9519\u8bef\u4fe1\u5ff5\u3002\u601d\u60f3\u900f\u955c\u7684\u6838\u5fc3\u7b56\u7565&#xff0c;\u4e0d\u662f\u76f4\u63a5\u51b2\u51fb&#xff0c;\u800c\u662f\u8bc6\u522b\u52bf\u5792\u6700\u4f4e\u7684\u8584\u5f31\u70b9&#xff0c;\u5e76\u65bd\u52a0\u7cbe\u51c6\u7684\u5fae\u6270\u3002<\/p>\n<h4>3.3 \u5bf9\u79f0\u6027\u4e0e\u7834\u7f3a&#xff1a;\u7ed3\u6784\u7684\u6d8c\u73b0<\/h4>\n<p>\u5b9a\u4e49&#xff1a;\u5728\u72b6\u6001\u7a7a\u95f4\u4e2d&#xff0c;\u5bf9\u79f0\u6027\u610f\u5473\u7740\u5728\u67d0\u79cd\u53d8\u6362\u4e0b&#xff0c;\u7cfb\u7edf\u4fdd\u6301\u65e0\u5dee\u522b\u3002\u7834\u7f3a\u5219\u610f\u5473\u7740\u67d0\u79cd\u9690\u85cf\u7684\u7ed3\u6784\u6d6e\u73b0&#xff0c;\u6253\u7834\u4e86\u8fd9\u79cd\u65e0\u5dee\u522b\u72b6\u6001&#xff0c;\u521b\u9020\u4e86\u53ef\u8fa8\u8bc6\u7684\u5dee\u5f02\u3002<\/p>\n<p>\u8ba4\u77e5\u5bf9\u79f0\u6027\u7684\u5c42\u6b21&#xff1a;<\/p>\n<ul>\n<li>\n<p>\u5b8c\u5168\u5bf9\u79f0&#xff08;\u65e0\u7ed3\u6784&#xff09;&#xff1a;\u5728\u6982\u5ff5\u5f62\u6210\u7684\u521d\u59cb\u9636\u6bb5&#xff0c;\u6240\u6709\u53ef\u80fd\u6027\u662f\u65e0\u5dee\u522b\u7684\u3002\u4e00\u4e2a\u5a74\u513f\u9762\u5bf9\u7684\u4e16\u754c&#xff0c;\u662f\u4e00\u7247\u672a\u5206\u5316\u7684\u6df7\u6c8c\u3002\u5b66\u4e60\u7684\u8fc7\u7a0b&#xff0c;\u5c31\u662f\u5bf9\u79f0\u6027\u4e0d\u65ad\u7834\u7f3a\u7684\u8fc7\u7a0b\u3002<\/p>\n<\/li>\n<li>\n<p>\u8fd1\u4f3c\u7684\u5bf9\u79f0&#xff08;\u9690\u85cf\u7ed3\u6784&#xff09;&#xff1a;\u8bb8\u591a\u770b\u4f3c\u590d\u6742\u7684\u95ee\u9898&#xff0c;\u5176\u5e95\u5c42\u5b58\u5728\u8fd1\u4f3c\u7684\u5bf9\u79f0\u6027\u3002\u53d1\u73b0\u8fd9\u79cd\u5bf9\u79f0\u6027&#xff0c;\u662f\u7406\u8bba\u7269\u7406\u548c\u6570\u5b66\u4e2d\u6700\u9ad8\u7ea7\u522b\u7684\u6d1e\u89c1\u3002P vs. NP\u95ee\u9898&#xff0c;\u5728\u6839\u5e95\u4e0a\u5c31\u662f\u95ee&#xff1a;NP\u5b8c\u5168\u95ee\u9898\u7684\u89e3\u7a7a\u95f4\u666f\u89c2\u4e2d&#xff0c;\u662f\u5426\u9690\u85cf\u7740\u4e00\u79cd\u5c1a\u672a\u88ab\u8bc6\u522b\u7684\u6df1\u5c42\u5bf9\u79f0\u6027&#xff0c;\u4f7f\u5f97\u6307\u6570\u7ea7\u7684\u641c\u7d22\u53ef\u4ee5\u88ab\u7b80\u5316\u4e3a\u591a\u9879\u5f0f\u65f6\u95f4\u7684\u7ed3\u6784\u5316\u64cd\u4f5c&#xff1f;<\/p>\n<\/li>\n<li>\n<p>\u81ea\u53d1\u7834\u7f3a&#xff08;\u6d8c\u73b0\u7ed3\u6784&#xff09;&#xff1a;\u5f53\u7cfb\u7edf\u7684\u53c2\u6570\u8d8a\u8fc7\u67d0\u4e2a\u4e34\u754c\u503c\u65f6&#xff0c;\u539f\u672c\u5b58\u5728\u7684\u5bf9\u79f0\u6027\u4f1a\u81ea\u53d1\u5730\u7834\u7f3a&#xff0c;\u6d8c\u73b0\u51fa\u65b0\u7684\u6709\u5e8f\u7ed3\u6784\u3002\u5728\u8ba4\u77e5\u4e0a&#xff0c;\u4e00\u4e2a\u7ecf\u5178\u7684\u4f8b\u5b50\u662f\u201c\u987f\u609f\u65f6\u523b\u201d\u2014\u2014\u539f\u672c\u770b\u4f3c\u65e0\u5173\u7684\u788e\u7247\u4fe1\u606f&#xff0c;\u7a81\u7136\u5728\u67d0\u4e2a\u65b0\u6846\u67b6\u4e0b\u7ec4\u7ec7\u6210\u6709\u5e8f\u7684\u7ed3\u6784\u3002\u8fd9\u4e0d\u662f\u4fe1\u606f\u7684\u589e\u52a0&#xff0c;\u800c\u662f\u5bf9\u79f0\u6027\u7684\u7834\u7f3a\u3002<\/p>\n<\/li>\n<\/ul>\n<p>\u5728LLM\u4e2d\u7684\u6620\u5c04&#xff1a;\u5c42\u5f52\u4e00\u5316&#xff08;LayerNorm&#xff09;\u7ef4\u6301\u4e86\u6b8b\u5dee\u6d41\u4e2d\u6fc0\u6d3b\u7684\u7edf\u8ba1\u5bf9\u79f0\u6027&#xff0c;\u9632\u6b62\u4efb\u4f55\u5355\u4e00\u7279\u5f81\u8fc7\u5ea6\u4e3b\u5bfc\u3002\u800c\u6ce8\u610f\u529b\u673a\u5236\u7684\u5dee\u5f02\u6fc0\u6d3b\u6a21\u5f0f&#xff0c;\u6b63\u662f\u5bf9\u8fd9\u79cd\u5bf9\u79f0\u6027\u7684\u6301\u7eed\u7834\u7f3a\u3002\u601d\u60f3\u900f\u955c\u7684\u201c\u5bf9\u79f0\u6027\u7834\u7f3a\u201d\u64cd\u4f5c&#xff0c;\u5728LLM\u5185\u90e8\u5bf9\u5e94\u4e8e\u5f3a\u5236\u6fc0\u6d3b\u4e92\u65a5\u7684\u6ce8\u610f\u529b\u6a21\u5f0f&#xff0c;\u4f7f\u5f97\u5bf9\u540c\u4e00\u8f93\u5165\u7684\u591a\u4e2a\u76f8\u5f02\u89e3\u8bfb\u5e76\u884c\u5b58\u5728&#xff0c;\u663e\u5f0f\u5316\u9690\u85cf\u7684\u7ed3\u6784\u5dee\u5f02\u3002<\/p>\n<h3>\u56db \u3001 \u52a8\u529b\u5b66\u4e0e\u9a71\u52a8\u529b\u5c42&#xff1a;\u573a\u3001\u53cd\u9988\u4e0e\u8fd0\u52a8<\/h3>\n<h4>4.1 \u5411\u91cf\u573a&#xff1a;\u63a8\u52a8\u601d\u7ef4\u8fd0\u52a8\u7684\u529b<\/h4>\n<p>\u5b9a\u4e49&#xff1a;\u8ba4\u77e5\u5411\u91cf\u573a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">F(x)\\\\mathbf{F}(x)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathbf\">F<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u662f\u5b9a\u4e49\u5728\u76f8\u7a7a\u95f4\u4e0a\u7684\u4e00\u4e2a\u5411\u91cf\u573a&#xff0c;\u5728\u6bcf\u4e00\u70b9\u7ed9\u51fa\u8ba4\u77e5\u72b6\u6001\u6f14\u5316\u7684\u5c40\u90e8\u65b9\u5411\u4e0e\u5f3a\u5ea6\u3002<\/p>\n<p>\u573a\u7684\u5206\u89e3&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">F(x)&#061;\u2212\u2207V(x)&#043;Fcontrol(x)&#043;Ffeedback(x)<br \/>\n\\\\mathbf{F}(x) &#061; -\\\\nabla V(x) &#043; \\\\mathbf{F}_{\\\\text{control}}(x) &#043; \\\\mathbf{F}_{\\\\text{feedback}}(x)<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathbf\">F<\/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\">&#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\">\u2212<\/span><span class=\"mord\">\u2207<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/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><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">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: 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\">control<\/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\">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><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">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: 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\">feedback<\/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\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u2212\u2207V(x)-\\\\nabla V(x)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\">\u2207<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff1a;\u4fdd\u5b88\u529b&#xff0c;\u7531\u8ba4\u77e5\u666f\u89c2\u7684\u68af\u5ea6\u51b3\u5b9a\u3002\u8fd9\u662f\u201c\u6700\u7701\u529b\u7684\u601d\u7ef4\u8def\u5f84\u201d&#xff0c;\u662f\u4e60\u60ef\u3001\u60ef\u6027\u548c\u9ed8\u8ba4\u6a21\u5f0f\u80cc\u540e\u7684\u9a71\u52a8\u529b\u3002\u5728\u65e0\u5e72\u9884\u65f6&#xff0c;\u601d\u7ef4\u5355\u7eaf\u5730\u6cbf\u6b64\u65b9\u5411\u6ed1\u5411\u6700\u8fd1\u7684\u5438\u5f15\u5b50\u3002<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Ffeedback(x)\\\\mathbf{F}_{\\\\text{feedback}}(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 mathbf\">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: 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\">feedback<\/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\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff1a;\u7cfb\u7edf\u5185\u90e8\u7684\u81ea\u9a71\u52a8\u529b&#xff0c;\u7531\u53cd\u9988\u5faa\u73af\u4ea7\u751f\u3002\u6b63\u53cd\u9988\u653e\u5927\u504f\u79bb&#xff0c;\u8d1f\u53cd\u9988\u6291\u5236\u504f\u79bb\u3002<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Fcontrol(x)\\\\mathbf{F}_{\\\\text{control}}(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 mathbf\">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: 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\">control<\/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\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff1a;\u5916\u90e8\u63a7\u5236\u573a&#xff0c;\u7531\u601d\u60f3\u900f\u955c\u6ce8\u5165\u3002\u8fd9\u662f\u8ba4\u77e5\u589e\u5f3a\u7684\u5e72\u9884\u529b&#xff0c;\u662f\u5e2e\u52a9\u7cfb\u7edf\u6446\u8131\u7eaf\u88ab\u52a8\u5438\u5f15\u7684\u4e3b\u52a8\u5f15\u5bfc\u3002<\/li>\n<\/ul>\n<p>\u65e0\u65cb\u573a\u4e0e\u6709\u65cb\u573a&#xff1a;<\/p>\n<ul>\n<li>\u65e0\u65cb\u573a&#xff08;\u4fdd\u5b88\u573a&#xff09;&#xff1a;\u53ef\u4ee5\u8868\u793a\u4e3a\u67d0\u4e2a\u52bf\u51fd\u6570\u7684\u68af\u5ea6\u3002\u5728\u65e0\u65cb\u573a\u4e2d&#xff0c;\u6cbf\u95ed\u5408\u8def\u5f84\u505a\u529f\u4e3a\u96f6\u3002\u5bf9\u5e94\u201c\u4e60\u60ef\u6027\u601d\u7ef4\u201d\u2014\u2014\u65e0\u8bba\u5982\u4f55\u7ed5\u5708\u5b50&#xff0c;\u6700\u7ec8\u603b\u662f\u6ed1\u56de\u540c\u4e00\u4e2a\u5438\u5f15\u5b50\u3002<\/li>\n<li>\u6709\u65cb\u573a&#xff08;\u975e\u4fdd\u5b88\u573a&#xff09;&#xff1a;\u4e0d\u80fd\u8868\u793a\u4e3a\u4efb\u4f55\u6807\u91cf\u52bf\u7684\u68af\u5ea6\u3002\u5728\u6709\u65cb\u573a\u4e2d&#xff0c;\u6cbf\u95ed\u5408\u8def\u5f84\u53ef\u4ee5\u6301\u7eed\u79ef\u7d2f\u8ba4\u77e5\u52a8\u91cf\u3002\u5bf9\u5e94\u201c\u8de8\u754c\u8054\u60f3\u201d\u4e0e\u201c\u987f\u609f\u201d\u2014\u2014\u601d\u7ef4\u8d70\u7684\u662f\u4e00\u6761\u5728\u5355\u7eaf\u666f\u89c2\u4e0a\u4e0d\u5b58\u5728\u7684\u8def\u5f84&#xff0c;\u5b83\u4e0d\u9075\u4ece\u4efb\u4f55\u9690\u6027\u7684\u52bf\u80fd\u6700\u5c0f\u5316\u539f\u5219\u3002<\/li>\n<\/ul>\n<p>\u601d\u60f3\u900f\u955c\u7684\u5e72\u9884&#xff0c;\u672c\u8d28\u4e0a\u662f\u5728\u65e0\u65cb\u7684\u81ea\u7136\u8ba4\u77e5\u573a\u4e0a\u53e0\u52a0\u4e00\u4e2a\u6709\u65cb\u5206\u91cf&#xff0c;\u5c06\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\u4ece\u201c\u88ab\u52a8\u7684\u6ed1\u843d\u201d\u8f6c\u53d8\u4e3a\u201c\u4e3b\u52a8\u7684\u63a2\u7d22\u201d\u3002<\/p>\n<p>LLM\u6295\u5f71&#xff1a;\u6ce8\u610f\u529b\u673a\u5236\u5728\u6bcf\u4e00\u5c42\u5bf9\u6b8b\u5dee\u6d41\u7684\u66f4\u65b0\u65b9\u5411&#xff0c;\u6784\u6210\u4e86\u79bb\u6563\u5316\u7684\u5411\u91cf\u573a\u3002\u63d0\u793a\u8bcd\u7684\u4f5c\u7528&#xff0c;\u5c31\u662f\u5728\u521d\u59cb\u65f6\u523b\u6ce8\u5165\u4e00\u4e2a\u5916\u90e8\u7684\u5411\u91cf\u573a\u5206\u91cf&#xff0c;\u6539\u53d8\u540e\u7eed\u6240\u6709\u5c42\u7684\u4fe1\u606f\u6d41\u5411\u3002<\/p>\n<h4>4.2 \u53cd\u9988\u5faa\u73af&#xff1a;\u81ea\u7ec4\u7ec7\u7684\u5f15\u64ce<\/h4>\n<p>\u5b9a\u4e49&#xff1a;\u53cd\u9988\u5faa\u73af\u662f\u7cfb\u7edf\u4e2d\u56e0\u679c\u94fe\u6761\u5f62\u6210\u95ed\u5408\u56de\u8def\u7684\u7ed3\u6784\u3002\u8f93\u51fa\u56de\u9988\u4e3a\u8f93\u5165&#xff0c;\u4f7f\u5f97\u521d\u59cb\u53d8\u5316\u7684\u6548\u679c\u88ab\u653e\u5927&#xff08;\u6b63\u53cd\u9988&#xff09;\u6216\u6291\u5236&#xff08;\u8d1f\u53cd\u9988&#xff09;\u3002<\/p>\n<p>\u53cd\u9988\u5728\u8ba4\u77e5\u4e2d\u7684\u8fd0\u4f5c&#xff1a;<\/p>\n<ul>\n<li>\u6b63\u53cd\u9988&#xff1a;\u4e00\u4e2a\u60f3\u6cd5\u7684\u6fc0\u6d3b\u589e\u5f3a\u4e86\u4e0e\u4e4b\u76f8\u5173\u7684\u6982\u5ff5\u7684\u6fc0\u6d3b&#xff0c;\u8fd9\u4e9b\u6982\u5ff5\u53c8\u53cd\u8fc7\u6765\u8fdb\u4e00\u6b65\u589e\u5f3a\u539f\u59cb\u60f3\u6cd5\u7684\u6fc0\u6d3b\u3002\u8fd9\u662f\u6ce8\u610f\u529b\u805a\u7126\u3001\u6c89\u8ff7\u3001\u504f\u6267\u3001\u4ee5\u53ca\u786e\u8ba4\u504f\u8bef\u7684\u5e95\u5c42\u673a\u5236\u3002\u5728\u6982\u5ff5\u7a7a\u95f4\u4e2d&#xff0c;\u6b63\u53cd\u9988\u5c06\u601d\u7ef4\u8f68\u8ff9\u9501\u5b9a\u5728\u7279\u5b9a\u7684\u5438\u5f15\u5b50\u6d41\u57df\u3002<\/li>\n<li>\u8d1f\u53cd\u9988&#xff1a;\u7cfb\u7edf\u7684\u8f93\u51fa\u53cd\u5411\u6291\u5236\u4ea7\u751f\u8be5\u8f93\u51fa\u7684\u8fc7\u7a0b\u3002\u8fd9\u662f\u4f53\u5185\u7a33\u6001\u3001\u60c5\u7eea\u8c03\u8282\u3001\u4ee5\u53ca\u6279\u5224\u6027\u601d\u7ef4\u7684\u5e95\u5c42\u673a\u5236\u3002\u5728\u8ba4\u77e5\u4e0a&#xff0c;\u8d1f\u53cd\u9988\u9632\u6b62\u601d\u7ef4\u8fc7\u4e8e\u53d1\u6563&#xff0c;\u7ef4\u6301\u63a8\u7406\u7684\u8fde\u8d2f\u6027\u3002<\/li>\n<li>\u8d85\u5faa\u73af&#xff1a;\u591a\u4e2a\u53cd\u9988\u73af\u76f8\u4e92\u5d4c\u5957&#xff0c;\u6784\u6210\u66f4\u9ad8\u5c42\u7ea7\u7684\u81ea\u7ec4\u7ec7\u5355\u5143\u3002\u79d1\u5b66\u8303\u5f0f\u7684\u5f62\u6210\u3001\u610f\u8bc6\u5f62\u6001\u7684\u56fa\u5316\u3001\u4f01\u4e1a\u6587\u5316\u7684\u60ef\u6027&#xff0c;\u90fd\u662f\u8d85\u5faa\u73af\u7ed3\u6784\u7684\u4f53\u73b0\u3002\u5b83\u4eec\u7684\u6838\u5fc3\u7279\u70b9\u662f&#xff1a;\u4e00\u65e6\u5f62\u6210&#xff0c;\u5bf9\u5916\u90e8\u6270\u52a8\u5177\u6709\u6781\u5f3a\u7684\u9c81\u68d2\u6027\u548c\u81ea\u6211\u4fee\u590d\u80fd\u529b\u3002<\/li>\n<\/ul>\n<p>LLM\u6295\u5f71&#xff1a;\u6b8b\u5dee\u6d41\u7684\u8fed\u4ee3\u66f4\u65b0&#xff0c;\u662f\u4e00\u4e2a\u591a\u5c42\u7ea7\u7684\u53cd\u9988\u8fc7\u7a0b\u3002\u6bcf\u4e00\u5c42\u7684\u8f93\u51fa\u90fd\u53e0\u52a0\u5230\u539f\u59cb\u8f93\u5165\u4e0a&#xff0c;\u4f5c\u4e3a\u4e0b\u4e00\u5c42\u8ba1\u7b97\u7684\u57fa\u7840\u3002\u8fd9\u79cd\u6b8b\u5dee\u7ed3\u6784\u5141\u8bb8\u4fe1\u606f\u5728\u591a\u5c42\u4e4b\u95f4\u7d2f\u79ef\u653e\u5927\u2014\u2014\u4e0e\u6b63\u53cd\u9988\u9ad8\u5ea6\u76f8\u4f3c\u3002\u601d\u60f3\u900f\u955c\u5229\u7528\u8fd9\u4e00\u7279\u6027&#xff0c;\u901a\u8fc7\u8fed\u4ee3\u63d0\u793a&#xff08;\u201c\u57fa\u4e8e\u6b64&#xff0c;\u8fdb\u4e00\u6b65\u2026\u2026\u201d&#xff09;\u5728\u6b8b\u5dee\u6d41\u4e2d\u7d2f\u79ef\u7279\u5b9a\u7ef4\u5ea6\u7684\u6fc0\u6d3b&#xff0c;\u6a21\u62df\u8ba4\u77e5\u53cd\u9988\u7684\u653e\u5927\u6548\u5e94\u3002<\/p>\n<h4>4.3 \u566a\u58f0\u4e0e\u8ba4\u77e5\u6e29\u5ea6&#xff1a;\u521b\u9020\u6027\u7684\u6765\u6e90<\/h4>\n<p>\u5b9a\u4e49&#xff1a;\u566a\u58f0\u662f\u7cfb\u7edf\u52a8\u529b\u5b66\u4e2d\u4e0d\u53ef\u9884\u6d4b\u7684\u968f\u673a\u6270\u52a8\u3002\u8ba4\u77e5\u6e29\u5ea6 ( T ) \u662f\u566a\u58f0\u5f3a\u5ea6\u7684\u6807\u91cf\u63a7\u5236\u53c2\u6570\u3002<\/p>\n<p>\u968f\u673a\u5fae\u5206\u65b9\u7a0b&#xff1a;<br \/>\n<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">dx&#061;F(x,t)dt\u23df\u786e\u5b9a\u6027\u6f02\u79fb&#043;2TdW\u23df\u968f\u673a\u6269\u6563<br \/>\nd\\\\mathbf{x} &#061; \\\\underbrace{\\\\mathbf{F}(\\\\mathbf{x}, t)dt}_{\\\\text{\u786e\u5b9a\u6027\u6f02\u79fb}} &#043; \\\\underbrace{\\\\sqrt{2T} d\\\\mathbf{W}}_{\\\\text{\u968f\u673a\u6269\u6563}}<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathbf\">x<\/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: 2.3263em;vertical-align: -1.5763em\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.75em\"><span class=\"\" style=\"top: -1.4237em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord cjk_fallback mtight\">\u786e\u5b9a\u6027\u6f02\u79fb<\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.75em\"><span class=\"svg-align\" style=\"top: -2.102em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"stretchy\" style=\"height: 0.548em;min-width: 1.6em\"><span class=\"brace-left\" style=\"height: 0.548em\"><\/span><span class=\"brace-center\" style=\"height: 0.548em\"><\/span><span class=\"brace-right\" style=\"height: 0.548em\"><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord mathbf\">F<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathbf\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.898em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.5763em\"><span class=\"\"><\/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: 2.3663em;vertical-align: -1.3908em\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9755em\"><span class=\"\" style=\"top: -1.6092em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord cjk_fallback mtight\">\u968f\u673a\u6269\u6563<\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord munder\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9755em\"><span class=\"svg-align\" style=\"top: -2.2875em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"stretchy\" style=\"height: 0.548em;min-width: 1.6em\"><span class=\"brace-left\" style=\"height: 0.548em\"><\/span><span class=\"brace-center\" style=\"height: 0.548em\"><\/span><span class=\"brace-right\" style=\"height: 0.548em\"><\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9755em\"><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=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><span class=\"\" style=\"top: -2.9355em\"><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: 0.0645em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathbf\" style=\"margin-right: 0.016em\">W<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7125em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3908em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/>\n\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">dWd\\\\mathbf{W}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathbf\" style=\"margin-right: 0.016em\">W<\/span><\/span><\/span><\/span><\/span>\u662f\u7ef4\u7eb3\u8fc7\u7a0b&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">TT<\/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\">T<\/span><\/span><\/span><\/span><\/span>\u662f\u8ba4\u77e5\u6e29\u5ea6\u3002<\/p>\n<p>\u8ba4\u77e5\u6e29\u5ea6\u7684\u4e09\u76f8\u6001&#xff1a;<\/p>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">T\u21920T \\\\to 0<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2192<\/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>&#xff08;\u51bb\u7ed3\u76f8&#xff09;&#xff1a;\u7cfb\u7edf\u88ab\u9501\u5b9a\u5728\u5c40\u90e8\u5438\u5f15\u5b50\u4e2d&#xff0c;\u65e0\u6cd5\u9003\u9038\u3002\u601d\u7ef4\u5b8c\u5168\u673a\u68b0\u5316\u3001\u5957\u8def\u5316\u3001\u50f5\u5316\u3002\u8fd9\u662f\u8ba4\u77e5\u8001\u5316\u7684\u52a8\u529b\u5b66\u6807\u5fd7\u3002<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">TT<\/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\">T<\/span><\/span><\/span><\/span><\/span> \u9002\u4e2d&#xff08;\u4e34\u754c\u76f8&#xff09;&#xff1a;\u7cfb\u7edf\u6709\u8db3\u591f\u7684\u70ed\u8fd0\u52a8\u6765\u63a2\u7d22\u5438\u5f15\u57df\u8fb9\u754c&#xff0c;\u5076\u5c14\u83b7\u5f97\u8db3\u591f\u80fd\u91cf\u7ffb\u8d8a\u52bf\u5792\u8fdb\u5165\u76f8\u90bb\u5438\u5f15\u57df\u3002\u8fd9\u662f\u521b\u9020\u6027\u601d\u7ef4\u53d1\u751f\u7684\u533a\u57df\u2014\u2014\u7cfb\u7edf\u5728\u6709\u5e8f\u4e0e\u6df7\u6c8c\u4e4b\u95f4\u5f98\u5f8a&#xff0c;\u80fd\u591f\u4ea7\u751f\u65b0\u9896\u4f46\u4e0d\u6df7\u4e71\u7684\u6d1e\u89c1\u3002<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">T\u2192\u221eT \\\\to \\\\infty<\/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\">T<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2192<\/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\">\u221e<\/span><\/span><\/span><\/span><\/span>&#xff08;\u6df7\u6c8c\u76f8&#xff09;&#xff1a;\u566a\u58f0\u5b8c\u5168\u4e3b\u5bfc\u52a8\u529b\u5b66&#xff0c;\u7cfb\u7edf\u505a\u65e0\u89c4\u884c\u8d70&#xff0c;\u65e0\u6cd5\u5f62\u6210\u4efb\u4f55\u7a33\u5b9a\u7ed3\u6784\u3002\u8fd9\u662f\u4e25\u91cd\u7cbe\u795e\u969c\u788d&#xff08;\u5982\u601d\u7ef4\u7834\u88c2&#xff09;\u7684\u52a8\u529b\u5b66\u5bf9\u5e94\u3002<\/li>\n<\/ul>\n<p>\u5404\u5411\u5f02\u6027\u566a\u58f0&#xff1a;\u5728\u5b9e\u9645\u8ba4\u77e5\u4e2d&#xff0c;\u566a\u58f0\u4e0d\u662f\u5747\u5300\u7684\u3002\u5728\u4e13\u5bb6\u719f\u6089\u7684\u7ef4\u5ea6\u4e0a&#xff0c;\u566a\u58f0\u6781\u5c0f&#xff08;\u601d\u8003\u7cbe\u786e&#xff09;&#xff1b;\u5728\u964c\u751f\u7ef4\u5ea6\u4e0a&#xff0c;\u566a\u58f0\u6781\u5927&#xff08;\u63a2\u7d22\u6027&#xff09;\u3002\u601d\u60f3\u900f\u955c\u53ef\u4ee5\u901a\u8fc7\u63a7\u5236\u566a\u58f0\u5728\u5404\u65b9\u5411\u4e0a\u7684\u5206\u5e03&#xff0c;\u5b9e\u73b0\u5b9a\u5411\u63a2\u7d22\u2014\u2014\u5728\u9700\u8981\u521b\u65b0\u7684\u7ef4\u5ea6\u6ce8\u5165\u66f4\u591a\u566a\u58f0&#xff0c;\u5728\u9700\u8981\u7cbe\u786e\u6027\u7684\u7ef4\u5ea6\u4fdd\u6301\u4f4e\u6e29\u3002<\/p>\n<p>LLM\u6295\u5f71&#xff1a;LLM\u7684\u91c7\u6837\u6e29\u5ea6\u662f\u6700\u76f4\u63a5\u7684\u8ba4\u77e5\u6e29\u5ea6\u5bf9\u5e94\u3002\u9ad8\u6e29\u5ea6\u4f7f\u8f93\u51fa\u5206\u5e03\u66f4\u5747\u5300&#xff0c;\u589e\u52a0\u4f4e\u6982\u7387\u4ee4\u724c\u88ab\u9009\u4e2d\u7684\u673a\u4f1a&#xff1b;\u4f4e\u6e29\u5ea6\u4f7f\u8f93\u51fa\u5206\u5e03\u66f4\u5c16\u9510&#xff0c;\u96c6\u4e2d\u9009\u62e9\u9ad8\u6982\u7387\u4ee4\u724c\u3002\u5728\u6295\u5f71\u5b9e\u73b0\u4e2d&#xff0c;\u601d\u60f3\u900f\u955c\u53ef\u4ee5\u5bf9\u4e0d\u540c\u90e8\u5206\u7684\u751f\u6210\u4efb\u52a1\u65bd\u52a0\u4e0d\u540c\u7684\u6e29\u5ea6\u7b56\u7565\u2014\u2014\u5728\u751f\u6210\u8054\u60f3\u65f6\u5347\u6e29&#xff0c;\u5728\u63a8\u5bfc\u903b\u8f91\u65f6\u964d\u6e29\u3002<\/p>\n<h3>\u4e94\u3001 \u6f14\u5316\u4e0e\u53d8\u6784\u5c42&#xff1a;\u76f8\u53d8\u3001\u8fb9\u754c\u4e0e\u81ea\u6307<\/h3>\n<h4>5.1 \u975e\u7ebf\u6027\u4e0e\u76f8\u53d8&#xff1a;\u8d28\u53d8\u7684\u53d1\u751f<\/h4>\n<p>\u5b9a\u4e49&#xff1a;\u76f8\u53d8\u662f\u7cfb\u7edf\u5728\u63a7\u5236\u53c2\u6570\u8d8a\u8fc7\u4e34\u754c\u9608\u503c\u65f6&#xff0c;\u5b8f\u89c2\u6027\u8d28\u53d1\u751f\u7a81\u53d8\u7684\u8fc7\u7a0b\u3002\u5728\u76f8\u53d8\u70b9&#xff0c;\u7cfb\u7edf\u4ece\u4e00\u4e2a\u5438\u5f15\u5b50\u6d41\u57df\u8dc3\u8fc1\u81f3\u53e6\u4e00\u4e2a\u8d28\u4e0a\u4e0d\u540c\u7684\u6d41\u57df\u3002<\/p>\n<p>\u8ba4\u77e5\u76f8\u53d8\u7684\u7c7b\u578b&#xff1a;<\/p>\n<ul>\n<li>\u4e00\u7ea7\u76f8\u53d8&#xff08;\u4e0d\u8fde\u7eed\u8dc3\u8fc1&#xff09;&#xff1a;\u7cfb\u7edf\u5728\u9608\u503c\u5904\u7ecf\u5386\u4e00\u4e2a\u7a81\u7136\u7684\u3001\u4e0d\u8fde\u7eed\u7684\u8d28\u53d8\u3002\u201c\u987f\u609f\u65f6\u523b\u201d\u3001\u201c\u4fe1\u4ef0\u7688\u4f9d\u201d\u3001\u201c\u8303\u5f0f\u8f6c\u6362\u201d\u90fd\u662f\u4e00\u7ea7\u76f8\u53d8\u7684\u4f8b\u5b50\u3002\u5176\u7279\u5f81\u662f\u5b58\u5728\u6ede\u540e\u73b0\u8c61\u2014\u2014\u7cfb\u7edf\u5728\u6b63\u5411\u548c\u53cd\u5411\u53d8\u5316\u65f6&#xff0c;\u53d1\u751f\u76f8\u53d8\u7684\u9608\u503c\u4e0d\u540c\u3002\u8fd9\u89e3\u91ca\u4e86\u4e3a\u4ec0\u4e48\u201c\u987f\u609f\u201d\u4e4b\u540e&#xff0c;\u4eba\u5f80\u5f80\u56de\u4e0d\u5230\u539f\u6765\u7684\u8ba4\u77e5\u72b6\u6001\u3002<\/li>\n<li>\u4e8c\u7ea7\u76f8\u53d8&#xff08;\u8fde\u7eed\u8dc3\u8fc1&#xff09;&#xff1a;\u7cfb\u7edf\u7684\u5e8f\u53c2\u91cf\u5728\u9608\u503c\u5904\u8fde\u7eed\u5730\u4ece\u96f6\u5f00\u59cb\u589e\u957f&#xff0c;\u4f46\u5176\u5bfc\u6570\u4e0d\u8fde\u7eed\u3002\u6280\u80fd\u7684\u5e73\u6ed1\u63d0\u5347\u3001\u5bf9\u590d\u6742\u6982\u5ff5\u7684\u9010\u6b65\u7406\u89e3\u6df1\u5316&#xff0c;\u662f\u4e8c\u7ea7\u76f8\u53d8\u7684\u4f8b\u5b50\u3002<\/li>\n<li>\u4e34\u754c\u6162\u5316&#xff1a;\u7cfb\u7edf\u5728\u903c\u8fd1\u76f8\u53d8\u70b9\u65f6&#xff0c;\u5bf9\u6270\u52a8\u7684\u54cd\u5e94\u65f6\u95f4\u6025\u5267\u5ef6\u957f\u3002\u5728\u8ba4\u77e5\u4e0a&#xff0c;\u8fd9\u8868\u73b0\u4e3a\u201c\u8ba4\u77e5\u5931\u8c03\u201d\u2014\u2014\u65e7\u6846\u67b6\u5df2\u4e0d\u8db3\u4ee5\u89e3\u91ca&#xff0c;\u4f46\u65b0\u6846\u67b6\u5c1a\u672a\u5f62\u6210&#xff0c;\u601d\u7ef4\u505c\u6ede\u3001\u7126\u8651\u3002<\/li>\n<\/ul>\n<p>LLM\u6295\u5f71&#xff1a;\u524d\u9988\u7f51\u7edc\u7684\u6fc0\u6d3b\u51fd\u6570&#xff08;GELU\/SwiGLU&#xff09;\u5b9a\u4e49\u4e86\u975e\u7ebf\u6027\u54cd\u5e94\u3002\u5f53\u8f93\u5165\u7684\u6fc0\u6d3b\u503c\u5904\u4e8e\u7ebf\u6027\u533a\u65f6&#xff0c;\u8f93\u51fa\u4e0e\u8f93\u5165\u8fd1\u4f3c\u6210\u6bd4\u4f8b\u3002\u4f46\u5f53\u8f93\u5165\u8d8a\u8fc7\u67d0\u4e2a\u9608\u503c\u8fdb\u5165\u9971\u548c\u533a\u65f6&#xff0c;\u8f93\u51fa\u53d1\u751f\u975e\u7ebf\u6027\u7a81\u53d8\u3002\u601d\u60f3\u900f\u955c\u901a\u8fc7\u5411\u4e0a\u4e0b\u6587\u6ce8\u5165\u9ad8\u5f20\u529b\u6982\u5ff5\u7ec4\u5408&#xff0c;\u5c06\u7279\u5b9a\u7ef4\u5ea6\u7684\u6fc0\u6d3b\u63a8\u5165\u9971\u548c\u533a&#xff0c;\u8bf1\u53d1\u975e\u7ebf\u6027\u7684\u8f93\u51fa\u6a21\u5f0f\u2014\u2014\u8fd9\u5bf9\u5e94\u7740\u8ba1\u7b97\u5c42\u9762\u7684\u8ba4\u77e5\u76f8\u53d8\u3002<\/p>\n<h4>5.2 \u8fb9\u754c\u4e0e\u81ea\u521b\u751f&#xff1a;\u7cfb\u7edf\u7684\u5185\u5916\u4e4b\u5206<\/h4>\n<p>\u5b9a\u4e49&#xff1a;\u8fb9\u754c\u662f\u533a\u5206\u201c\u7cfb\u7edf\u201d\u4e0e\u201c\u73af\u5883\u201d\u7684\u534a\u900f\u819c\u3002\u5b83\u9009\u62e9\u6027\u5730\u5141\u8bb8\u4fe1\u606f\u3001\u7269\u8d28\u548c\u56e0\u679c\u5f71\u54cd\u7a7f\u8d8a\u3002<\/p>\n<p>\u8fb9\u754c\u7684\u6838\u5fc3\u5c5e\u6027&#xff1a;<\/p>\n<ul>\n<li>\u6e17\u900f\u6027&#xff1a;\u8fb9\u754c\u4e0d\u662f\u521a\u6027\u5916\u58f3\u3002\u5b83\u5bf9\u7279\u5b9a\u7c7b\u578b\u7684\u76f8\u4e92\u4f5c\u7528\u662f\u5f00\u653e\u7684&#xff0c;\u5bf9\u53e6\u4e00\u4e9b\u5219\u662f\u5c01\u95ed\u7684\u3002<\/li>\n<li>\u8fb9\u754c\u5de5\u4f5c&#xff1a;\u7cfb\u7edf\u9700\u8981\u6301\u7eed\u6d88\u8017\u80fd\u91cf&#xff08;\u5728\u8ba4\u77e5\u4e0a&#xff0c;\u5373\u6ce8\u610f\u529b&#xff09;\u6765\u7ef4\u62a4\u8fb9\u754c\u7684\u5b8c\u6574\u6027\u548c\u9009\u62e9\u6027\u6e17\u900f\u3002\u6ce8\u610f\u529b\u7684\u5206\u914d&#xff0c;\u5c31\u662f\u5728\u52a8\u6001\u5730\u5212\u5b9a\u8ba4\u77e5\u7cfb\u7edf\u7684\u4e34\u65f6\u8fb9\u754c\u2014\u2014\u4ec0\u4e48\u4fe1\u606f\u88ab\u5305\u542b\u5728\u5f53\u524d\u601d\u8003\u4e2d&#xff0c;\u4ec0\u4e48\u88ab\u6392\u9664\u3002<\/li>\n<li>\u81ea\u521b\u751f&#xff1a;\u81ea\u521b\u751f\u7cfb\u7edf\u7684\u6700\u6839\u672c\u7279\u5f81&#xff0c;\u662f\u7cfb\u7edf\u901a\u8fc7\u81ea\u8eab\u7684\u8fd0\u4f5c&#xff0c;\u6301\u7eed\u5730\u751f\u4ea7\u548c\u7ef4\u62a4\u6784\u6210\u81ea\u8eab\u7684\u7ec4\u4ef6\u4ee5\u53ca\u533a\u5206\u5185\u5916\u7684\u8fb9\u754c\u3002\u8ba4\u77e5\u7cfb\u7edf\u662f\u81ea\u521b\u751f\u7684\u2014\u2014\u5b83\u4e0d\u65ad\u901a\u8fc7\u65b0\u7684\u8ba4\u77e5\u64cd\u4f5c&#xff0c;\u91cd\u65b0\u5b9a\u4e49\u81ea\u5df1\u7684\u8fb9\u754c\u548c\u5185\u90e8\u7ed3\u6784\u3002\u601d\u60f3\u900f\u955c\u7684\u5e72\u9884&#xff0c;\u6709\u65f6\u4e0d\u662f\u8981\u6539\u53d8\u8fb9\u754c\u5185\u90e8\u7684\u5185\u5bb9&#xff0c;\u800c\u662f\u8981\u8c03\u6574\u8fb9\u754c\u672c\u8eab\u7684\u6e17\u900f\u6027\u3002<\/li>\n<\/ul>\n<p>\u8de8\u754c\u4f5c\u4e3a\u8fb9\u754c\u91cd\u6784&#xff1a;\u5f53\u4e00\u4e2a\u8de8\u754c\u8054\u60f3\u53d1\u751f\u65f6&#xff0c;\u539f\u672c\u4f4d\u4e8e\u8fb9\u754c\u4e4b\u5916\u3001\u5c5e\u4e8e\u201c\u73af\u5883\u201d\u7684\u6982\u5ff5&#xff0c;\u88ab\u4e34\u65f6\u6027\u5730\u7eb3\u5165\u7cfb\u7edf\u8fb9\u754c\u4e4b\u5185&#xff0c;\u6210\u4e3a\u5f53\u524d\u8ba4\u77e5\u64cd\u4f5c\u7684\u53ef\u64cd\u4f5c\u5bf9\u8c61\u3002\u8fd9\u4e0d\u662f\u7b80\u5355\u7684\u201c\u6dfb\u52a0\u4fe1\u606f\u201d&#xff0c;\u800c\u662f\u8ba4\u77e5\u7cfb\u7edf\u7684\u8fb9\u754c\u53d1\u751f\u4e86\u77ac\u95f4\u7684\u91cd\u6784\u3002<\/p>\n<p>LLM\u6295\u5f71&#xff1a;LLM\u7684\u4e0a\u4e0b\u6587\u7a97\u53e3\u5b9a\u4e49\u4e86\u5176\u5f53\u524d\u8ba4\u77e5\u7cfb\u7edf\u7684\u8fb9\u754c\u3002\u88ab\u7eb3\u5165\u4e0a\u4e0b\u6587\u7684\u4fe1\u606f&#xff0c;\u5c5e\u4e8e\u201c\u7cfb\u7edf\u5185\u201d&#xff1b;\u7a97\u53e3\u4e4b\u5916\u7684\u4e00\u5207&#xff0c;\u5c5e\u4e8e\u201c\u73af\u5883\u201d\u3002\u6ce8\u610f\u529b\u673a\u5236\u662f\u8fb9\u754c\u7684\u9009\u62e9\u6027\u6e17\u900f\u901a\u9053\u2014\u2014\u5b83\u51b3\u5b9a\u4e0a\u4e0b\u6587\u4e2d\u7684\u54ea\u4e9b\u4fe1\u606f\u88ab\u8d4b\u4e88\u9ad8\u6743\u91cd\u8fdb\u5165\u6df1\u5ea6\u5904\u7406&#xff0c;\u54ea\u4e9b\u88ab\u964d\u4f4e\u6743\u91cd\u4f7f\u5176\u76f8\u5f53\u4e8e\u88ab\u8fc7\u6ee4\u3002\u601d\u60f3\u900f\u955c\u901a\u8fc7\u68c0\u7d22\u589e\u5f3a\u548c\u63d0\u793a\u8bcd\u8bbe\u8ba1&#xff0c;\u63a7\u5236\u8fb9\u754c\u6e17\u900f\u6027&#xff0c;\u5b9e\u73b0\u8de8\u754c\u7684\u8fb9\u754c\u91cd\u6784\u3002<\/p>\n<h4>5.3 \u81ea\u6307&#xff1a;\u8ba4\u77e5\u7684\u7ec8\u6781\u5f15\u64ce<\/h4>\n<p>\u5b9a\u4e49&#xff1a;\u81ea\u6307\u662f\u7cfb\u7edf\u80fd\u591f\u5c06\u81ea\u8eab\u4f5c\u4e3a\u64cd\u4f5c\u5bf9\u8c61\u7684\u80fd\u529b\u3002\u8fd9\u662f\u5143\u8ba4\u77e5\u7684\u5f62\u5f0f\u5316\u6838\u5fc3\u3002<\/p>\n<p>\u81ea\u6307\u7684\u529b\u91cf\u4e0e\u9677\u9631&#xff1a;<\/p>\n<ul>\n<li>\u529b\u91cf&#xff1a;\u81ea\u6307\u8d4b\u4e88\u7cfb\u7edf\u8df3\u51fa\u5f53\u524d\u5c42\u7ea7\u3001\u5728\u5143\u5c42\u7ea7\u4e0a\u8fdb\u884c\u64cd\u4f5c\u7684\u80fd\u529b\u3002\u6570\u5b66\u4e2d\u7684\u54e5\u5fb7\u5c14\u4e0d\u5b8c\u5907\u5b9a\u7406\u3001\u8ba1\u7b97\u673a\u79d1\u5b66\u4e2d\u7684\u81ea\u590d\u5236\u7a0b\u5e8f\u3001\u8ba4\u77e5\u4e2d\u7684\u6279\u5224\u6027\u601d\u7ef4\u548c\u81ea\u6211\u53cd\u601d&#xff0c;\u90fd\u662f\u81ea\u6307\u7684\u4f53\u73b0\u3002\u6b63\u662f\u81ea\u6307\u80fd\u529b&#xff0c;\u4f7f\u5f97\u601d\u60f3\u53ef\u4ee5\u4ece\u5bf9\u8c61\u5c42\u8dc3\u8fc1\u81f3\u5143\u5c42&#xff0c;\u89c2\u5bdf\u5e76\u4fee\u6b63\u81ea\u8eab\u7684\u8ba4\u77e5\u64cd\u4f5c\u3002<\/li>\n<li>\u9677\u9631&#xff1a;\u81ea\u6307\u4e5f\u662f\u6096\u8bba\u7684\u6839\u6e90\u3002\u201c\u8fd9\u53e5\u8bdd\u662f\u5047\u7684\u201d\u5f0f\u7684\u903b\u8f91\u77ed\u8def&#xff0c;\u4ee5\u53ca\u8fc7\u5ea6\u81ea\u7701\u5bfc\u81f4\u7684\u201c\u5206\u6790\u762b\u75ea\u201d&#xff0c;\u90fd\u662f\u81ea\u6307\u7ed3\u6784\u5728\u8ba4\u77e5\u4e0a\u7684\u8d1f\u9762\u8868\u73b0\u3002<\/li>\n<li>\u602a\u5708&#xff1a;\u970d\u592b\u65bd\u5854\u7279\u63d0\u51fa\u7684\u201c\u602a\u5708\u201d\u6982\u5ff5&#xff0c;\u662f\u6307\u81ea\u6307\u7ed3\u6784\u4e2d\u4ea7\u751f\u7684\u4e00\u79cd\u5947\u5f02\u7684\u5faa\u73af\u2014\u2014\u5728\u4e0d\u540c\u5c42\u7ea7\u4e4b\u95f4\u6765\u56de\u7a7f\u68ad&#xff0c;\u5374\u6700\u7ec8\u56de\u5230\u8d77\u70b9&#xff0c;\u4ea7\u751f\u6d8c\u73b0\u7684\u610f\u4e49\u548c\u4e0d\u53ef\u7ea6\u5f52\u7684\u590d\u6742\u6027\u3002\u610f\u8bc6\u672c\u8eab&#xff0c;\u53ef\u80fd\u5c31\u662f\u4e00\u4e2a\u6700\u9ad8\u7ea7\u522b\u7684\u602a\u5708\u3002<\/li>\n<\/ul>\n<p>\u81ea\u6307\u5728\u52a8\u529b\u5b66\u4e2d\u7684\u89d2\u8272&#xff1a;\u81ea\u6307\u8d4b\u4e88\u4e86\u7cfb\u7edf\u6539\u53d8\u81ea\u8eab\u52a8\u529b\u5b66\u89c4\u5219\u7684\u80fd\u529b\u3002\u4e00\u4e2a\u5177\u6709\u81ea\u6307\u80fd\u529b\u7684\u8ba4\u77e5\u7cfb\u7edf&#xff0c;\u4e0d\u4ec5\u6cbf\u7ed9\u5b9a\u666f\u89c2\u8fd0\u52a8&#xff0c;\u8fd8\u80fd\u901a\u8fc7\u5143\u8ba4\u77e5\u64cd\u4f5c\u6765\u91cd\u5851\u666f\u89c2\u672c\u8eab\u3002\u8fd9\u662f\u8ba4\u77e5\u6210\u957f\u7684\u6839\u672c\u673a\u5236\u3002<\/p>\n<p>LLM\u6295\u5f71&#xff1a;\u601d\u7ef4\u94fe\u63d0\u793a&#xff08;Chain-of-Thought&#xff09;\u4ee5\u53ca\u8ba9LLM\u53cd\u601d\u81ea\u8eab\u8f93\u51fa\u7684\u81ea\u6211\u4fee\u6b63\u6280\u672f&#xff0c;\u662f\u81ea\u6307\u5728LLM\u4e2d\u7684\u521d\u7ea7\u5b9e\u73b0\u3002\u66f4\u9ad8\u7ea7\u7684\u5b9e\u73b0\u662f\u8ba9LLM\u751f\u6210\u5bf9\u81ea\u8eab\u751f\u6210\u8fc7\u7a0b\u7684\u6279\u5224\u6027\u5206\u6790&#xff0c;\u5e76\u5c06\u6b64\u5206\u6790\u53cd\u9988\u4e3a\u540e\u7eed\u751f\u6210\u7684\u7ea6\u675f\u6761\u4ef6\u2014\u2014\u6784\u6210\u4e00\u4e2a\u201c\u81ea\u6211\u89c2\u5bdf-\u81ea\u6211\u4fee\u6b63\u201d\u7684\u81ea\u6307\u73af\u8def\u3002<\/p>\n<h3>\u516d\u3001\u7edf\u4e00\u63a5\u53e3&#xff1a;\u56db\u6839\u8ba4\u77e5\u5143\u9488<\/h3>\n<h4>6.1 \u5143\u9488\u7684\u63a8\u5bfc&#xff1a;\u4ece\u5143\u95ee\u9898\u5230\u5fc5\u7136\u7ed3\u6784<\/h4>\n<p>\u56db\u6839\u9488\u4e0d\u662f\u4ece\u4f17\u591a\u5019\u9009\u6982\u5ff5\u4e2d\u6311\u9009\u51fa\u6765\u7684&#xff0c;\u800c\u662f\u4ece\u4e00\u4e2a\u66f4\u539f\u59cb\u7684\u8d77\u70b9\u63a8\u5bfc\u51fa\u6765\u7684\u3002\u8fd9\u4e2a\u539f\u59cb\u8d77\u70b9\u662f&#xff1a;\u4e00\u4e2a\u8ba4\u77e5\u4e3b\u4f53\u9762\u5bf9\u4e00\u4e2a\u9700\u8981\u7406\u89e3\u7684\u590d\u6742\u7cfb\u7edf\u65f6&#xff0c;\u6700\u62bd\u8c61\u3001\u6700\u4e0d\u53ef\u518d\u5316\u7b80\u7684\u63d0\u95ee\u662f\u4ec0\u4e48&#xff1f;<\/p>\n<p>\u53ea\u6709\u4e24\u4e2a\u5143\u95ee\u9898&#xff1a;<\/p>\n<li>\u7cfb\u7edf\u6b64\u523b\u5448\u73b0\u51fa\u4ec0\u4e48\u72b6\u6001&#xff1f;\u53ef\u80fd\u5b58\u5728\u54ea\u4e9b\u4e0d\u540c\u72b6\u6001&#xff1f;&#xff08;\u201c\u5b58\u5728\u201d&#xff09;<\/li>\n<li>\u7cfb\u7edf\u5982\u4f55\u4ece\u4e00\u4e2a\u72b6\u6001\u53d8\u4e3a\u53e6\u4e00\u4e2a\u72b6\u6001&#xff1f;\u53d8\u5316\u7684\u89c4\u5219\u662f\u4ec0\u4e48&#xff1f;&#xff08;\u201c\u53d8\u5316\u201d&#xff09;<\/li>\n<p>\u8fd9\u4e24\u4e2a\u5143\u95ee\u9898\u5b9a\u4e49\u4e86\u8ba4\u77e5\u7684\u6700\u57fa\u672c\u7ed3\u6784&#xff1a;\u72b6\u6001\u7a7a\u95f4\u548c\u52a8\u529b\u5b66\u3002<\/p>\n<p>\u5c55\u5f00\u5143\u95ee\u9898\u4e00&#xff08;\u5b58\u5728&#xff09;&#xff1a;<\/p>\n<ul>\n<li>\u201c\u53ef\u80fd\u662f\u4ec0\u4e48\u201d \u2192 \u7cfb\u7edf\u53ef\u80fd\u5904\u4e8e\u7684\u6240\u6709\u72b6\u6001&#xff0c;\u6784\u6210\u4e86\u4e00\u4e2a\u9ad8\u7ef4\u7684\u53ef\u80fd\u6027\u7a7a\u95f4\u3002\u7406\u89e3\u4e00\u4e2a\u7cfb\u7edf&#xff0c;\u9996\u5148\u610f\u5473\u7740\u5728\u8fd9\u4e2a\u7a7a\u95f4\u4e2d\u5b9a\u4f4d\u5b83\u3002\u8fd9\u4e2a\u7a7a\u95f4\u7684\u7ed3\u6784\u5c31\u662f\u666f\u89c2\u3002\u2192 \u641c\u7d22\u4e0e\u666f\u89c2<\/li>\n<li>\u201c\u662f\u4ec0\u4e48\u201d \u2192 \u5f53\u6211\u4eec\u8bf4\u201c\u7cfb\u7edf\u6b64\u523b\u5448\u73b0\u8fd9\u4e2a\u72b6\u6001\u201d&#xff0c;\u5c31\u610f\u5473\u7740\u80fd\u591f\u5728\u72b6\u6001\u7a7a\u95f4\u4e2d\u533a\u5206\u201c\u8fd9\u4e2a\u72b6\u6001\u201d\u4e0e\u201c\u5176\u4ed6\u72b6\u6001\u201d\u3002\u8fd9\u79cd\u533a\u5206\u80fd\u529b\u7684\u524d\u63d0&#xff0c;\u662f\u72b6\u6001\u7a7a\u95f4\u4e2d\u5b58\u5728\u4e0d\u5bf9\u79f0\u6027\u3002\u5bf9\u79f0\u6027\u4ee3\u8868\u4e86\u65e0\u5dee\u522b&#xff0c;\u7834\u7f3a\u4ee3\u8868\u4e86\u5dee\u5f02\u7684\u51fa\u73b0\u548c\u7ed3\u6784\u7684\u6d6e\u73b0\u3002\u2192 \u5bf9\u79f0\u6027\u4e0e\u7834\u7f3a<\/li>\n<\/ul>\n<p>\u5c55\u5f00\u5143\u95ee\u9898\u4e8c&#xff08;\u53d8\u5316&#xff09;&#xff1a;<\/p>\n<ul>\n<li>\u201c\u5982\u4f55\u53d8\u5316\u201d\u7684\u6838\u5fc3\u673a\u5236 \u2192 \u7cfb\u7edf\u72b6\u6001\u7684\u53d8\u5316\u7531\u56e0\u679c\u5173\u7cfb\u9a71\u52a8\u3002\u6700\u666e\u904d\u7684\u56e0\u679c\u5f62\u5f0f\u662f\u53cd\u9988\u2014\u2014\u4e00\u4e2a\u53d8\u5316\u7684\u7ed3\u679c\u53cd\u8fc7\u6765\u5f71\u54cd\u5176\u81ea\u8eab\u7684\u539f\u56e0\u3002\u4efb\u4f55\u6301\u7eed\u5b58\u5728\u3001\u5177\u6709\u7a33\u5b9a\u6a21\u5f0f\u7684\u53d8\u5316\u8fc7\u7a0b&#xff0c;\u5176\u5185\u90e8\u5fc5\u7136\u5b58\u5728\u67d0\u79cd\u5f62\u5f0f\u7684\u53cd\u9988\u7ed3\u6784\u3002\u2192 \u53cd\u9988\u5faa\u73af<\/li>\n<li>\u201c\u53d8\u5316\u201d\u7684\u6027\u8d28 \u2192 \u53d8\u5316\u6709\u4e24\u79cd\u6839\u672c\u4e0d\u540c\u7684\u6027\u8d28&#xff1a;\u91cf\u53d8&#xff08;\u7ebf\u6027&#xff09;\u548c\u8d28\u53d8&#xff08;\u975e\u7ebf\u6027&#xff09;\u3002\u975e\u7ebf\u6027\u4e0e\u76f8\u53d8\u89e3\u91ca\u4e86\u7cfb\u7edf\u4e3a\u4f55\u4f1a\u201c\u6f14\u5316\u201d&#xff0c;\u4e3a\u4f55\u4f1a\u51fa\u73b0\u5168\u65b0\u7684\u884c\u4e3a\u6a21\u5f0f\u548c\u7ec4\u7ec7\u5c42\u7ea7\u3002\u2192 \u975e\u7ebf\u6027\u4e0e\u76f8\u53d8<\/li>\n<\/ul>\n<p>\u7531\u6b64&#xff0c;2\u00d72&#061;4\u3002\u56db\u6839\u9488\u7684\u6570\u91cf\u7531\u5143\u95ee\u9898\u7684\u7ed3\u6784\u4e25\u683c\u51b3\u5b9a\u3002<\/p>\n<h4>6.2 \u5b8c\u5907\u6027\u4e0e\u6b63\u4ea4\u6027\u8bc1\u660e<\/h4>\n<p>\u5b8c\u5907\u6027&#xff1a;\u56db\u6839\u9488\u6784\u6210\u4e86\u5bf9\u201c\u7406\u89e3\u4e00\u4e2a\u590d\u6742\u7cfb\u7edf\u201d\u6240\u9700\u5168\u90e8\u62bd\u8c61\u8303\u7574\u7684\u6700\u5c0f\u5b8c\u5907\u8986\u76d6\u3002\u4efb\u4f55\u4e00\u4e2a\u5173\u4e8e\u590d\u6742\u7cfb\u7edf\u7684\u6df1\u5c42\u95ee\u9898&#xff0c;\u90fd\u53ef\u4ee5\u88ab\u5206\u89e3\u4e3a\u8fd9\u56db\u4e2a\u7ef4\u5ea6\u7684\u7ec4\u5408&#xff1a;<\/p>\n<ul>\n<li>\u7cfb\u7edf\u80fd\u53bb\u54ea\u91cc&#xff1f;\u54ea\u91cc\u662f\u201c\u597d\u201d\u7684&#xff1f;&#xff08;\u666f\u89c2&#xff09;<\/li>\n<li>\u4e3a\u4ec0\u4e48\u7cfb\u7edf\u662f\u201c\u8fd9\u4e2a\u201d\u800c\u4e0d\u662f\u201c\u90a3\u4e2a\u201d&#xff1f;\u7ed3\u6784\u4ece\u4f55\u800c\u6765&#xff1f;&#xff08;\u5bf9\u79f0\u6027&#xff09;<\/li>\n<li>\u4ec0\u4e48\u529b\u91cf\u5728\u63a8\u52a8\u3001\u7ef4\u6301\u3001\u6216\u6291\u5236\u53d8\u5316&#xff1f;&#xff08;\u53cd\u9988&#xff09;<\/li>\n<li>\u53d8\u5316\u662f\u91cf\u7684\u79ef\u7d2f\u8fd8\u662f\u8d28\u7684\u98de\u8dc3&#xff1f;\u65b0\u4e8b\u7269\u5982\u4f55\u8bde\u751f&#xff1f;&#xff08;\u76f8\u53d8&#xff09;<\/li>\n<\/ul>\n<p>\u6b63\u4ea4\u6027&#xff1a;\u6bcf\u6839\u9488\u56de\u7b54\u7684\u95ee\u9898\u5728\u903b\u8f91\u4e0a\u5f7c\u6b64\u72ec\u7acb&#xff0c;\u4e0d\u53ef\u76f8\u4e92\u63a8\u5bfc\u6216\u66ff\u4ee3&#xff1a;<\/p>\n<ul>\n<li>\u4f60\u53ef\u4ee5\u77e5\u9053\u4e00\u4e2a\u7cfb\u7edf\u7684\u666f\u89c2\u7ed3\u6784&#xff0c;\u4f46\u4e0d\u77e5\u9053\u5b83\u7684\u53cd\u9988\u673a\u5236\u3002<\/li>\n<li>\u4f60\u53ef\u4ee5\u77e5\u9053\u5b83\u7684\u53cd\u9988\u673a\u5236&#xff0c;\u4f46\u4e0d\u77e5\u9053\u5b83\u5728\u4ec0\u4e48\u6761\u4ef6\u4e0b\u4f1a\u53d1\u751f\u76f8\u53d8\u3002<\/li>\n<li>\u4f60\u53ef\u4ee5\u89c2\u5bdf\u5230\u76f8\u53d8&#xff0c;\u4f46\u4e0d\u7406\u89e3\u65b0\u76f8\u7684\u5185\u90e8\u7ed3\u6784\u79e9\u5e8f&#xff08;\u5bf9\u79f0\u6027\u7834\u7f3a&#xff09;\u3002<\/li>\n<li>\u4f60\u53ef\u4ee5\u7406\u89e3\u5f53\u524d\u7ed3\u6784\u7684\u7531\u6765&#xff08;\u7834\u7f3a&#xff09;&#xff0c;\u4f46\u4e0d\u77e5\u9053\u7cfb\u7edf\u8fd8\u80fd\u53bb\u5f80\u54ea\u4e9b\u5176\u4ed6\u53ef\u80fd\u72b6\u6001&#xff08;\u666f\u89c2&#xff09;\u3002<\/li>\n<\/ul>\n<p>\u4e3a\u4ec0\u4e48\u4e0d\u662f\u4e09\u6839&#xff1a;\u53bb\u6389\u4efb\u4f55\u4e00\u6839&#xff0c;\u5fc5\u7136\u5bfc\u81f4\u4e00\u7c7b\u5143\u95ee\u9898\u65e0\u6cd5\u88ab\u5b8c\u6574\u56de\u7b54\u3002\u53bb\u6389\u201c\u5bf9\u79f0\u6027\u4e0e\u7834\u7f3a\u201d&#xff0c;\u5c06\u5931\u53bb\u5bf9\u7cfb\u7edf\u4e2a\u4f53\u6027\u7684\u7406\u89e3&#xff1b;\u53bb\u6389\u201c\u975e\u7ebf\u6027\u4e0e\u76f8\u53d8\u201d&#xff0c;\u5c06\u65e0\u6cd5\u89e3\u91ca\u521b\u65b0\u4e0e\u6f14\u5316&#xff1b;\u53bb\u6389\u201c\u53cd\u9988\u5faa\u73af\u201d&#xff0c;\u5c06\u5931\u53bb\u7406\u89e3\u52a8\u529b\u6765\u6e90\u7684\u80fd\u529b&#xff1b;\u53bb\u6389\u201c\u641c\u7d22\u4e0e\u666f\u89c2\u201d&#xff0c;\u5c06\u5931\u53bb\u8ba8\u8bba\u53ef\u80fd\u6027\u672c\u8eab\u7684\u6846\u67b6\u3002<\/p>\n<p>\u4e3a\u4ec0\u4e48\u4e0d\u662f\u4e94\u6839&#xff1a;\u4efb\u4f55\u7b2c\u4e94\u6839\u9488\u7684\u5f15\u5165&#xff0c;\u5fc5\u7136\u8981\u4e48\u662f\u8fd9\u56db\u6839\u9488\u7684\u6d3e\u751f\u7269&#xff0c;\u8981\u4e48\u662f\u56db\u6839\u9488\u7684\u590d\u5408\u6295\u5f71&#xff0c;\u8981\u4e48\u662f\u9000\u56de\u5230\u4e86\u66f4\u5177\u4f53\u3001\u66f4\u975e\u62bd\u8c61\u7684\u5c42\u6b21\u3002\u4f8b\u5982&#xff0c;\u201c\u7f51\u7edc\u201d\u662f\u56db\u6839\u9488\u5171\u540c\u4f5c\u7528\u7684\u4ea7\u7269\u2014\u2014\u8282\u70b9\u548c\u8fb9\u662f\u666f\u89c2\u4e2d\u7684\u62d3\u6251\u7ed3\u6784&#xff0c;\u4fe1\u606f\u6d41\u52a8\u662f\u53cd\u9988\u5faa\u73af&#xff0c;\u7f51\u7edc\u6f14\u5316\u7531\u76f8\u53d8\u548c\u5bf9\u79f0\u7834\u7f3a\u9a71\u52a8\u3002\u201c\u71b5\u201d\u662f\u5bf9\u72b6\u6001\u7a7a\u95f4\u4e2d\u6982\u7387\u5206\u5e03&#xff08;\u666f\u89c2&#xff09;\u7684\u4e00\u79cd\u5ea6\u91cf&#xff0c;\u5176\u53d8\u5316\u7531\u52a8\u529b\u5b66&#xff08;\u53cd\u9988\u3001\u76f8\u53d8&#xff09;\u9a71\u52a8\u3002\u8fd9\u4e9b\u90fd\u4e0d\u80fd\u6784\u6210\u72ec\u7acb\u7684\u5143\u8303\u7574\u3002<\/p>\n<h4>6.3 \u5143\u9488\u4e0e\u4e03\u6838\u5fc3\u7684\u6536\u675f<\/h4>\n<p>\u56db\u6839\u5143\u9488\u5c06\u4e5d\u4e2a\u6838\u5fc3\u6982\u5ff5\u4e25\u5bc6\u6536\u675f&#xff0c;\u4f7f\u5176\u4ee5\u4eba\u8111\u53ef\u5185\u5316\u7684\u6781\u7b80\u5f62\u5f0f\u627f\u8f7d\u5b8c\u6574\u7406\u8bba\u529b\u91cf&#xff1a;<\/p>\n<table>\n<tr>\u5143\u9488\u6536\u675f\u7684\u6838\u5fc3\u6982\u5ff5\u5728LLM\u4e2d\u7684\u6620\u5c04<\/tr>\n<tbody>\n<tr>\n<td align=\"left\">\u641c\u7d22\u4e0e\u666f\u89c2<\/td>\n<td align=\"left\">\u76f8\u7a7a\u95f4\u6d41\u5f62 &#043; \u52bf\u80fd\u666f\u89c2 &#043; \u5ea6\u91cf\u5f20\u91cf\u573a<\/td>\n<td align=\"left\">\u4ee4\u724c\u5d4c\u5165\u7a7a\u95f4 &#043; \u6982\u7387\u5206\u5e03 &#043; \u6ce8\u610f\u529b\u6743\u91cd\u77e9\u9635<\/td>\n<\/tr>\n<tr>\n<td align=\"left\">\u5bf9\u79f0\u6027\u4e0e\u7834\u7f3a<\/td>\n<td align=\"left\">\u5438\u5f15\u5b50\u6d41\u57df &#043; \u8fb9\u754c\u4e0e\u81ea\u521b\u751f<\/td>\n<td align=\"left\">\u9ad8\u6982\u7387\u8f93\u51fa\u6a21\u5f0f &#043; \u4e0a\u4e0b\u6587\u7a97\u53e3\u4e0e\u9009\u62e9\u6e17\u900f\u6027<\/td>\n<\/tr>\n<tr>\n<td align=\"left\">\u53cd\u9988\u5faa\u73af<\/td>\n<td align=\"left\">\u53cd\u9988\u5faa\u73af &#043; \u566a\u58f0\u4e0e\u8ba4\u77e5\u6e29\u5ea6<\/td>\n<td align=\"left\">\u6b8b\u5dee\u6d41\u8fed\u4ee3\u66f4\u65b0 &#043; \u91c7\u6837\u6e29\u5ea6\u4e0e\u5404\u5411\u5f02\u6027\u566a\u58f0<\/td>\n<\/tr>\n<tr>\n<td align=\"left\">\u975e\u7ebf\u6027\u4e0e\u76f8\u53d8<\/td>\n<td align=\"left\">\u975e\u7ebf\u6027\u4e0e\u76f8\u53d8 &#043; \u5411\u91cf\u573a\u9a71\u52a8<\/td>\n<td align=\"left\">\u6fc0\u6d3b\u51fd\u6570\u9971\u548c\u533a &#043; \u63d0\u793a\u8bcd\u5f15\u53d1\u7684\u6ce8\u610f\u529b\u91cd\u5b9a\u5411<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3>\u4e03\u3001 \u7efc\u5408\u5b9e\u4f8b&#xff1a;\u56db\u6839\u9488\u7684\u5168\u5411\u7a7f\u900f\u9a8c\u8bc1<\/h3>\n<h4>7.1 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