{"id":89523,"date":"2026-08-03T07:48:51","date_gmt":"2026-08-02T23:48:51","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/89523.html"},"modified":"2026-08-03T07:48:51","modified_gmt":"2026-08-02T23:48:51","slug":"ai%e5%a4%a7%e6%a8%a1%e5%9e%8b%e4%b8%8e%e6%95%b0%e5%ad%a6%e7%ac%ac16%e8%af%be%ef%bc%9a%e5%ae%9a%e7%a7%af%e5%88%86%e5%87%a0%e4%bd%95%e5%ba%94%e7%94%a8%e3%80%81%e9%9d%a2%e7%a7%af%e4%bd%93%e7%a7%af","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/89523.html","title":{"rendered":"AI\u5927\u6a21\u578b\u4e0e\u6570\u5b66\u7b2c16\u8bfe\uff1a\u5b9a\u79ef\u5206\u51e0\u4f55\u5e94\u7528\u3001\u9762\u79ef\u4f53\u79ef\u8ba1\u7b97\uff08\u9ad8\u7ef4\u635f\u5931\u7a7a\u95f4\u3001\u6a21\u578b\u51e0\u4f55\u5ea6\u91cf\u5e95\u5c42\uff09"},"content":{"rendered":"

\u7b2c15\u8bfe\u6211\u4eec\u638c\u63e1\u4e86\u5b9a\u79ef\u5206\u6570\u503c\u8ba1\u7b97\u3001\u725b\u987f-\u83b1\u5e03\u5c3c\u8328\u516c\u5f0f\u3002
\n\u672c\u8bfe\u7528\u79ef\u5206\u7b97\u300c\u9762\u79ef\u3001\u65cb\u8f6c\u4f53\u4f53\u79ef\u300d\u3002
\n\u4e3a\u4ec0\u4e48AI\u4eba\u5fc5\u987b\u5b66\u9762\u79ef\u3001\u4f53\u79ef？
\n\u666e\u901a\u4eba\u5b66\u79ef\u5206：\u7b97\u56fe\u5f62\u9762\u79ef\u3002
\nAI\u5b66\u79ef\u5206：\u770b\u61c2\u9ad8\u7ef4\u635f\u5931\u66f2\u9762\u7684\u51e0\u4f55\u5f62\u6001\u3002<\/p>\n

  • \u9762\u79ef = \u8bef\u5dee\u7d2f\u79ef\u603b\u91cf（\u4e8c\u7ef4\u635f\u5931\u66f2\u7ebf\u8bef\u5dee）<\/li>\n
  • \u4f53\u79ef = \u9ad8\u7ef4\u53c2\u6570\u7a7a\u95f4\u8bef\u5dee\u5bb9\u79ef<\/li>\n
  • \u6a21\u578b\u8fc7\u62df\u5408\/\u6b20\u62df\u5408\u3001\u66f2\u9762\u5e73\u5766\/\u9661\u5ced\u3001\u6cdb\u5316\u80fd\u529b，\u5168\u90e8\u662f\u51e0\u4f55\u5f62\u6001\u95ee\u9898<\/li>\n
  • \u540e\u7eed：\u9ad8\u7ef4\u6d41\u5f62\u3001\u5411\u91cf\u7a7a\u95f4\u5bb9\u79ef\u3001\u96c5\u53ef\u6bd4\u884c\u5217\u5f0f\u4f53\u79ef\u53d8\u6362，\u672c\u8bfe\u662f\u524d\u7f6e\u57fa\u7840
    \n\u672c\u8bfe\u5b66\u4e60\u95ed\u73af
    \n\u6570\u503c\u79ef\u5206 \u2192 \u51e0\u4f55\u79ef\u5206 \u2192 AI\u9ad8\u7ef4\u7a7a\u95f4\u51e0\u4f55\u8ba4\u77e5
    \n\u5728\u5f00\u7bc7\u524d，\u4e3a\u4e86\u66f4\u597d\u4fbf\u4e8e\u5927\u5bb6\u7406\u89e3，\u5b9a\u79ef\u5206\u5728\u5927\u6a21\u578b\u8bad\u7ec3\u4e2d\u7684\u4f5c\u7528，\u6211\u5148\u7528\u5927\u767d\u8bdd\u8bb2\u900f\u539f\u7406，\u770b\u660e\u767d\u539f\u7406，\u518d\u8fdb\u884c\u8ba1\u7b97\u8bad\u7ec3\u3002<\/li>\n

    \u5148\u8bb0\u4f4f\u6838\u5fc3：\u5b9a\u79ef\u5206\u672c\u8d28 = \u7d2f\u79ef\u6c42\u548c，\u51e0\u4f55\u5e94\u7528\u53ea\u662f\u5b9a\u79ef\u5206\u6700\u76f4\u89c2\u7684\u53ef\u89c6\u5316\u4f8b\u5b50\u3002<\/p>\n

    \u4e00\u3001\u5b9a\u79ef\u5206\u51e0\u4f55\u5e94\u7528\u672c\u8eab\u662f\u4ec0\u4e48<\/p>\n

  • \u66f2\u7ebf\u56f4\u6210\u9762\u79ef；
    \n\u200b2. \u5e73\u9762\u56fe\u5f62\u65cb\u8f6c\u5f97\u5230\u65cb\u8f6c\u4f53\u4f53\u79ef；
    \n\u200b3. \u66f2\u7ebf\u5f27\u957f\u3001\u66f2\u9762\u9762\u79ef\u3002
    \n\u5e95\u5c42\u903b\u8f91：
    \n\u628a\u8fde\u7eed\u53d8\u5316\u7684\u56fe\u5f62\u5207\u6210\u65e0\u7a77\u591a\u5fae\u5c0f\u788e\u7247（\u5fae\u5206），\u518d\u5168\u90e8\u7d2f\u52a0（\u79ef\u5206），\u7b97\u51fa\u6574\u4f53\u603b\u91cf\u3002<\/li>\n

    \u4e8c\u3001\u6620\u5c04\u5230AI\u5927\u6a21\u578b\u8bad\u7ec3，\u5b83\u5728\u5e72\u4ec0\u4e48？<\/p>\n

  • \n

    \u635f\u5931\u671f\u671b（\u6700\u6838\u5fc3\u7528\u9014）
    \n\u6a21\u578b\u771f\u6b63\u4f18\u5316\u76ee\u6807\u4e0d\u662f\u5355\u6761\u6837\u672c\u635f\u5931，\u800c\u662f\u671f\u671b\u635f\u5931：
    \n\\\\mathcal{L}=\\\\mathbb{E}{x\\\\sim p{data}}[L(x)]
    \n\u8fde\u7eed\u5206\u5e03\u4e0b，\u6570\u5b66\u5b9a\u4e49\u5c31\u662f\u5b9a\u79ef\u5206
    \n\\\\mathbb{E}[L]=\\\\int p(x)\\\\cdot L(x)dx
    \n\u51e0\u4f55\u89c6\u89d2\u7406\u89e3：
    \n\u6a2a\u8f74：\u6240\u6709\u53ef\u80fd\u8f93\u5165\u6570\u636ex；\u7eb5\u8f74：\u6982\u7387\u5bc6\u5ea6\u00d7\u635f\u5931\u3002
    \n\u5b9a\u79ef\u5206 = \u8fd9\u6761\u66f2\u7ebf\u4e0b\u65b9\u7684\u603b\u9762\u79ef，\u4e5f\u5c31\u662f\u5168\u5c40\u5e73\u5747\u635f\u5931\u3002
    \n\u8bad\u7ec3\u76ee\u6807：\u4e0d\u65ad\u8c03\u6574\u795e\u7ecf\u7f51\u7edc\u53c2\u6570，\u538b\u7f29\u8fd9\u5757\u201c\u603b\u9762\u79ef\u201d\u3002<\/p>\n<\/li>\n

  • \n

    \u548c\u91c7\u6837\u7684\u5173\u7cfb（\u91cd\u70b9！AI\u4e0d\u4f1a\u76f4\u63a5\u7b97\u79ef\u5206）
    \n\u7edd\u5927\u591a\u6570\u771f\u5b9e\u6570\u636e\u5206\u5e03\u65e0\u6cd5\u5199\u51fa\u516c\u5f0f，\u6ca1\u529e\u6cd5\u76f4\u63a5\u8ba1\u7b97\u5b9a\u79ef\u5206\u3002
    \n\u6240\u4ee5\u5927\u6a21\u578b\u4f7f\u7528\u8499\u7279\u5361\u6d1b\u91c7\u6837：\u62ff\u4e00\u6279\u6837\u672c（batch）\u7684\u5747\u503c，\u8fd1\u4f3c\u4ee3\u66ff\u79ef\u5206\u7ed3\u679c\u3002
    \n\u901a\u4fd7\u6bd4\u55bb：
    \n\u5b9a\u79ef\u5206=\u6d4b\u7b97\u6574\u7247\u6e56\u6cca\u603b\u9762\u79ef；
    \n\u91c7\u6837=\u968f\u673a\u4e22\u82e5\u5e72\u6d6e\u6807，\u7528\u5c40\u90e8\u70b9\u4f4d\u4f30\u7b97\u6574\u7247\u6e56\u5927\u5c0f\u3002<\/p>\n<\/li>\n

  • \n

    \u5ef6\u4f38\u51e0\u4e2a\u573a\u666f<\/p>\n<\/li>\n

  • \n

    \u6982\u7387\u3001\u71b5\u3001KL\u6563\u5ea6
    \n\u8fde\u7eed\u968f\u673a\u53d8\u91cf\u7684\u71b5\u3001\u5206\u5e03\u4e4b\u95f4KL\u6563\u5ea6，\u5168\u90e8\u4f9d\u9760\u5b9a\u79ef\u5206\u5b9a\u4e49；\u8861\u91cf\u6a21\u578b\u751f\u6210\u5206\u5e03\u548c\u771f\u5b9e\u6570\u636e\u5206\u5e03\u5dee\u8ddd\u3002<\/p>\n<\/li>\n

  • \n

    \u751f\u6210\u6a21\u578b（\u6269\u6563\u6a21\u578b）
    \n\u6269\u6563\u8fc7\u7a0b\u662f\u8fde\u7eed\u65f6\u95f4\u5fae\u5206\u65b9\u7a0b，\u91c7\u6837\u3001\u5bf9\u6570\u4f3c\u7136\u8ba1\u7b97，\u5927\u91cf\u7528\u5230\u79ef\u5206\u601d\u60f3；\u200b<\/p>\n<\/li>\n

  • \n

    \u5f3a\u5316\u5b66\u4e60\u8fde\u7eed\u52a8\u4f5c\u7a7a\u95f4
    \n\u8fde\u7eed\u52a8\u4f5c\u56de\u62a5\u671f\u671b，\u4f9d\u9760\u79ef\u5206\u63cf\u8ff0\u3002<\/p>\n<\/li>\n

    \u5fae\u5206：\u622a\u53d6\u4e00\u77ac\u95f4\u3001\u6781\u5c0f\u7247\u6bb5\u7684\u53d8\u5316；
    \n\u5b9a\u79ef\u5206：\u628a\u65e0\u7a77\u591a\u6781\u5c0f\u7247\u6bb5\u7d2f\u79ef\u6c47\u603b\u5f97\u5230\u6574\u4f53\u7ed3\u679c\u3002<\/p>\n

    \u5927\u6a21\u578b\u8bad\u7ec3：
    \n\u6570\u636e\u662f\u8fde\u7eed\u7a7a\u95f4\u3001\u8bef\u5dee\u6301\u7eed\u53d8\u5316；
    \n\u6211\u4eec\u60f3\u8981\u7684\u4e0d\u662f\u5355\u4e00\u4e2a\u6837\u672c\u7684\u8bef\u5dee，\u800c\u662f\u5168\u90e8\u8f93\u5165\u8303\u56f4\u4e0a\u6574\u4f53\u8bef\u5dee\u603b\u548c\u2014\u2014\u8fd9\u5c31\u662f\u5b9a\u79ef\u5206\u8981\u89e3\u51b3\u7684\u95ee\u9898\u3002<\/p>\n

    \u5b9a\u79ef\u5206\u51e0\u4f55\u5e94\u7528\u6559\u4f1a\u6211\u4eec：\u5982\u4f55\u628a\u65e0\u7a77\u591a\u5fae\u5c0f\u7247\u6bb5\u7d2f\u52a0\u5f97\u5230\u6574\u4f53\u603b\u91cf\u3002\u653e\u5230AI\u8bad\u7ec3\u4e2d，\u5b83\u5c31\u662f\u7528\u6765\u8ba1\u7b97\u5168\u5c40\u671f\u671b\u635f\u5931\u7684\u6570\u5b66\u539f\u578b；\u53d7\u9650\u4e8e\u7b97\u529b，\u6211\u4eec\u65e0\u6cd5\u7cbe\u786e\u6c42\u89e3\u79ef\u5206，\u53ea\u80fd\u4f9d\u9760\u6279\u91cf\u91c7\u6837\u505a\u8fd1\u4f3c\u4f30\u7b97\u3002<\/p>\n

    \u8865\u5145\u533a\u5206\u5bb9\u6613\u6df7\u6dc6\u7684\u70b9
    \n\u5927\u6a21\u578b\u524d\u5411\u4f20\u64ad\u3001\u53cd\u5411\u6c42\u5bfc\u4e3b\u8981\u4f9d\u9760\u5bfc\u6570（\u5fae\u5206）；
    \n\u5b9a\u79ef\u5206\u8d1f\u8d23\u5b9a\u4e49\u201c\u6211\u4eec\u6700\u7ec8\u8981\u4f18\u5316\u7684\u76ee\u6807\u51fd\u6570（\u671f\u671b\u635f\u5931）\u201d\u3002
    \n\u5fae\u5206\u8d1f\u8d23\u627e\u4e0b\u5761\u65b9\u5411，\u79ef\u5206\u5b9a\u4e49\u7ec8\u70b9\u76ee\u6807\u3002<\/p>\n

    \u6b63\u5f0f\u8ba1\u7b97\u8bad\u7ec3\u5f00\u59cb（\u5148\u7406\u89e3\u4ee5\u4e0a，\u5728\u770b\u4e0b\u6587）
    \n\u4e00\u3001\u5b9a\u79ef\u5206\u6c42\u5e73\u9762\u9762\u79ef（\u4e8c\u7ef4\u6838\u5fc3\u3001\u635f\u5931\u66f2\u7ebf\u5e95\u5c42）
    \n\u6838\u5fc3\u539f\u7406
    \n\u8fde\u7eed\u51fd\u6570\u5728\u533a\u95f4 [a,b] \u4e0ex\u8f74\u56f4\u6210\u7684\u9762\u79ef：
    \nS = \\\\int_{a}^{b} |f(x)| dx
    \n\u89c4\u5219<\/p>\n

  • f(x)\\\\ge0：\u9762\u79ef\u76f4\u63a5\u79ef\u5206 \\\\int_a^b f(x)dx<\/li>\n
  • f(x)\\\\le0：\u9762\u79ef\u53d6\u7edd\u5bf9\u503c -\\\\int_a^b f(x)dx<\/li>\n
  • \u6b63\u8d1f\u4ea4\u66ff：\u5206\u6bb5\u79ef\u5206\u53d6\u7edd\u5bf9\u503c\u76f8\u52a0
    \nAI\u6df1\u5ea6\u91ca\u4e49（\u5173\u952e）
    \n\u4e8c\u7ef4\u51fd\u6570\u9762\u79ef = \u6a21\u578b\u5728\u53c2\u6570\u533a\u95f4\u5185\u7684\u603b\u8bef\u5dee\u7d2f\u79ef
    \n\u66f2\u7ebf\u9ad8：\u77ac\u65f6\u8bef\u5dee\u5927
    \n\u66f2\u7ebf\u4f4e：\u77ac\u65f6\u8bef\u5dee\u5c0f
    \n\u79ef\u5206\u9762\u79ef\u5927：\u6574\u4f53\u8bef\u5dee\u5927\u3001\u6a21\u578b\u5dee
    \n\u79ef\u5206\u9762\u79ef\u5c0f：\u6574\u4f53\u8bef\u5dee\u5c0f\u3001\u6a21\u578b\u6536\u655b\u597d
    \n\u8bad\u7ec3\u5168\u7a0b\u5c31\u662f：\u4e0d\u65ad\u538b\u7f29\u635f\u5931\u51fd\u6570\u7684\u79ef\u5206\u9762\u79ef\u3002
    \n\u7ecf\u5178\u4f8b\u98981：\u5355\u533a\u95f4\u6b63\u9762\u79ef
    \n\u6c42 y=x^2 \u5728 [0,2] \u4e0ex\u8f74\u56f4\u6210\u9762\u79ef
    \n\u89e3：
    \nS=\\\\int_0^2 x^2 dx
    \n=\\\\left.\\\\frac{1}{3}x3\\\\right|_0<\/sup>2
    \n=\\\\frac{8}{3} \\\\approx 2.67
    \n\u7406\u89e3：\u8be5\u53c2\u6570\u533a\u95f4\u5185，\u6a21\u578b\u6574\u4f53\u8bef\u5dee\u7d2f\u79ef\u91cf\u4e3a \\\\frac{8}{3}
    \n\u7ecf\u5178\u4f8b\u98982：\u6b63\u8d1f\u4ea4\u66ff\u9762\u79ef（AI\u9707\u8361\u8bad\u7ec3\u573a\u666f）
    \n\u6c42 y=\\\\sin x \u5728 [0,2\\\\pi] \u4e0ex\u8f74\u56f4\u6210\u771f\u5b9e\u51e0\u4f55\u9762\u79ef
    \n\u6ce8\u610f：
    \n\u76f4\u63a5\u5b9a\u79ef\u5206 = 0（\u6b63\u8d1f\u62b5\u6d88）
    \n\u771f\u5b9e\u9762\u79ef\u5fc5\u987b\u5206\u6bb5
    \nS = \\\\int_0^\\\\pi \\\\sin x dx + \\\\int_\\\\pi^{2\\\\pi} -\\\\sin x dx
    \n\u8ba1\u7b97：
    \n\\\\int_0^\\\\pi \\\\sin x dx = -\\\\cos\\\\pi+\\\\cos0=2
    \n\\\\int_\\\\pi^{2\\\\pi} -\\\\sin x dx = 2
    \n\u603b\u9762\u79ef：S=4
    \nAI\u91cd\u78c5\u5bf9\u5e94
    \n\u79ef\u5206\u503c\u4e3a0 \u2260 \u65e0\u8bef\u5dee
    \n\u5bf9\u5e94\u6a21\u578b：
    \n\u6b63\u8d1f\u68af\u5ea6\u9707\u8361\u3001\u6765\u56de\u66f4\u65b0\u3001\u53c2\u6570\u539f\u5730\u6253\u8f6c
    \n\u635f\u5931\u6570\u503c\u770b\u4f3c\u5e73\u7a33，\u5b9e\u9645\u8bad\u7ec3\u5267\u70c8\u9707\u8361
    \n\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48：\u4e0d\u80fd\u53ea\u770bloss\u6570\u503c，\u8981\u770b\u51e0\u4f55\u9762\u79ef\u6ce2\u52a8<\/li>\n

    \u4e8c\u3001\u4e24\u51fd\u6570\u4e4b\u95f4\u56f4\u6210\u7684\u9762\u79ef（AI\u6b8b\u5dee\u3001\u5dee\u503c\u8bef\u5dee\u6838\u5fc3）
    \n\u516c\u5f0f
    \n\u4e0a\u51fd\u6570 – \u4e0b\u51fd\u6570
    \nS=\\\\int_a^b \\\\big[ f(x)-g(x) \\\\big] dx,\\\\quad f(x)\\\\ge g(x)
    \nAI\u7ec8\u6781\u89e3\u91ca
    \nf(x)：\u771f\u5b9e\u6807\u7b7e\u5206\u5e03
    \ng(x)：\u6a21\u578b\u9884\u6d4b\u5206\u5e03
    \n\u4e24\u66f2\u7ebf\u56f4\u6210\u9762\u79ef = \u6a21\u578b\u9884\u6d4b\u4e0e\u771f\u5b9e\u6570\u636e\u7684\u6574\u4f53\u504f\u5dee\u603b\u91cf
    \n\u6b8b\u5dee\u7f51\u7edcResNet\u5e95\u5c42\u51e0\u4f55\u903b\u8f91
    \n\u6b8b\u5dee = \u771f\u5b9e\u503c – \u9884\u6d4b\u503c
    \n\u6b8b\u5dee\u79ef\u5206\u9762\u79ef\u8d8a\u5c0f \u2192 \u62df\u5408\u8d8a\u7cbe\u51c6\u3001\u6cdb\u5316\u8d8a\u5f3a
    \n\u5b9e\u64cd\u4f8b\u9898
    \n\u6c42 y=x \u4e0e y=x^2 \u5728 [0,1] \u56f4\u6210\u9762\u79ef<\/p>\n

  • \u4e0a\u4f4d\u51fd\u6570 y=x，\u4e0b\u4f4d\u51fd\u6570 y=x^2<\/li>\n
  • S=\\\\int_0^1 (x-x^2)dx<\/li>\n
  • =\\\\left(\\\\frac12x2-\\\\frac13x<\/sup>3\\\\right)\\\\bigg|_0^1<\/li>\n
  • =\\\\frac12-\\\\frac13=\\\\frac16
    \nAI\u7406\u89e3：
    \n\u8be5\u6a21\u578b\u5728\u5f53\u524d\u53c2\u6570\u57df\u5185，\u6574\u4f53\u9884\u6d4b\u504f\u5dee\u4ec5 1\/6，\u62df\u5408\u6548\u679c\u4f18\u79c0\u3002<\/li>\n

    \u4e09\u3001\u5b9a\u79ef\u5206\u6c42\u65cb\u8f6c\u4f53\u4f53\u79ef（\u4e09\u7ef4\u51e0\u4f55\u4f53\u3001AI\u9ad8\u7ef4\u7a7a\u95f4\u96cf\u5f62）
    \n\u6838\u5fc3\u8ba4\u77e5\u5347\u7ea7
    \n\u9762\u79ef\u662f\u4e8c\u7ef4，\u4f53\u79ef\u662f\u4e09\u7ef4\u7a7a\u95f4\u7d2f\u79ef
    \n\u5927\u6a21\u578b\u662f\u51e0\u767e\u4e0a\u5343\u4e07\u7ef4\u7a7a\u95f4，\u672c\u8d28\u662f：\u8d85\u9ad8\u7ef4\u51e0\u4f55\u4f53
    \n\u5148\u5b66\u4f1a\u4e09\u7ef4\u4f53\u79ef，\u624d\u80fd\u770b\u61c2\u9ad8\u7ef4\u7a7a\u95f4\u5f62\u53d8\u3002
    \n\u7ed5X\u8f74\u65cb\u8f6c\u4f53\u79ef\u516c\u5f0f（\u5706\u76d8\u6cd5）
    \n\u51fd\u6570 y=f(x) \u5728 [a,b] \u7ed5x\u8f74\u65cb\u8f6c\u6210\u7acb\u4f53：
    \nV=\\\\pi \\\\int_a^b f^2(x) dx<\/p>\n

    \u6bcf\u4e00\u4e2a\u6781\u5c0f\u7ad6\u6761，\u65cb\u8f6c\u6210\u4e00\u4e2a\u8584\u5706\u76d8
    \n\u5706\u76d8\u9762\u79ef \\\\pi r^2，\u539a\u5ea6 dx
    \n\u79ef\u5206 = \u65e0\u6570\u8584\u5706\u76d8\u53e0\u52a0\u6210\u6574\u4f53\u7acb\u4f53\u4f53\u79ef
    \nAI\u72ec\u5bb6\u6620\u5c04<\/p>\n

  • f(x)^2：\u5e73\u65b9\u635f\u5931MSE\u5e95\u5c42\u6765\u6e90<\/li>\n
  • \u4f53\u79ef\u5927\u5c0f：\u53c2\u6570\u7a7a\u95f4\u7684\u8bef\u5dee\u5bb9\u79ef<\/li>\n
  • \u4f53\u79ef\u8d8a\u6536\u655b\u8d8a\u5c0f：\u6a21\u578b\u8bef\u5dee\u7a7a\u95f4\u88ab\u538b\u7f29
    \n\u7ecf\u5178\u5b9e\u64cd\u4f8b\u9898
    \ny=\\\\sqrt{x}，\u533a\u95f4 [0,4]，\u7ed5x\u8f74\u65cb\u8f6c\u4f53\u79ef
    \nV=\\\\pi\\\\int_0^4 (\\\\sqrt{x})^2 dx
    \n=\\\\pi\\\\int_0^4 x dx
    \n=\\\\pi\\\\cdot \\\\frac12x2\\\\bigg|_0<\/sup>4
    \n=\\\\pi\\\\cdot 8 = 8\\\\pi<\/li>\n

    \u56db\u3001\u7ed5Y\u8f74\u65cb\u8f6c\u4f53\u79ef（\u58f3\u5c42\u6cd5，\u6a21\u578b\u8fb9\u754c\u7a7a\u95f4）
    \n\u516c\u5f0f
    \nV=2\\\\pi\\\\int_a^b x\\\\cdot f(x) dx
    \nAI\u610f\u4e49
    \n\u8868\u5f81\u6a21\u578b\u8fb9\u7f18\u53c2\u6570\u3001\u8fb9\u754c\u6743\u91cd\u7684\u7a7a\u95f4\u5bb9\u79ef
    \n\u5bf9\u5e94\u5927\u6a21\u578b：\u7a00\u758f\u53c2\u6570\u3001\u8fb9\u7f18\u7279\u5f81\u3001\u6b21\u8981\u6743\u91cd\u7a7a\u95f4<\/p>\n

    \u4e94\u3001\u672c\u8bfe\u6700\u5f3aAI\u5e95\u5c42\u6253\u901a（\u6838\u5fc3\u5347\u534e）
    \n\u4e3a\u4ec0\u4e48MSE\u662f\u5e73\u65b9？
    \n\u4f53\u79ef\u516c\u5f0f\u81ea\u5e26 f^2(x)
    \n\u5e73\u65b9\u635f\u5931\u4e0d\u662f\u4eba\u4e3a\u5b9a\u4e49，\u662f\u4e09\u7ef4\u51e0\u4f55\u8bef\u5dee\u7684\u5929\u7136\u5f62\u6001
    \n\u4e3a\u4ec0\u4e48\u4ea4\u53c9\u71b5\u6bd4MSE\u6536\u655b\u5feb？
    \nMSE：\u57fa\u4e8e\u65cb\u8f6c\u4f53\u4f53\u79ef\u7d2f\u79ef（\u7acb\u4f53\u8bef\u5dee）
    \n\u4ea4\u53c9\u71b5：\u57fa\u4e8e\u6982\u7387\u9762\u79ef\u5dee（\u5e73\u9762\u5206\u5e03\u5dee）
    \n\u5e73\u9762\u51e0\u4f55\u4fee\u6b63\u901f\u5ea6 > \u7acb\u4f53\u51e0\u4f55\u4fee\u6b63\u901f\u5ea6
    \n\u8fc7\u62df\u5408\u7684\u51e0\u4f55\u89e3\u91ca
    \n\u8bad\u7ec3\u96c6\u9762\u79ef\u6781\u5c0f（\u62df\u5408\u5b8c\u7f8e）
    \n\u6d4b\u8bd5\u96c6\u9762\u79ef\u6781\u5927（\u66f2\u9762\u8fc7\u4e8e\u626d\u66f2\u3001\u7a7a\u95f4\u5bb9\u79ef\u7578\u5f62）
    \n\u5927\u6a21\u578b\u8bad\u7ec3\u672c\u8d28\u51e0\u4f55\u63cf\u8ff0
    \n\u4e0d\u65ad\u538b\u7f29\u8bef\u5dee\u9762\u79ef\u3001\u89c4\u6574\u8bef\u5dee\u4f53\u79ef，\u8ba9\u9ad8\u7ef4\u635f\u5931\u51e0\u4f55\u4f53\u8d8b\u4e8e\u5e73\u6ed1\u3001\u5bf9\u79f0\u3001\u6700\u5c0f\u5bb9\u79ef\u3002<\/p>\n

    \u516d\u300112\u201316\u8bfe\u5fae\u79ef\u5206\u5b8c\u6574AI\u4f53\u7cfb\u603b\u95ed\u73af<\/p>\n

  • \u4e00\u9636\u5bfc：\u66f2\u9762\u65b9\u5411\u3001\u53c2\u6570\u66f4\u65b0\u8def\u5f84<\/li>\n
  • \u4e8c\u9636\u5bfc：\u66f2\u9762\u51f9\u51f8\u3001\u6536\u655b\u7a33\u5b9a\u6027<\/li>\n
  • \u4e0d\u5b9a\u79ef\u5206：\u66f4\u65b0\u89c4\u5f8b\u516c\u5f0f<\/li>\n
  • \u5b9a\u79ef\u5206\u6570\u503c：\u6279\u91cf\u603b\u8bef\u5dee\u6570\u503c<\/li>\n
  • \u5b9a\u79ef\u5206\u51e0\u4f55（\u672c\u8bfe）：\u8bef\u5dee\u7a7a\u95f4\u9762\u79ef\u3001\u4f53\u79ef\u5f62\u6001
    \n\u81f3\u6b64：\u5927\u6a21\u578b\u635f\u5931\u66f2\u9762\u7684\u300c\u4ee3\u6570+\u51e0\u4f55\u300d\u5168\u90e8\u5403\u900f\u3002<\/li>\n

    \u4e03\u3001\u672c\u8bfe\u6838\u5fc3\u53e3\u8bc0（\u6c38\u4e45\u8bb0\u5fc6）
    \n6. \u5355\u51fd\u6570\u9762\u79ef：\u4e0a\u51cf\u96f6\u3001\u8d1f\u53d6\u53cd
    \n7. \u53cc\u51fd\u6570\u9762\u79ef：\u4e0a\u51cf\u4e0b\u3001\u5dee\u503c\u79ef
    \n8. \u65cb\u8f6c\u4f53\u4f53\u79ef：\u5e73\u65b9\u79ef\u3001\u4e58\u6d3e\u503c
    \n9. AI\u51e0\u4f55\u771f\u7406：\u9762\u79ef\u662f\u8bef\u5dee\u603b\u91cf，\u4f53\u79ef\u662f\u8bef\u5dee\u7a7a\u95f4<\/p>\n

    \u516b\u3001\u8bfe\u540e\u81ea\u6d4b\u9898（\u7cbe\u51c6\u901a\u5173）
    \n10. \u8ba1\u7b97 y=4-x^2 \u5728 [0,2] \u4e0ex\u8f74\u56f4\u6210\u9762\u79ef
    \n11. \u6c42 y=x\u3001y=x^2 \u5728 [1,2] \u4e4b\u95f4\u56f4\u6210\u7684\u9762\u79ef
    \n12. \u6c42 y=2x \u5728 [0,3] \u7ed5x\u8f74\u65cb\u8f6c\u4f53\u4f53\u79ef
    \n13. \u7b80\u7b54：\u4e3a\u4ec0\u4e48\u6a21\u578bloss\u63a5\u8fd10\u4f46\u4f9d\u7136\u9707\u8361？\u7528\u672c\u8bfe\u51e0\u4f55\u77e5\u8bc6\u89e3\u91ca<\/p>\n

    \u672c\u7bc7\u4e3a\u300aAI\u5927\u6a21\u578b\u4e0e\u6570\u5b66\u300b\u8fde\u7eed\u8bfe\u7a0b，\u7528\u5fae\u79ef\u5206\u5e95\u5c42\u903b\u8f91\u770b\u61c2\u5927\u6a21\u578b\u8bad\u7ec3\u539f\u7406\u3002
    \n\u5982\u679c\u5185\u5bb9\u5bf9\u4f60\u6709\u542f\u53d1，\u6b22\u8fce\u70b9\u8d5e\u6536\u85cf\u3002
    \n\u6301\u7eed\u66f4\u65b0\u5168\u595740\u8282\u5fae\u79ef\u5206\u8bfe\u7a0b，\u70b9\u51fb\u5173\u6ce8\u4e0d\u9519\u8fc7\u540e\u7eed\u5185\u5bb9\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

    \u7b2c15\u8bfe\u6211\u4eec\u638c\u63e1\u4e86\u5b9a\u79ef\u5206\u6570\u503c\u8ba1\u7b97\u3001\u725b\u987f-\u83b1\u5e03\u5c3c\u8328\u516c\u5f0f\u3002
    \n\u672c\u8bfe\u7528\u79ef\u5206\u7b97\u300c\u9762\u79ef\u3001\u65cb\u8f6c\u4f53\u4f53\u79ef\u300d\u3002
    \n\u4e3a\u4ec0\u4e48AI\u4eba\u5fc5\u987b\u5b66\u9762\u79ef\u3001\u4f53\u79ef？
    \n\u666e\u901a\u4eba\u5b66\u79ef\u5206：\u7b97\u56fe\u5f62\u9762\u79ef\u3002
    \nAI\u5b66\u79ef\u5206：\u770b\u61c2\u9ad8\u7ef4\u635f\u5931\u66f2\u9762\u7684\u51e0\u4f55\u5f62\u6001\u3002
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