{"id":97649,"date":"2026-08-29T23:00:45","date_gmt":"2026-08-29T15:00:45","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/97649.html"},"modified":"2026-08-29T23:00:45","modified_gmt":"2026-08-29T15:00:45","slug":"%e3%80%90%e6%b7%b1%e5%ba%a6%e5%ad%a6%e4%b9%a0%e3%80%91%e5%a4%9a%e5%b1%82%e6%84%9f%e7%9f%a5%e6%9c%ba%ef%bc%88mlp%ef%bc%89","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/97649.html","title":{"rendered":"\u3010\u6df1\u5ea6\u5b66\u4e60\u3011\u591a\u5c42\u611f\u77e5\u673a\uff08MLP\uff09"},"content":{"rendered":"<h3>1.\u591a\u5c42\u611f\u77e5\u673a<\/h3>\n<p>\u591a\u5c42\u611f\u77e5\u673a\uff08Multi-Layer Perceptron, MLP\uff09 \u662f\u7ed3\u6784\u6700\u7b80\u5355\u7684\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u3002\u5b83\u5728\\&#8221;\u8f93\u5165\u5c42\\&#8221;\u548c\\&#8221;\u8f93\u51fa\u5c42\\&#8221;\u4e4b\u95f4\u52a0\u5165\u4e86\u4e00\u5c42\u6216\u591a\u5c42\u9690\u85cf\u5c42\uff0c\u5e76\u4e14\u5728\u6bcf\u4e00\u5c42\u7684\u7ebf\u6027\u53d8\u6362\u4e4b\u540e\u7d27\u8ddf\u4e00\u4e2a\u975e\u7ebf\u6027\u6fc0\u6d3b\u51fd\u6570\u3002<\/p>\n<p>\u4e3a\u4ec0\u4e48\u8981\u52a0\u9690\u85cf\u5c42\uff1f\u4ee5\u7ecf\u5178\u7684 XOR \u95ee\u9898\u4e3a\u4f8b\uff0c\u5355\u5c42\u611f\u77e5\u673a\uff08\u6ca1\u6709\u9690\u85cf\u5c42\uff09\u662f\u4e00\u4e2a\u7ebf\u6027\u5206\u7c7b\u5668\uff0c\u53ea\u80fd\u753b\u4e00\u6761\u76f4\u7ebf\u628a\u4e24\u7c7b\u6837\u672c\u5206\u5f00\uff1b\u800c XOR \u95ee\u9898\u7684\u51b3\u7b56\u8fb9\u754c\u4e0d\u662f\u7ebf\u6027\u53ef\u5206\u7684\uff0c\u5fc5\u987b\u5f15\u5165\u81f3\u5c11\u4e00\u4e2a\u9690\u85cf\u5c42\u6765\\&#8221;\u63d0\u5347\u7ef4\u5ea6 + \u6fc0\u6d3b\u51fd\u6570\u5f2f\u6298\\&#8221;\u624d\u80fd\u89e3\u51b3\u3002<\/p>\n<p>\u4e00\u4e2a\u5355\u9690\u85cf\u5c42\u7684 MLP \u7684\u7ed3\u6784\u793a\u610f\u5982\u4e0b\uff1a<\/p>\n<p>    [\u8f93\u5165\u5c42]  \u2500\u2500\u25ba  [\u9690\u85cf\u5c42]  \u2500\u2500\u25ba   [\u8f93\u51fa\u5c42]<br \/>\n   \uff08784\u7ef4\uff09     \u7ebf\u6027+ReLU \uff08256\u7ef4\uff09   \u7ebf\u6027+Softmax   \uff0810\u7ef4\uff09<\/p>\n<h4>1.1 \u524d\u5411\u4f20\u64ad\u7684\u6570\u5b66\u5f62\u5f0f<\/h4>\n<p>\u7ed9\u5b9a\u4e00\u4e2a\u6837\u672c\u5411\u91cf <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">x\u2208Rdx \\\\in \\\\mathbb{R}^{d}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5782em;vertical-align: -0.0391em\"><\/span><span class=\"mord mathnormal\">x<\/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 mtight\"><span class=\"mord mathnormal mtight\">d<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff08<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> \u4e3a\u8f93\u5165\u7279\u5f81\u7ef4\u6570\uff09\uff0c\u5355\u9690\u85cf\u5c42 MLP \u7684\u8ba1\u7b97\u8fc7\u7a0b\u53ef\u4ee5\u5f62\u5f0f\u5316\u5199\u4e3a\uff1a<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">h=\u03c3\u2009\u2063(W1Tx+b1),o=W2Th+b2,y^=softmax(o) \\\\boldsymbol{h} = \\\\sigma\\\\!\\\\left( \\\\boldsymbol{W}_{1}^{T}\\\\boldsymbol{x} + \\\\boldsymbol{b}_{1} \\\\right), \\\\quad \\\\boldsymbol{o} = \\\\boldsymbol{W}_{2}^{T}\\\\boldsymbol{h} + \\\\boldsymbol{b}_{2}, \\\\quad \\\\hat{\\\\boldsymbol{y}} = \\\\mathrm{softmax}(\\\\boldsymbol{o}) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\">h<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.8em;vertical-align: -0.65em\"><\/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 size2\">(<\/span><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\" style=\"margin-right: 0.1597em\">W<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9173em\"><span class=\"\" style=\"top: -2.453em;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\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.139em;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: 0.1389em\">T<\/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\"><span class=\"mord\"><span class=\"mord boldsymbol\">x<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\">b<\/span><\/span><\/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-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\">1<\/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 delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size2\">)<\/span><\/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\"><span class=\"mord\"><span class=\"mord boldsymbol\">o<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1643em;vertical-align: -0.247em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\" style=\"margin-right: 0.1597em\">W<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9173em\"><span class=\"\" style=\"top: -2.453em;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\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.139em;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: 0.1389em\">T<\/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\"><span class=\"mord\"><span class=\"mord boldsymbol\">h<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.9023em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\">b<\/span><\/span><\/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-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\">2<\/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: 1em\"><\/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: 0.7079em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\" style=\"margin-right: 0.037em\">y<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.0134em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"accent-body\" style=\"left: -0.25em\"><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\">=<\/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 mathrm\">softmax<\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord boldsymbol\">o<\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d\uff1a<\/p>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c3(\u22c5)\\\\sigma(\\\\cdot)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c3<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">\u22c5<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u662f\u9010\u5143\u7d20\u975e\u7ebf\u6027\u6fc0\u6d3b\u51fd\u6570\uff08ReLU\u3001Sigmoid\u3001Tanh \u7b49\uff09<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">W1\u2208Rd\u00d7h,b1\u2208RhW_1 \\\\in \\\\mathbb{R}^{d \\\\times h}, b_1 \\\\in \\\\mathbb{R}^{h}<\/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\">W<\/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\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0435em;vertical-align: -0.1944em\"><\/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 mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/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\">b<\/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: 0.2778em\"><\/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 mtight\"><span class=\"mord mathnormal mtight\">h<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u2014 \u8f93\u5165\u5c42 \u2192 \u9690\u85cf\u5c42\u7684\u53c2\u6570<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">W2\u2208Rh\u00d7q,b2\u2208RqW_2 \\\\in \\\\mathbb{R}^{h \\\\times q}, b_2 \\\\in \\\\mathbb{R}^{q}<\/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\">W<\/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\">2<\/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\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0435em;vertical-align: -0.1944em\"><\/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 mtight\"><span class=\"mord mathnormal mtight\">h<\/span><span class=\"mbin mtight\">\u00d7<\/span><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/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\">b<\/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\">2<\/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\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6889em\"><\/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: 0.6644em\"><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 mathnormal mtight\" style=\"margin-right: 0.0359em\">q<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u2014 \u9690\u85cf\u5c42 \u2192 \u8f93\u51fa\u5c42\u7684\u53c2\u6570<\/li>\n<li>softmax \u5c06\u8f93\u51fa\u5411\u91cf <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">oo<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">o<\/span><\/span><\/span><\/span><\/span> \u5f52\u4e00\u5316\u4e3a\u4e00\u4e2a\u5408\u6cd5\u7684\u7c7b\u522b\u6982\u7387\u5206\u5e03<\/li>\n<\/ul>\n<p>\u4e3a\u4ec0\u4e48\u4e00\u5b9a\u8981\u975e\u7ebf\u6027\uff1f \u5982\u679c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c3\\\\sigma<\/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\">\u03c3<\/span><\/span><\/span><\/span><\/span> \u53d6\u6052\u7b49\u51fd\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u03c3(z)=z\\\\sigma(z)=z<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">\u03c3<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.044em\">z<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">=<\/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\" style=\"margin-right: 0.044em\">z<\/span><\/span><\/span><\/span><\/span>\uff0c\u90a3\u4e48\u628a\u4e0a\u5f0f\u8054\u7acb\u53ef\u5f97 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">y^=W2TW1Tx+W2Tb1+b2\\\\hat y = W_2^T W_1^T x + W_2^T b_1 + b_2<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/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\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0894em;vertical-align: -0.2481em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8413em\"><span class=\"\" style=\"top: -2.4519em;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\">2<\/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 mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2481em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8413em\"><span class=\"\" style=\"top: -2.4519em;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 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\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2481em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.0894em;vertical-align: -0.2481em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">W<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8413em\"><span class=\"\" style=\"top: -2.4519em;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\">2<\/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 mathnormal mtight\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2481em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/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\">+<\/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\">b<\/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\">2<\/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>\uff0c\u5373\u9000\u5316\u6210\u4e00\u4e2a\u5355\u5c42\u7ebf\u6027\u6a21\u578b\u3002\u8fd9\u5c31\u662f\\&#8221;\u6df1\u5c42\u7f51\u7edc\u82e5\u6ca1\u6709\u6fc0\u6d3b\u51fd\u6570\u7b49\u4ef7\u4e8e\u5355\u5c42\u6a21\u578b\\&#8221;\u7684\u6838\u5fc3\u539f\u56e0\u3002<\/p>\n<hr>\n<h3>2. \u8f93\u5165\u5c42\uff1a\u63a5\u6536\u5916\u90e8\u539f\u59cb\u6570\u636e<\/h3>\n<p>MLP \u7684\u8f93\u5165\u662f\u56fa\u5b9a\u957f\u5ea6\u7684\u4e00\u7ef4\u5411\u91cf\uff0c\u8fd9\u610f\u5473\u7740\u65e0\u8bba\u539f\u59cb\u6570\u636e\u662f\u56fe\u50cf\u3001\u6587\u672c\u8fd8\u662f\u97f3\u9891\uff0c\u90fd\u5fc5\u987b\u5148\u5411\u91cf\u5316\u3002<\/p>\n<p>\u672c\u6587\u4ee5 Fashion-MNIST \u6570\u636e\u96c6\u4e3a\u4f8b\uff0c\u6bcf\u4e2a\u6837\u672c\u7684\u539f\u59cb\u5f62\u6001\u662f\u4e00\u5f20 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">28\u00d72828 \\\\times 28<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">28<\/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\">28<\/span><\/span><\/span><\/span><\/span> \u7684\u7070\u5ea6\u56fe\u3002\u5728\u9001\u5165 MLP \u4e4b\u524d\uff0c\u9700\u8981\u901a\u8fc7 reshape \u628a\u5b83\u5c55\u5e73\u6210\u957f\u5ea6\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">784784<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">784<\/span><\/span><\/span><\/span><\/span> \u7684\u5411\u91cf\uff1a<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">(1,&nbsp;28,&nbsp;28)\u23df\u539f\u59cb\u5f20\u91cf\u2192reshape(784,)\u23dfMLP&nbsp;\u8f93\u5165 \\\\underbrace{\\\\text{(1, 28, 28)}}_{\\\\text{\u539f\u59cb\u5f20\u91cf}} \\\\xrightarrow{\\\\text{reshape}} \\\\underbrace{\\\\text{(784,)}}_{\\\\text{MLP \u8f93\u5165}} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 2.6844em;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\">\u539f\u59cb\u5f20\u91cf<\/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\"> <\/p>\n<p>                  <\/span><span class=\"brace-center\" style=\"height: 0.548em\"> <\/p>\n<p>                  <\/span><span class=\"brace-right\" style=\"height: 0.548em\"> <\/p>\n<p>                  <\/span><\/span><\/span><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">(1,&nbsp;28,&nbsp;28)<\/span><\/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: 0.2778em\"><\/span><span class=\"mrel x-arrow\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.1081em\"><span class=\"\" style=\"top: -3.322em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight x-arrow-pad\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">reshape<\/span><\/span><\/span><\/span><\/span><span class=\"svg-align\" style=\"top: -2.689em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"hide-tail\" style=\"height: 0.522em;min-width: 1.469em\"> <\/p>\n<p>            <\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.011em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/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><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>1.\u591a\u5c42\u611f\u77e5\u673a<br \/>\n\u591a\u5c42\u611f\u77e5\u673a\uff08Multi-Layer Perceptron, MLP\uff09 \u662f\u7ed3\u6784\u6700\u7b80\u5355\u7684\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u3002\u5b83\u5728\\&#8221;\u8f93\u5165\u5c42\\&#8221;\u548c\\&#8221;\u8f93\u51fa\u5c42\\&#8221;\u4e4b\u95f4\u52a0\u5165\u4e86\u4e00\u5c42\u6216\u591a\u5c42\u9690\u85cf\u5c42\uff0c\u5e76\u4e14\u5728\u6bcf\u4e00\u5c42\u7684\u7ebf\u6027\u53d8\u6362\u4e4b\u540e\u7d27\u8ddf\u4e00\u4e2a\u975e\u7ebf\u6027\u6fc0\u6d3b\u51fd\u6570\u3002<br \/>\n\u4e3a\u4ec0\u4e48\u8981\u52a0\u9690\u85cf\u5c42\uff1f\u4ee5\u7ecf\u5178\u7684 XOR \u95ee\u9898\u4e3a\u4f8b\uff0c\u5355\u5c42\u611f\u77e5\u673a\uff08\u6ca1\u6709\u9690\u85cf\u5c42\uff09\u662f\u4e00\u4e2a\u7ebf\u6027\u5206\u7c7b\u5668\uff0c\u53ea\u80fd\u753b\u4e00\u6761\u76f4\u7ebf\u628a\u4e24\u7c7b\u6837\u672c\u5206\u5f00\uff1b\u800c XOR \u95ee\u9898\u7684\u51b3\u7b56\u8fb9\u754c\u4e0d\u662f\u7ebf\u6027\u53ef\u5206\u7684\uff0c\u5fc5\u987b\u5f15\u5165\u81f3\u5c11\u4e00\u4e2a\u9690\u85cf\u5c42\u6765\\&#8221;\u63d0\u5347\u7ef4\u5ea6 + \u6fc0\u6d3b\u51fd\u6570\u5f2f\u6298\\&#8221;\u624d\u80fd\u89e3\u51b3\u3002<br \/>\n\u4e00\u4e2a\u5355\u9690\u85cf\u5c42\u7684 MLP \u7684\u7ed3<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[50,86],"topic":[],"class_list":["post-97649","post","type-post","status-publish","format-standard","hentry","category-server","tag-50","tag-86"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u3010\u6df1\u5ea6\u5b66\u4e60\u3011\u591a\u5c42\u611f\u77e5\u673a\uff08MLP\uff09 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/97649.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u3010\u6df1\u5ea6\u5b66\u4e60\u3011\u591a\u5c42\u611f\u77e5\u673a\uff08MLP\uff09 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"1.\u591a\u5c42\u611f\u77e5\u673a \u591a\u5c42\u611f\u77e5\u673a\uff08Multi-Layer Perceptron, MLP\uff09 \u662f\u7ed3\u6784\u6700\u7b80\u5355\u7684\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u3002\u5b83\u5728&quot;\u8f93\u5165\u5c42&quot;\u548c&quot;\u8f93\u51fa\u5c42&quot;\u4e4b\u95f4\u52a0\u5165\u4e86\u4e00\u5c42\u6216\u591a\u5c42\u9690\u85cf\u5c42\uff0c\u5e76\u4e14\u5728\u6bcf\u4e00\u5c42\u7684\u7ebf\u6027\u53d8\u6362\u4e4b\u540e\u7d27\u8ddf\u4e00\u4e2a\u975e\u7ebf\u6027\u6fc0\u6d3b\u51fd\u6570\u3002 \u4e3a\u4ec0\u4e48\u8981\u52a0\u9690\u85cf\u5c42\uff1f\u4ee5\u7ecf\u5178\u7684 XOR 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