{"id":2563,"date":"2025-04-28T17:08:26","date_gmt":"2025-04-28T09:08:26","guid":{"rendered":"https:\/\/www.lanxy.ink\/?p=2563"},"modified":"2025-09-11T19:43:05","modified_gmt":"2025-09-11T11:43:05","slug":"%e4%bb%8e-0-%e5%bc%80%e5%a7%8b%e7%9a%84-transformer-%e6%a2%b3%e7%90%86%ef%bc%881%ef%bc%89%e6%9c%ba%e5%99%a8%e5%ad%a6%e4%b9%a0%e5%9f%ba%e7%a1%80","status":"publish","type":"post","link":"https:\/\/www.lanxy.ink\/?p=2563","title":{"rendered":"\u4ece 0 \u5f00\u59cb\u7684 Transformer \u68b3\u7406\uff081\uff09\u673a\u5668\u5b66\u4e60\u57fa\u7840"},"content":{"rendered":"\n

\u524d\u8a00<\/h2>\n\n\n\n

\u4e4b\u524d\u4e00\u76f4\u6709\u6574\u7406\u51e0\u5e74\u6765\u6240\u770b\u6240\u5b66\u7684\u6df1\u5ea6\u5b66\u4e60 \/ \u673a\u5668\u5b66\u4e60\u77e5\u8bc6\u7684\u60f3\u6cd5\uff0c\u4f46\u662f\u603b\u4f1a\u56e0\u4e3a\u5404\u79cd\u5404\u6837\u7684\u539f\u56e0\u803d\u6401\uff0c\u4eca\u5929\u51b3\u5b9a\u5f00\u5751\uff0c\u4ece\u5934\u628a\u8fd9\u4e9b\u77e5\u8bc6\u68b3\u7406\u4e00\u4e0b\uff0c\u5148\u60f3\u5230\u54ea\u91cc\u5199\u54ea\u91cc\uff0c\u6846\u67b6\u5148\u642d\u597d\uff0c\u540e\u9762\u5728\u56de\u987e\u8fc7\u7a0b\u4e2d\u9010\u6e10\u5b8c\u5584\u3002<\/p>\n\n\n\n

latex\u516c\u5f0f\u6ca1\u6709\u6b63\u5e38\u6e32\u67d3\u5219\u5237\u65b0\u4e00\u4e0b<\/span><\/div>\n\n\n\n

\u524d\u9988\u795e\u7ecf\u7f51\u7edc\uff08Forward Neural Network, FNN\uff09<\/h2>\n\n\n\n

FNN \u662f\u6700\u57fa\u7840\u7684\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u3002\u7531\u8f93\u5165\u5c42\u3001\u82e5\u5e72\u9690\u85cf\u5c42\u548c\u8f93\u51fa\u5c42\u7ec4\u6210\u3002\u9690\u85cf\u5c42\u91cc\u6709\u82e5\u5e72\u4e2a\u795e\u7ecf\u5143\uff0c\u5c06\u8f93\u5165\u8fdb\u884c\u201c\u52a0\u5de5\u201d\uff0c\u6700\u7ec8\u5f97\u5230\u8f93\u51fa\u3002<\/p>\n\n\n\n

\u591a\u5c42\u611f\u77e5\u673a\uff08Multilayer Perceptron, MLP\uff09<\/h3>\n\n\n\n

\u6bcf\u4e2a\u795e\u7ecf\u5143\u4e0e\u524d\u540e\u5c42\u7684\u6240\u6709\u795e\u7ecf\u5143\u90fd\u76f8\u8fde\uff08\u5168\u8fde\u63a5\uff09\uff0c\u53ef\u4ee5\u8bf4\u7531\u82e5\u5e72\u4e2a\u5168\u8fde\u63a5\u5c42\u5806\u53e0\u800c\u6210\uff0c\u4f46\u662f\u591a\u5c42\u611f\u77e5\u673a\u7684\u9690\u85cf\u5c42\u91cc\u9762\uff0c\u8fd8\u6709\u6fc0\u6d3b\u51fd\u6570\uff08\u975e\u7ebf\u6027\u53d8\u6362\uff09\u3002<\/p>\n\n\n\n

\n

\u60f3\u8c61\u4f60\u8981\u505a\u4e00\u9053\u591a\u6b65\u9aa4\u7684\u624b\u5de5\u827a\u54c1\uff1a<\/p>\n\n\n\n

    \n
  1. \u62ff\u5230\u539f\u6599<\/strong>\uff08\u8f93\u5165\uff09\uff0c<\/li>\n\n\n\n
  2. \u7ecf\u8fc7\u7b2c\u4e00\u4e2a\u5de5\u5e8f<\/strong>\uff08\u7b2c\u4e00\u5c42\u795e\u7ecf\u5143\uff09\u505a\u7b80\u5355\u52a0\u5de5\uff0c<\/li>\n\n\n\n
  3. \u5f97\u5230\u534a\u6210\u54c1<\/strong>\uff0c\u518d\u4ea4\u7ed9\u7b2c\u4e8c\u4e2a\u5de5\u5e8f\uff08\u7b2c\u4e8c\u5c42\u795e\u7ecf\u5143\uff09\uff0c<\/li>\n\n\n\n
  4. \u5982\u6b64\u4f9d\u6b21\u63a8\u8fdb<\/strong>\uff0c\u76f4\u5230\u6700\u540e\u4e00\u6b65\u62ff\u5230\u6210\u54c1\uff08\u8f93\u51fa\uff09\u3002<\/li>\n<\/ol>\n\n\n\n

    \u5728\u8fd9\u4e2a\u201c\u6d41\u6c34\u7ebf\u201d\u91cc\uff0c\u539f\u6599\u6c38\u8fdc\u53ea\u5f80\u524d\u6d41\uff0c\u4e0d\u4f1a\u56de\u5934\u4fee\u6539\uff1b\u6bcf\u9053\u5de5\u5e8f\u53ea\u5173\u5fc3\u5b83\u6536\u5230\u7684\u534a\u6210\u54c1\u5982\u4f55\u53d8\u5f97\u66f4\u597d\u3002\u524d\u9988\u795e\u7ecf\u7f51\u7edc\u5c31\u662f\u8fd9\u6837\u4e00\u4e2a\u6ca1\u6709\u53cd\u9988\u3001\u4e0d\u5f62\u6210\u5faa\u73af\u7684\u591a\u5c42\u201c\u52a0\u5de5\u201d\u7ed3\u6784\u3002
    \uff08\u7531 GPT-o4 \u7ed9\u51fa\u89e3\u91ca\uff09<\/p>\n<\/blockquote>\n\n\n

    \n
    \"\"<\/div><\/figure>\n<\/div>\n\n\n

    \u6fc0\u6d3b\u51fd\u6570<\/h3>\n\n\n\n

    \u6fc0\u6d3b\u51fd\u6570\u5c31\u76f8\u5f53\u4e8e\u5bf9\u8fd9\u4e00\u5c42\u795e\u7ecf\u5143\u7684\u8f93\u51fa\u505a\u4e00\u6b21\u975e\u7ebf\u6027\u7684\u53d8\u6362\u3002<\/p>\n\n\n\n

    \n

    \u6fc0\u6d3b\u51fd\u6570\u5c31\u50cf\u795e\u7ecf\u5143\u91cc\u7684\u201c\u5f00\u5173\u201d\u6216\u201c\u9600\u95e8\u201d\uff1a\u5f53\u4e00\u4e2a\u795e\u7ecf\u5143\u6536\u5230\u4fe1\u53f7\uff08\u5373\u4e0a\u4e00\u5c42\u7684\u52a0\u6743\u548c\uff09\u65f6\uff0c\u6fc0\u6d3b\u51fd\u6570\u51b3\u5b9a\u5b83\u201c\u653e\u884c\u201d\u591a\u5c11\u4fe1\u53f7\u5230\u4e0b\u4e00\u5c42\u3002\u6ca1\u6709\u6fc0\u6d3b\u51fd\u6570\uff0c\u795e\u7ecf\u7f51\u7edc\u91cc\u6240\u6709\u7684\u5c42\u90fd\u53ea\u662f\u7b80\u5355\u5730\u53e0\u52a0\u548c\u7f29\u653e\u4fe1\u53f7\u2014\u2014\u5c31\u50cf\u628a\u591a\u5757\u900f\u660e\u73bb\u7483\u53e0\u5728\u4e00\u8d77\uff0c\u5149\u7ebf\u4f9d\u7136\u662f\u76f4\u7ebf\uff0c\u7f51\u7edc\u5c31\u53ea\u80fd\u8868\u793a\u7ebf\u6027\u5173\u7cfb\uff1b\u6709\u4e86\u6fc0\u6d3b\u51fd\u6570\uff0c\u4fe1\u53f7\u53ef\u4ee5\u88ab\u201c\u626d\u66f2\u201d\u6216\u201c\u622a\u65ad\u201d\uff0c\u7f51\u7edc\u624d\u5177\u5907\u8868\u8fbe\u5404\u79cd\u590d\u6742\u3001\u975e\u7ebf\u6027\u7684\u80fd\u529b\u3002
    \uff08\u7531 GPT-o4 \u7ed9\u51fa\u89e3\u91ca\uff09<\/p>\n<\/blockquote>\n\n\n\n

    \u6fc0\u6d3b\u51fd\u6570\u7684\u4f5c\u7528\uff1f\u4e5f\u53ef\u4ee5\u8bf4\u4e3a\u4ec0\u4e48\u8981\u5f15\u5165\u975e\u7ebf\u6027\u53d8\u6362\uff1f\u5f15\u5165\u975e\u7ebf\u6027\u53d8\u6362\u4e4b\u540e\u4e3a\u4ec0\u4e48\u6a21\u578b\u7684\u8868\u8fbe\u80fd\u529b\u5c31\u53d8\u5f3a\u4e86\uff1f<\/strong><\/p>\n\n\n\n

    \u5982\u679c\u6ca1\u6709\u6fc0\u6d3b\u51fd\u6570\uff0c\u8f93\u5165\u5c31\u76f8\u5f53\u4e8e\u5728\u548c\u4e00\u5806\u77e9\u9635\u505a\u76f8\u4e58\u8fd0\u7b97\uff0c\u4e58\u6765\u4e58\u53bb\u603b\u662f\u7ebf\u6027\u7684\u53d8\u6362\uff08\u8981\u4e0d\u7136\u4e3a\u5565\u77e9\u9635\u8981\u53eb\u505a\u7ebf\u6027\u4ee3\u6570\uff09\uff0c\u53ef\u4ee5\u60f3\u8c61\u6210\u5bf9\u4e00\u4e2a\u53d8\u91cf x \u53cd\u590d\u5730\u4e58\u4e0a\u4e00\u4e9b\u6570\u5b57\uff08x\u2192ax\uff09\uff0c\u52a0\u518d\u591a\u5c42\u90fd\u548c\u53ea\u7528\u4e00\u5c42\u4e00\u6837\u3002<\/p>\n\n\n\n

    \u8fd8\u6709\u4e00\u4e2a\u539f\u56e0\uff0c\u5c06\u7279\u5f81\u8fdb\u884c\u975e\u7ebf\u6027\u6620\u5c04\u7684\u53e6\u4e00\u4e2a\u7528\u5904\uff0c\u53ef\u4ee5\u8ba9\u8f93\u51fa\u6ee1\u8db3\u4e0b\u6e38\u4efb\u52a1\u7684\u8981\u6c42\uff0c\u5c06\u8f93\u51fa\u7684\u503c\u9650\u5236\u5728\u4e00\u5b9a\u7684\u8303\u56f4\u5185\uff08\u7279\u5f81\u7a7a\u95f4\uff09\uff0c\u4e5f\u80fd\u63d0\u5347\u6a21\u578b\u7684\u6027\u80fd\u3002<\/p>\n\n\n\n

    \u5e38\u89c1\u7684\u6fc0\u6d3b\u51fd\u6570<\/h4>\n\n\n\n
    \u540d\u79f0<\/td>\u8868\u8fbe\u5f0f<\/td>\u7279\u70b9<\/td><\/tr>
    Sigmoid<\/td>$$\\sigma (x) = \\frac {1} {1+e^{-x}}$$<\/td>\u8f93\u51fa\u8303\u56f4 (0,1)\uff0c\u9002\u5408\u4e8c\u5206\u7c7b\uff1b\u6613\u9971\u548c\uff0c\u68af\u5ea6\u6d88\u5931\u95ee\u9898<\/td><\/tr>
    Tanh<\/td>$$\\tanh (x) = \\frac {e^{x}-e^{-x}} {e^{x}+e^{-x}}$$<\/td>\u8f93\u51fa\u8303\u56f4 (\u22121,1)\uff0c\u4e2d\u5fc3\u5bf9\u79f0\uff1b\u540c\u6837\u5b58\u5728\u68af\u5ea6\u6d88\u5931<\/td><\/tr>
    ReLU<\/td>$$\\max (0,x)$$<\/td>\u8ba1\u7b97\u7b80\u5355\uff0c\u7a00\u758f\u6fc0\u6d3b\uff0c\u6536\u655b\u5feb\uff1b\u8d1f\u533a\u95f4\u6052\u4e3a0\uff0c\u53ef\u80fd\u5bfc\u81f4\u795e\u7ecf\u5143\u6b7b\u4ea1<\/td><\/tr>
    LeakyReLU<\/td>$$\\max (\\alpha x,x), \\alpha \\in (0, 1)$$<\/td>\u5bf9\u8d1f\u533a\u95f4\u4fdd\u7559\u5c0f\u659c\u7387\uff0c\u89e3\u51b3 ReLU \u6b7b\u795e\u7ecf\u5143<\/td><\/tr>
    ELU<\/td>\\(x>0\u65f6\uff1ax\\)
    \\(x \\le 0\u65f6\uff1a\\alpha (e^{x}-1)\\)<\/td>    		\u8d1f\u533a\u95f4\u5e73\u6ed1\u3001\u8f93\u51fa\u5747\u503c\u66f4\u63a5\u8fd1\u96f6\uff0c\u6536\u655b\u66f4\u7a33\u5b9a<\/td><\/tr>
    Softmax<\/td>$$\\frac {e^{x_i}} {\\Sigma_{j}e^{x_j}}$$<\/td>\u5c06\u5411\u91cf\u6620\u5c04\u4e3a\u6982\u7387\u5206\u5e03\uff0c\u591a\u5206\u7c7b\u8f93\u51fa\u5e38\u7528<\/td><\/tr>
    GELU<\/td>$$x\\Phi (x) $$<\/td>Transformer \u4e2d\u5e38\u7528\uff0c\u5e73\u6ed1\u53c8\u5177\u5907\u81ea\u6b63\u5219\u5316\u7279\u6027<\/td><\/tr>
    Swish<\/td>$$x\\sigma (x) $$<\/td>\u6bd4 ReLU \u66f4\u5e73\u6ed1\uff0c\u5b9e\u9a8c\u8bc1\u660e\u6027\u80fd\u7565\u4f18<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    \u635f\u5931\u51fd\u6570\uff08Loss Function\uff09<\/h2>\n\n\n\n

    \u6a21\u578b\u5728\u5b8c\u6210\u52a0\u5de5\u540e\u4f1a\u5f97\u5230\u4e00\u4efd\u8f93\u51fa \\( \\hat y \\) \uff0c\u7528\u8be5\u8f93\u51fa\u548c\u771f\u5b9e\u7684\u6807\u7b7e\u8fdb\u884c\u8bef\u5dee\u7684\u8ba1\u7b97\uff0c\u6211\u4eec\u5e0c\u671b\u6a21\u578b\u7684\u8f93\u51fa\u548c\u771f\u5b9e\u6807\u7b7e\u4e4b\u95f4\u8d8a\u63a5\u8fd1\u8d8a\u597d\uff0c\u6240\u4ee5\u795e\u7ecf\u7f51\u7edc\u8bad\u7ec3\u65f6\uff0c\u4f1a\u5c3d\u53ef\u80fd\u8ba9\u635f\u5931\u51fd\u6570\u7684\u503c\u5c0f\uff0c\u4e00\u822c\u6c42\u51fa\u6574\u4e2a\u8bad\u7ec3\u96c6\u7684\u635f\u5931\u518d\u6c42\u671f\u671b\uff0c\u7136\u540e\u6700\u5c0f\u5316\u8fd9\u4e2a\u503c\u3002<\/p>\n\n\n\n

    \n

    \u635f\u5931\u51fd\u6570\u5c31\u50cf\u8003\u8bd5\u4e2d\u7684\u201c\u5206\u6570\u201d\uff0c\u7528\u6765\u8861\u91cf\u6a21\u578b\u7684\u201c\u7b54\u9898\u201d\u7ed3\u679c\uff08\u9884\u6d4b\uff09\u8ddf\u201c\u6b63\u786e\u7b54\u6848\u201d\u4e4b\u95f4\u5dee\u4e86\u591a\u5c11\u3002\u5206\u6570\u8d8a\u4f4e\uff0c\u8bf4\u660e\u6a21\u578b\u8868\u73b0\u8d8a\u597d\uff1b\u5206\u6570\u8d8a\u9ad8\uff0c\u8bf4\u660e\u6a21\u578b\u548c\u4f60\u671f\u671b\u7684\u7ed3\u679c\u5dee\u8ddd\u8d8a\u5927\u3002\u8bad\u7ec3\u795e\u7ecf\u7f51\u7edc\u7684\u8fc7\u7a0b\uff0c\u5c31\u662f\u4e0d\u505c\u5730\u201c\u6279\u6539\u8003\u8bd5\u5377\u201d\u2014\u2014\u6839\u636e\u635f\u5931\u5206\u6570\u8c03\u6574\u6a21\u578b\u53c2\u6570\uff0c\u8ba9\u5b83\u4e0b\u4e00\u6b21\u7b54\u9898\u65f6\u66f4\u63a5\u8fd1\u6ee1\u5206\u3002
    \uff08\u7531 GPT-o4 \u7ed9\u51fa\u89e3\u91ca\uff09<\/p>\n<\/blockquote>\n\n\n\n

    \u5982\u4f55\u6700\u5c0f\u5316\uff1f\u901a\u8fc7\u53cd\u5411\u4f20\u64ad<\/strong>\u8ba1\u7b97\u68af\u5ea6\uff0c\u518d\u7528\u8bf8\u5982\u68af\u5ea6\u4e0b\u964d\u7684\u65b9\u6cd5\u53bb\u4f18\u5316\u53c2\u6570\u3002<\/p>\n\n\n\n

    \u53cd\u5411\u4f20\u64ad\uff08Backpropagation, BP\uff09<\/h2>\n\n\n\n

    \u6839\u636e\u5f97\u5230\u7684\u635f\u5931\u503c\uff0c\u56de\u8fc7\u5934\u53bb\u8ba1\u7b97\u5404\u4e2a\u795e\u7ecf\u5143\u7684\u8bef\u5dee\u3002\u901a\u8fc7\u635f\u5931\u8ba1\u7b97\u6bcf\u5c42\u53c2\u6570\u7684\u68af\u5ea6\uff0c\u518d\u5229\u7528\u68af\u5ea6\u4e0b\u964d\u7b49\u4f18\u5316\u65b9\u6cd5\u66f4\u65b0\u795e\u7ecf\u5143\u7684\u6743\u91cd\u548c\u504f\u7f6e\u53c2\u6570\u3002<\/p>\n\n\n\n

    \u7531\u635f\u5931\u503c \\( \\mathcal{L} \\) \u8ba1\u7b97\u53c2\u6570 \\( \\omega \\) \u7684\u68af\u5ea6\u6d89\u53ca\u5bfc\u6570\u7684\u94fe\u5f0f\u6cd5\u5219\uff0c\u6bd4\u5982\u7b2c \\( z – 1 \\) \u4e2a\u795e\u7ecf\u5143\u7684\u53c2\u6570 \\( \\omega_{z-1} \\)\uff0c\u5148\u5f71\u54cd\u5230\u7b2c \\( z \\) \u4e2a\u8f93\u51fa\u5c42\u795e\u7ecf\u5143\u7684\u8f93\u5165 \\( \\beta \\)\uff0c\u518d\u5f71\u54cd\u5230\u5176\u8f93\u51fa\u503c \\( \\hat y \\) \uff0c\u6700\u540e\u5f71\u54cd\u5230\u635f\u5931\u51fd\u6570\u503c\uff0c\u8fd9\u4e2a\u8fc7\u7a0b\u6709\uff1a<\/p>\n\n\n\n

    $$ \\frac {\\partial \\mathcal {L} } {\\partial \\omega_{z – 1}} = \\frac {\\partial \\mathcal {L} } {\\partial \\hat {y}} \\cdot \\frac {\\partial \\hat {y}} {\\partial \\beta} \\cdot \\frac {\\partial \\beta} {\\partial \\omega_{z}} $$<\/p>\n\n\n\n

    \uff08\u6765\u81ea\u5468\u5fd7\u534e\u7684\u300a\u673a\u5668\u5b66\u4e60\u300b\u4e00\u8457\u3002\u56de\u987e\u8fd9\u90e8\u5206\u65f6\u4ecd\u7136\u82b1\u4e86\u5f88\u591a\u65f6\u95f4\u624d\u7a0d\u5fae\u7406\u89e3\u4e00\u70b9\uff09<\/p>\n\n\n\n

    \u6c42\u5f97\u68af\u5ea6\u540e\uff0c\u6309\u68af\u5ea6\u7684\u53cd\u65b9\u5411\u5728\u7ed9\u5b9a\u7684\u5b66\u4e60\u7387\u4e0b\u5bf9\u53c2\u6570\u8fdb\u884c\u66f4\u65b0\uff1a\\( \\theta \\gets \\theta – \\nabla \\theta \\)\u3002\u800c\u4e0d\u540c\u7684\u66f4\u65b0\u65b9\u5f0f\u53c8\u6d89\u53ca\u5230\u4e0d\u540c\u7684\u4f18\u5316\u7b97\u6cd5<\/strong>\u3002<\/p>\n\n\n\n

    \u4f18\u5316\u5668\uff08Optimizer\uff09<\/h2>\n\n\n\n

    \u968f\u673a\u68af\u5ea6\u4e0b\u964d\uff08Stochastic Gradient Descent, SGD\uff09<\/h3>\n\n\n\n

    \u6700\u57fa\u672c\u7684\u4f18\u5316\u5668\uff0c\u66f4\u65b0\u53c2\u6570\u65f6\u6bcf\u6b21\u53ea\u7528\u4e00\u5c0f\u6279\u6837\u672c\u8ba1\u7b97\u68af\u5ea6\uff1a<\/p>\n\n\n\n

    $$ \\theta \\gets \\theta – \\eta \\nabla_{\\theta} $$<\/p>\n\n\n\n

    \u7ecf\u5178\u800c\u7b80\u5355\uff0c\u4f46\u5bb9\u6613\u5361\u5728\u68af\u5ea6\u8f83\u5c0f\u7684\u70b9\u6216\u5c40\u90e8\u6700\u4f18\u70b9\u3002<\/p>\n\n\n\n

    \u5e26\u52a8\u91cf\u7684 SGD\uff08SGD with Momentum, SGDM\uff09<\/h3>\n\n\n\n

    \u5f53\u524d\u68af\u5ea6\u65b9\u5411\u80fd\u7531\u8fc7\u5f80\u7684\u65b9\u5411\u548c\u5f53\u524d\u68af\u5ea6\u5171\u540c\u51b3\u5b9a\uff1a<\/p>\n\n\n\n

    $$ \\begin{align} \\theta &\\gets \\theta – v, \\\\ v &\\gets \\alpha v + \\eta \\nabla_{\\theta} \\end{align} $$<\/p>\n\n\n\n

    \u76f8\u5f53\u4e8e\u4e3a\u53c2\u6570\u52a0\u4e0a\u4e86\u201c\u60ef\u6027\u201d\uff0c\u5728\u9047\u5230\u4e0b\u5761\u65f6\uff0c\u63d0\u5347\u6536\u655b\u901f\u5ea6\uff1b\u9047\u5230\u4f4e\u8c37\u65f6\uff0c\u6a21\u578b\u4e5f\u4f1a\u5c1d\u8bd5\u518d\u5f80\u524d\u8d70\u4e00\u70b9\uff0c\u5e73\u6ed1\u66f4\u65b0+\u52a0\u901f\u6536\u655b\u3002\uff08\u4e0d\u8fc7\u989d\u5916\u5f15\u5165\u4e86\u52a8\u91cf\u7cfb\u6570\uff0c\u591a\u4e00\u4e2a\u53c2\u6570\u9700\u8981\u8c03\uff09<\/p>\n\n\n\n

    \u81ea\u9002\u5e94\u68af\u5ea6\u4e0b\u964d\uff08AdaGrad \u548c RMSProp\uff09<\/h3>\n\n\n\n

    AdaGrad<\/strong> \u4f18\u5316\u7b97\u6cd5\u5c31\u662f\u5728\u6bcf\u6b21\u4f7f\u7528\u4e00\u4e2a batch size \u7684\u6570\u636e\u8fdb\u884c\u53c2\u6570\u66f4\u65b0\u7684\u65f6\u5019\uff0c\u7b97\u6cd5\u8ba1\u7b97\u6240\u6709\u53c2\u6570\u7684\u68af\u5ea6\uff0c\u90a3\u4e48\u5176\u60f3\u6cd5\u5c31\u662f\u5bf9\u4e8e\u6bcf\u4e2a\u53c2\u6570\uff0c\u521d\u59cb\u5316\u4e00\u4e2a\u53d8\u91cf s \u4e3a 0\uff0c\u7136\u540e\u6bcf\u6b21\u5c06\u8be5\u53c2\u6570\u7684\u68af\u5ea6\u5e73\u65b9\u6c42\u548c\u7d2f\u52a0\u5230\u8fd9\u4e2a\u53d8\u91cf s <\/strong>\u4e0a\uff0c\u7136\u540e\u5728\u66f4\u65b0\u8fd9\u4e2a\u53c2\u6570\u7684\u65f6\u5019\uff0c\u5b66\u4e60\u7387\u5c31\u53d8\u4e3a\uff1a<\/p>\n\n\n\n

    $$ \\frac {\\eta} {\\sqrt{s + \\epsilon}} $$<\/p>\n\n\n\n

    \\(\\epsilon\\) \u662f\u4e00\u4e2a\u6781\u5c0f\u7684\u6b63\u6570\uff0c\u9632\u6b62\u5206\u6bcd\u4e3a 0 \u7528\u7684\u3002\u5982\u679c\u4e00\u4e2a\u53c2\u6570\u7684\u68af\u5ea6\u4e00\u76f4\u90fd\u975e\u5e38\u5927\uff0c\u90a3\u4e48\u5176\u5bf9\u5e94\u7684\u5b66\u4e60\u7387\u5c31\u53d8\u5c0f\u4e00\u70b9\uff0c\u9632\u6b62\u9707\u8361\uff0c\u800c\u4e00\u4e2a\u53c2\u6570\u7684\u68af\u5ea6\u4e00\u76f4\u90fd\u975e\u5e38\u5c0f\uff0c\u90a3\u4e48\u8fd9\u4e2a\u53c2\u6570\u7684\u5b66\u4e60\u7387\u5c31\u53d8\u5927\u4e00\u70b9\uff0c\u4f7f\u5f97\u5176\u80fd\u591f\u66f4\u5feb\u5730\u66f4\u65b0\u3002\uff08\u4f46\u662f\u8fd9\u4e2a\u65f6\u5019\u53c8\u4f1a\u5bfc\u81f4\u5b66\u4e60\u7387\u8870\u51cf\u8fc7\u5feb\uff0c\u8bad\u7ec3\u540e\u671f\u51e0\u4e4e\u505c\u6b62\uff09<\/p>\n\n\n\n

    \uff08\u4e0a\u8ff0\u90e8\u5206\u53c2\u8003\u81ea\uff1a\u3010\u5feb\u901f\u7406\u89e3Adagrad\u3011\u901a\u4fd7\u89e3\u91caAdagrad\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5-CSDN\u535a\u5ba2<\/a>\uff09<\/p>\n\n\n\n

    RMSProp<\/strong> \u5728 AdaGrad \u7684\u57fa\u7840\u4e0a\u53c8\u505a\u4e86\u8fdb\u4e00\u6b65\u4fee\u6539\uff0c\u5f97\u5230\u6700\u65b0\u7684\u68af\u5ea6\u540e\u5e76\u4e0d\u662f\u76f4\u63a5\u5e73\u65b9\u540e\u52a0\u5230\u539f\u6765\u7684 s \u4e0a\uff0c\u800c\u662f\u548c\u539f\u6765\u7684 s \u8fdb\u884c\u52a0\u6743\u6c42\u548c\u3002\u5047\u8bbe\u6700\u65b0\u6c42\u5f97\u7684\u68af\u5ea6\u4e3a \\(g_t\\)\uff0cs \u7684\u66f4\u65b0\u65b9\u5f0f\u5c31\u53d8\u4e3a\uff1a<\/p>\n\n\n\n

    $$ s_{t} = \\beta s_{t-1} + (1-\\beta) g_{t}^{2} $$<\/p>\n\n\n\n

    \u5176\u4ed6\u8fd8\u662f\u548c AdaGrad \u4e00\u81f4\u3002\u8fd9\u6837\u5c31\u80fd\u5728\u81ea\u9002\u5e94\u8c03\u8282\u5b66\u4e60\u7387\u7684\u57fa\u7840\u4e0a\uff0c\u4fdd\u6301\u957f\u671f\u4e0e\u8fd1\u671f\u68af\u5ea6\u4fe1\u606f\u7684\u5e73\u8861\uff0c\u9002\u5e94\u6027\u66f4\u4f73\u3002\u4f46\u5f15\u5165\u65b0\u7684\u8d85\u53c2\u6570 \\(\\beta\\) \u53c8\u8ba9\u8c03\u53c2\u7684\u96be\u5ea6\u4e0a\u5347\u3002\uff08\u9ed8\u8ba4\u53d6 0.9\uff09<\/p>\n\n\n\n

    Adam \u4e0e AdamW<\/h3>\n\n\n\n

    Adam \u7ed3\u5408\u4e86 SGDM \u548c RMSProp \u7684\u4f18\u52bf\uff0c\u65e2\u5f15\u5165\u4e86\u52a8\u91cf\uff0c\u53c8\u5f15\u5165\u4e86\u81ea\u9002\u5e94\u66f4\u65b0\u3002\u9996\u5148\u662f\u5f15\u5165\u4e86\u52a8\u91cf\uff0c\u5176\u68af\u5ea6\u66f4\u65b0\uff08\u4e0d\u662f\u5b66\u4e60\u7387\uff09\u53d8\u6210\u4e86\u8fd9\u6837\uff1a<\/p>\n\n\n\n

    $$ \\theta_{t} \\gets \\theta_{t-1} – \\frac {\\eta} {\\sqrt{\\hat{v}_{t} + \\epsilon}} \\hat{m}_{t} $$<\/p>\n\n\n\n

    \u5176\u4e2d\u7684 \\(\\hat{v}_{t}\\) \u548c \\(\\hat{m}_{t}\\) \u90fd\u4f1a\u968f\u7740\u8bad\u7ec3\u800c\u81ea\u884c\u8c03\u6574\u3002\u5148\u770b\u4e0d\u5e26\u5e3d\u5b50\u7684 \\({v}_{t}\\) \u548c \\({m}_{t}\\) \uff1a<\/p>\n\n\n\n

    $$ \\begin{align} v_t &= \\beta_1 m_{t-1} + (1-\\beta_1) g_{t}^{2}, \\\\ m_t &= \\beta_2 m_{t-1} + (1-\\beta_2) g_t \\end{align} $$<\/p>\n\n\n\n

    \\({v}_{t}\\) \u5bf9 \\(g_{t}\\) \u6c42\u5e73\u65b9\uff0c \\({m}_{t}\\) \u6ca1\u6709\u5bf9\u68af\u5ea6\u6c42\u5e73\u65b9\uff0c \\({v}_{t}\\) \u548c \\({m}_{t}\\) \u90fd\u4f1a\u548c\u4e0a\u4e00\u65f6\u95f4\u6b65\u7684 \\({m}_{t}\\)\uff0c \\({v}_{t}\\) \u505a\u52a0\u6743\u6c42\u548c\u3002<\/p>\n\n\n\n

    \u4f46\u8fd9\u4e24\u4e2a\u503c\u5728\u8bad\u7ec3\u521d\u671f\u4f1a\u5f80 0 \u9760\u8fd1\uff0c\u6240\u4ee5\u53c8\u7ed9 \\({v}_{t}\\) \u548c \\({m}_{t}\\) \u505a\u504f\u5dee\u6821\u6b63\uff1a<\/p>\n\n\n\n

    $$ \\begin{align}\\hat{v}_{t} &= \\frac {v_t} {1-\\beta_{1}^{t}}, \\\\ \\hat{m}_{t} &= \\frac {m_t} {1-\\beta_{2}^{t}}\\end{align} $$<\/p>\n\n\n\n

    \u5206\u6bcd\u7684 \\( \\beta_{*}^{t} \\) \u662f\u5bf9\u8d85\u53c2\u6570\u6c42 t \u6b21\u65b9\u3002\u8fd9\u6837\u5728\u8bad\u7ec3\u521d\u671f\u7684\u5b66\u4e60\u7387\u5c31\u4e0a\u53bb\u4e86\uff0c\u800c\u8bad\u7ec3\u540e\u671f\u5b66\u4e60\u7387\u51cf\u5c11\uff0c\u5141\u8bb8\u6a21\u578b\u505a\u7ec6\u81f4\u7684\u63a2\u7d22\u3002<\/p>\n\n\n\n

    \u8fd9\u91cc\u9700\u8981\u6ce8\u610f\uff0c\\(g_{t}\\) \u662f\u5e26 L2 \u6b63\u5219\u5316\u7684\u68af\u5ea6\uff0c\u4f1a\u5728\u635f\u5931\u51fd\u6570\u91cc\u52a0\u4e0a \\(\\frac{\\lambda}{2}\\left | \\theta \\right |^2\\) \uff0c\u7136\u540e\u5bfc\u81f4 \\(g_{t}\\) \u91cc\u591a\u4e00\u9879 \\( \\lambda\\theta \\)\uff1a<\/p>\n\n\n\n

    $$ g_t = \\nabla_{\\theta} + \\lambda \\theta $$<\/p>\n\n\n\n

    AdamW<\/strong> \u7684\u601d\u8def\u5f88\u7b80\u5355\uff0c\u628a\u52a0\u5728 \\(g_{t}\\) \u4e0a\u7684\u6743\u91cd\u62ff\u51fa\u6765\uff0c\u6539\u4e3a\u76f4\u63a5\u52a0\u5728\u6700\u540e\u7684\u6743\u91cd\u66f4\u65b0\u6b65\u9aa4\u4e0a\uff0c\u8fd9\u65f6\u5019\u7684 \\(g_{t}\\) \u5c31\u662f \\(\\nabla_{\\theta}\\)\uff0c\u7136\u540e\u6c42 \\({v}_{t}\\) \u548c \\({m}_{t}\\)\uff08\u52a0\u4e2a\u6743 \u03b1\uff09\uff0c\u6700\u540e\u518d\u8fdb\u884c\u6743\u91cd\u8870\u51cf\uff1a<\/p>\n\n\n\n

    $$ \\theta_t \\gets \\theta_{t-1} – \\eta \\left( \\alpha \\frac {1} {\\sqrt{\\hat{v}_{t} + \\epsilon}} \\hat{m}_{t} + \\lambda \\theta_{t-1} \\right) $$<\/p>\n\n\n\n

    \u539f\u6765 Adam \u4e2d \u03bb \u4f1a\u540c\u65f6\u5f71\u54cd\u8870\u51cf\u548c\u81ea\u9002\u5e94\u8ba1\u7b97\uff0c\u4f46 AdamW \u53ea\u5f71\u54cd\u6700\u540e\u7684\u8870\u51cf\u6b65\u9aa4\uff0c\u4e0d\u4f1a\u5e72\u6270\u68af\u5ea6\u7684\u81ea\u9002\u5e94\u6bd4\u4f8b\u8ba1\u7b97\u3002\uff08\u770b\u4e86\u534a\u5929 AdamW \u89c9\u5f97\u8499\u8499\u7684\u3002\u3002\u3002\u590d\u6742\u4f46\u597d\u7528\uff09<\/p>\n\n\n

    \n
    \"\"<\/div><\/figure>\n<\/div>\n\n\n

    \u5173\u4e8e\u4e0d\u540c\u4f18\u5316\u5668\u7684\u53ef\u89c6\u5316\u6bd4\u8f83\uff08NAG \u548c Momentum \u7c7b\u4f3c\uff0cAdadelta \u548c RMSProp \u7c7b\u4f3c\uff09\uff1a<\/p>\n\n\n

    \n
    \"\"<\/div><\/figure>\n<\/div>\n\n\n

    \u6b63\u5219\u5316\u6280\u5de7<\/h2>\n\n\n\n

    Dropout<\/h3>\n\n\n\n

    \u7b80\u5355\u5730\u8bf4\u5c31\u662f\u8ba9\u6a21\u578b\u5728\u8bad\u7ec3\u65f6\u968f\u673a\u8ba9\u4e00\u90e8\u5206\u795e\u7ecf\u5143\u201c\u4f11\u606f\u201d\uff0c\u5f3a\u8feb\u6240\u6709\u795e\u7ecf\u5143\u90fd\u638c\u63e1\u5230\u77e5\u8bc6\u3002<\/p>\n\n\n\n

    \u8bf4\u662f\u4f11\u606f\uff0c\u5b9e\u9645\u4e0a\u53ea\u662f\u8fd9\u4e9b\u795e\u7ecf\u5143\u7684\u8f93\u51fa\u88ab\u5c4f\u853d\u6389\u4e86\uff08\u795e\u7ecf\u5143\uff1a\u6211\u4e0a\u65e9\u516b\uff09\u3002<\/p>\n\n\n\n

    \u5bf9\u6bcf\u4e00\u5c42\u7684\u6fc0\u6d3b\u540e\u7684\u8f93\u51fa\u52a0\u4e00\u4e2a\u670d\u4ece\u4f2f\u52aa\u5229\u5206\u5e03\u7684\u968f\u673a\u63a9\u7801\uff0c\u4ee5\u6982\u7387 p \u8ba9\u795e\u7ecf\u5143\u7684\u8f93\u51fa\u4e3a 0\uff0c\u7136\u540e\u5bf9\u5269\u4e0b\u6709\u6548\u7684\u8f93\u51fa\u9664\u4ee5 (1 – p) \u4fdd\u6301\u671f\u671b\u4e00\u81f4\uff08\u4e0d\u7136\u6574\u4f53\u671f\u671b\u4f1a\u53d8\u5c0f\uff09<\/p>\n\n\n

    \n
    \"\"<\/div><\/figure>\n<\/div>\n\n\n

    \u52a0 Dropout \u7684\u76ee\u7684\u5c31\u662f\u9632\u6b62\u8fc7\u62df\u5408\uff0c\u63d0\u5347\u6a21\u578b\u7684\u6cdb\u5316\u80fd\u529b\uff0c\u8ba9\u6a21\u578b\u5b66\u5230\u66f4\u5206\u6563\u7684\u4fe1\u606f\u8868\u793a\uff0c\u4e0d\u4f1a\u628a\u6240\u6709\u91cd\u4efb\u538b\u5728\u5c11\u6570\u795e\u7ecf\u5143\u4e0a\u3002\u9ed8\u8ba4\u7684 Dropout \u7387\u662f 0.3~0.5\uff0c\u8f93\u5165\u5c42\u8981\u66f4\u4f4e\u4e00\u4e9b\uff0c\u8f93\u51fa\u5c42\u4e0d\u8981\u505a Dropout\u3002<\/p>\n\n\n\n

    Dropout\u4e5f\u4e0d\u662f\u4e07\u80fd\u7684\uff0c\u5728 BatchNorm \u7684\u540e\u9762\u4f7f\u7528 Dropout \u9700\u8981\u8c28\u614e\u8003\u8651\uff0c\u5bf9\u8f93\u51fa\u7528\u4e24\u79cd\u6b63\u5219\u5316\u771f\u7684\u4f1a\u63d0\u5347\u6027\u80fd\u5417\uff1f<\/p>\n\n\n\n

    \u5bf9\u4e8e\u5e8f\u5217\u654f\u611f\u578b\u7684\u6a21\u578b\uff08\u5982 Transformer\uff09\u968f\u673a\u5c4f\u853d\u795e\u7ecf\u5143\u4e5f\u6709\u53ef\u80fd\u7834\u574f\u6389\u65f6\u5e8f\u4fe1\u606f<\/strong>\u3002<\/p>\n\n\n\n

    \u800c\u4e14Dropout \u4f1a\u51cf\u6162\u6a21\u578b\u7684\u6536\u655b\u901f\u5ea6\uff0c\u8fd9\u4e2a\u4e5f\u9700\u8981\u8003\u8651\u3002<\/p>\n\n\n\n

    \u6743\u91cd\u8870\u51cf\uff08Weight Decay\uff09<\/h3>\n\n\n\n

    \u5728\u539f\u6765\u7684\u635f\u5931\u57fa\u7840\u4e0a\u589e\u52a0\u4e00\u4e2a L2 \u6b63\u5219\u5316\u9879\uff0c\u53cd\u5411\u4f20\u64ad\u7684\u65f6\u5019\u68af\u5ea6\u540e\u9762\u5c31\u4f1a\u52a0\u4e00\u9879 \\( \\lambda \\theta \\)\uff0c\u6700\u540e\u4f1a\u5f71\u54cd\u53c2\u6570\u7684\u66f4\u65b0\uff1a<\/p>\n\n\n\n

    $$ \\theta \\gets \\theta – \\eta(\\nabla_\\theta + \\lambda \\theta) = (1-\\eta\\lambda)\\theta – \\eta\\nabla_theta $$<\/p>\n\n\n\n

    \u53ef\u4ee5\u770b\u5230\u76f8\u5f53\u4e8e\u5bf9\u539f\u6765\u7684\u53c2\u6570\u6309\u6bd4\u4f8b\u8fdb\u884c\u6536\u7f29\uff0c\u628a\u90a3\u4e9b\u5f88\u5927\u7684\u6743\u91cd\u5f80\u56de\u62c9\u4e00\u4e9b\uff0c\u51cf\u5c11\u6781\u7aef\u6743\u91cd\u5e26\u6765\u7684\u4e0d\u7a33\u5b9a\u68af\u5ea6\uff0c\u4e5f\u662f\u4e00\u79cd\u6b63\u5219\u5316\u7b56\u7565\u3002<\/p>\n\n\n\n

    \u6279\u5f52\u4e00\u5316\uff08BatchNorm\uff09\u548c\u5c42\u5f52\u4e00\u5316\uff08LayerNorm\uff09<\/h3>\n\n\n\n

    \u5f52\u4e00\u5316\uff0c\u5373\u51cf\u5747\u503c\u518d\u9664\u4ee5\u65b9\u5dee\uff0c\u4f46\u662f BatchNorm \u548c LayerNorm \u6c42\u5747\u503c\u548c\u65b9\u5dee\u7684\u65b9\u5f0f\u4e0d\u4e00\u6837\uff0cBatchNorm \u9488\u5bf9\u7684\u662f\u8fd9\u4e00\u6279\u7279\u5f81\u5f20\u91cf\u7684\u6bcf\u4e2a\u901a\u9053<\/strong>\uff0cLayerNorm \u9488\u5bf9\u7684\u662f\u8fd9\u4e00\u6279\u7279\u5f81\u5f20\u91cf\u7684\u6bcf\u4e2a\u7279\u5f81<\/strong>\uff0c\u770b\u4e0b\u9762\u8fd9\u5f20\u56fe\u7247\uff1a<\/p>\n\n\n

    \n
    \"\"<\/div><\/figure>\n<\/div>\n\n\n

    \u516c\u5f0f\u4e0d\u5217\u4e86\uff0cBatchNorm \u548c LayerNorm \u5404\u6709\u5404\u7684\u4f18\u70b9\u548c\u9002\u7528\u8303\u56f4\u3002<\/p>\n\n\n\n

    \u56e0\u4e3a BatchNorm \u662f\u5bf9\u6240\u6709\u7279\u5f81\u7684\u540c\u4e00\u4e2a\u901a\u9053\u505a\u5f52\u4e00\u5316\uff0c\u6240\u4ee5\u4f1a\u62b9\u6389\u4e0d\u540c\u7279\u5f81\u4e4b\u95f4\u7684\u5927\u5c0f\u5173\u7cfb\u3002
    \uff08\u60f3\u8c61\u73ed\u4e0a\u8003\u4e86\u4e94\u6b21\u8bd5\uff0c\u6700\u9ad8\u5206\u5206\u522b\u662f100\uff0c90\uff0c80\uff0c70\uff0c60\uff0c\u7136\u540e\u8001\u5e08\u5206\u522b\u628a\u6bcf\u6b21\u8003\u8bd5\u6240\u6709\u5b66\u751f\u7684\u5206\u6570\u6c42\u5f52\u4e00\u5316\uff0c\u8fd9\u4e2a\u65f6\u5019\u8fd9\u4e94\u6b21\u8003\u8bd5\u7684\u6700\u9ad8\u5206\u4e4b\u95f4\u5e76\u6ca1\u6709\u4ec0\u4e48\u53ef\u6bd4\u6027\uff0c\u90fd\u662f 1 \u4e86\uff09
    \u5982\u679c\u6a21\u578b\u7684\u4efb\u52a1\u5bf9\u7279\u5f81\u95f4\u7684\u5927\u5c0f\u5173\u7cfb\u6ca1\u6709\u7279\u522b\u7684\u4f9d\u8d56\uff08\u6570\u636e\u6ca1\u6709\u65f6\u5e8f\u5173\u8054\uff09\uff0c\u5c31\u53ef\u4ee5\u4f7f\u7528 BatchNorm\uff0c\u6bd4\u5982\u56fe\u50cf\u5206\u7c7b\u3001\u76ee\u6807\u68c0\u6d4b\u3001\u8bed\u4e49\u5206\u5272\u3002\u800c\u4e14 BatchNorm \u7684\u6267\u884c\u6548\u7387\u66f4\u9ad8\uff0c\u9002\u5408\u5927 Batch \u8bad\u7ec3\u3002\u4f46\u662f Batch \u5f88\u5c0f\u7684\u65f6\u5019\u4f1a\u5bfc\u81f4 BatchNorm \u4e0d\u7a33\u5b9a\uff0c\u800c LayerNorm \u5c31\u66f4\u5408\u9002\u3002<\/p>\n\n\n\n

    \u518d\u770b\u5230 LayerNorm\uff0c\u56e0\u4e3a\u5b83\u662f\u5bf9\u6bcf\u6761\u7279\u5f81\u505a\u5f52\u4e00\u5316\uff0c\u6240\u4ee5\u5c31\u4fdd\u7559\u4e86\u4e0d\u540c\u7279\u5f81\u95f4\u7684\u5927\u5c0f\u5173\u7cfb\u3002
    \uff08\u8fd8\u662f\u60f3\u8c61\u73ed\u4e0a\u8003\u4e86\u4e94\u6b21\u8bd5\uff0c\u8fd9\u6b21\u8001\u5e08\u628a\u6bcf\u4e2a\u5b66\u751f\u7684\u4e94\u6b21\u8003\u8bd5\u5206\u6570\u5206\u522b\u8fdb\u884c\u4e86\u5f52\u4e00\u5316\uff0c\u8fd9\u4e2a\u65f6\u5019\u8fd9\u4e94\u6b21\u8003\u8bd5\u7684\u6700\u9ad8\u5206\u5c31\u6709\u533a\u522b\u4e86\uff0c\u56e0\u4e3a\u53ef\u80fd\u88ab\u653e\u5728\u4e0d\u540c\u7684\u5b66\u751f\u8eab\u4e0a\u5e76\u5f52\u4e00\u5316\uff0c\u5e76\u4e0d\u90fd\u662f 1 \u4e86\uff09
    LayerNorm \u9002\u5408\u53d8\u957f\u5e8f\u5217\u548c\u5c0f Batch \u8bad\u7ec3\uff0c\u80fd\u4fdd\u6301\u5e8f\u5217\u5185\u90e8\u4e0d\u540c\u4f4d\u7f6e\u95f4\u7684\u5927\u5c0f\u5173\u7cfb\uff0c\u53ef\u4ee5\u7528\u5728\u9700\u8981\u5904\u7406\u8bed\u97f3\u3001\u6587\u672c\u6d41\u7684\u6a21\u578b\uff0c\u6bd4\u5982\u6ce8\u610f\u529b\u6a21\u578b\u3001Transformer\u3002<\/p>\n\n\n\n

    \u4e0b\u4e00\u7bc7\uff1a\u4ece 0 \u5f00\u59cb\u7684 Transformer \u68b3\u7406\uff082\uff09\u5e8f\u5217\u6a21\u578b\u4e0e\u6ce8\u610f\u529b\u673a\u5236<\/a><\/p>\n\n\n\n

    <\/p>\n","protected":false},"excerpt":{"rendered":"

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