{"id":96702,"date":"2026-08-28T07:56:40","date_gmt":"2026-08-27T23:56:40","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/96702.html"},"modified":"2026-08-28T07:56:40","modified_gmt":"2026-08-27T23:56:40","slug":"ai%e5%a4%a7%e6%a8%a1%e5%9e%8b%e4%b8%8e%e6%95%b0%e5%ad%a6%c2%b7%e7%ac%ac61%e8%af%be%ef%bc%88%e7%ac%ac%e4%ba%8c%e9%98%b6%e6%ae%b5%e7%ba%bf%e6%80%a7%e4%bb%a3%e6%95%b0%e4%b8%8e%e5%a4%a7%e6%a8%a1%e5%9e%8b","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/96702.html","title":{"rendered":"AI\u5927\u6a21\u578b\u4e0e\u6570\u5b66\u00b7\u7b2c61\u8bfe\uff08\u7b2c\u4e8c\u9636\u6bb5\u7ebf\u6027\u4ee3\u6570\u4e0e\u5927\u6a21\u578b\u7b2c1\u8282\uff09\u7ebf\u6027\u4ee3\u6570\u4e0e\u5927\u6a21\u578b\u603b\u6846\u67b6\uff5c\u5411\u91cf\u5b8c\u6574\u5165\u95e8 + Numpy\u624b\u5199\u5411\u91cf\u8fd0\u7b97\u5b9e\u6218"},"content":{"rendered":"<p>\u672c\u8bfe\u5b9a\u4f4d<br \/>\n\u524d60\u8bfe \u5fae\u79ef\u5206\u4e0e\u5927\u6a21\u578b\u9636\u6bb5\u6536\u5b98&#xff1a;<br \/>\n\u5fae\u79ef\u5206 &#061; \u5927\u6a21\u578b\u7684\u52a8\u529b\u7cfb\u7edf&#xff08;\u8bad\u7ec3\u3001\u66f4\u65b0\u3001\u5b66\u4e60\u3001\u4f18\u5316&#xff09;<\/p>\n<p>\u7b2c61\u8bfe\u6b63\u5f0f\u8fdb\u5165\u7b2c\u4e8c\u9636\u6bb5&#xff1a;\u7ebf\u6027\u4ee3\u6570\u4e0e\u5927\u6a21\u578b<br \/>\n\u7ebf\u6027\u4ee3\u6570 &#061; \u5927\u6a21\u578b\u7684\u9aa8\u9abc\u4e0e\u7a7a\u95f4\u7cfb\u7edf&#xff08;\u5b58\u50a8\u3001\u8868\u8fbe\u3001\u53d8\u6362\u3001\u6ce8\u610f\u529b\u3001Embedding\u3001\u538b\u7f29&#xff09;<\/p>\n<p>\u4e00\u53e5\u8bdd\u6982\u62ec\u4e0d\u540c\u6570\u5b66\u7684\u5206\u5de5&#xff1a;<br \/>\n\u5fae\u79ef\u5206\u8d1f\u8d23\u300c\u6a21\u578b\u600e\u4e48\u5b66\u300d<br \/>\n\u7ebf\u6027\u4ee3\u6570\u8d1f\u8d23\u300c\u6a21\u578b\u600e\u4e48\u60f3\u3001\u600e\u4e48\u5b58\u3001\u600e\u4e48\u8868\u8fbe\u77e5\u8bc6\u300d<\/p>\n<p>\u672c\u8282\u8bfe\u4e0d\u8bb2\u516c\u5f0f&#xff0c;\u5148\u5efa\u7acb\u7ebf\u6027\u4ee3\u6570\u5168\u5c40\u9876\u5c42\u6846\u67b6&#xff0c;\u8ba9\u4f60\u672a\u6765\u51e0\u5341\u8282\u7ebf\u6027\u4ee3\u6570\u8bfe\u5168\u90e8\u5b66\u7684\u6709\u65b9\u5411\u3001\u6709\u76ee\u7684\u3001\u5b8c\u5168\u5bf9\u6807\u5927\u6a21\u578b\u771f\u5b9e\u673a\u5236\u3002<\/p>\n<p>\u4e00\u3001\u7ebf\u6027\u4ee3\u6570\u5728\u5927\u6a21\u578b\u4e2d\u7684\u5730\u4f4d&#xff08;\u5168\u5c40\u603b\u89c8&#xff09;<\/p>\n<p>\u6240\u6709\u5927\u6a21\u578b\u3001\u6df1\u5ea6\u5b66\u4e60\u3001AIGC&#xff08;\u4eba\u5de5\u667a\u80fd\u751f\u6210\u5185\u5bb9&#xff09;&#xff0c;\u6240\u6709\u6570\u636e\u5168\u90e8\u662f\u5411\u91cf\u3001\u6240\u6709\u8fd0\u7b97\u5168\u90e8\u662f\u77e9\u9635\u8fd0\u7b97<\/p>\n<p>\u5927\u6a21\u578b\u4e00\u5207\u5e95\u5c42\u903b\u8f91&#xff1a;<\/p>\n<li>\u6587\u5b57 \u2192 \u5411\u91cfEmbedding<\/li>\n<li>\u56fe\u7247 \u2192 \u9ad8\u7ef4\u5411\u91cf<\/li>\n<li>\u8bed\u97f3 \u2192 \u5411\u91cf\u5e8f\u5217<\/li>\n<li>\u6a21\u578b\u6743\u91cd \u2192 \u5de8\u578b\u77e9\u9635<\/li>\n<li>\u6ce8\u610f\u529b\u673a\u5236 \u2192 \u77e9\u9635\u5185\u79ef\u8fd0\u7b97<\/li>\n<li>\u6a21\u578b\u63a8\u7406 \u2192 \u77e9\u9635\u4e58\u6cd5\u5806\u53e0<\/li>\n<li>\u6a21\u578b\u538b\u7f29\u964d\u7ef4 \u2192 SVD\u7ebf\u6027\u53d8\u6362<\/li>\n<p>\u603b\u7ed3&#xff08;\u8bb0\u4f4f\u8fd9\u4e00\u53e5\u5c31\u901a\u4e86&#xff09;<\/p>\n<p>\u5fae\u79ef\u5206\u662f\u6a21\u578b\u7684\u201c\u52a8\u6001\u5b66\u4e60\u5f15\u64ce\u201d&#xff0c;<br \/>\n\u7ebf\u6027\u4ee3\u6570\u662f\u6a21\u578b\u7684\u201c\u9759\u6001\u77e5\u8bc6\u7a7a\u95f4\u201d\u3002<\/p>\n<p>\u6ca1\u6709\u7ebf\u6027\u4ee3\u6570&#xff1a;<br \/>\n\u6a21\u578b\u65e0\u6cd5\u5b58\u77e5\u8bc6\u3001\u65e0\u6cd5\u7406\u89e3\u8bed\u4e49\u3001\u65e0\u6cd5\u505a\u6ce8\u610f\u529b\u3001\u65e0\u6cd5\u8868\u8fbe\u667a\u80fd\u3002<\/p>\n<p>\u4e8c\u3001\u7b2c\u4e8c\u9636\u6bb5\u5168\u90e8\u77e5\u8bc6\u5927\u6846\u67b6&#xff08;\u63d0\u524d\u5267\u900f&#xff09;<\/p>\n<p>\u672a\u6765\u51e0\u5341\u8282\u7ebf\u6027\u4ee3\u6570&#xff0c;\u4e3b\u8981\u56db\u5927\u6a21\u5757&#xff0c;\u5168\u90e8\u5bf9\u6807\u5927\u6a21\u578b&#xff1a;<\/p>\n<li>\u5411\u91cf\u4f53\u7cfb&#xff08;\u672c\u8bfe\u5f00\u59cb&#xff09;<\/li>\n<p>Embedding\u672c\u8d28\u3001\u9ad8\u7ef4\u7a7a\u95f4\u3001\u8bed\u4e49\u7a7a\u95f4\u3001\u76f8\u4f3c\u5ea6\u8ba1\u7b97<\/p>\n<li>\u77e9\u9635\u4f53\u7cfb<\/li>\n<p>\u6a21\u578b\u6743\u91cd\u3001\u7f51\u7edc\u5c42\u53d8\u6362\u3001\u7ef4\u5ea6\u6620\u5c04\u3001\u524d\u5411\u4f20\u64ad\u672c\u8d28<\/p>\n<li>\u7a7a\u95f4\u4e0e\u6295\u5f71\u4f53\u7cfb<\/li>\n<p>\u6ce8\u610f\u529b\u3001\u5411\u91cf\u68c0\u7d22\u3001\u8bed\u4e49\u5339\u914d\u3001\u76f8\u4f3c\u5ea6\u3001\u5bf9\u9f50<\/p>\n<li>\u7279\u5f81\u503c\u4e0eSVD\u4f53\u7cfb<\/li>\n<p>\u6a21\u578b\u964d\u7ef4\u3001\u526a\u679d\u3001\u538b\u7f29\u3001\u53bb\u5197\u4f59\u3001\u77e5\u8bc6\u63d0\u7eaf<\/p>\n<p>\u5168\u90e8\u5185\u5bb9&#xff1a;\u4e0d\u5b66\u65e0\u7528\u6570\u5b66&#xff0c;\u53ea\u5b66AI\u771f\u6b63\u5e95\u5c42\u3002<\/p>\n<p>\u4e09\u3001\u672c\u8bfe\u6838\u5fc3\u77e5\u8bc6\u70b9&#xff1a;\u5411\u91cf\u5b8c\u6574\u5165\u95e8&#xff08;\u5927\u6a21\u578b\u4e00\u5207\u7684\u8d77\u70b9&#xff09;<\/p>\n<li>\u4ec0\u4e48\u662f\u5411\u91cf<\/li>\n<p>\u6570\u5b66\u5b9a\u4e49<\/p>\n<p>\u5411\u91cf &#061; \u4e00\u7ec4\u6709\u5e8f\u6570\u5b57\u7ec4\u6210\u7684\u5217\u8868<br \/>\n\\\\boldsymbol v &#061; [v_1,v_2,\u2026,v_n]<\/p>\n<p>AI\u5b9a\u4e49<\/p>\n<p>\u5411\u91cf &#061; \u673a\u5668\u80fd\u8bfb\u61c2\u7684\u77e5\u8bc6\u3001\u7279\u5f81\u3001\u8bed\u4e49\u3001\u4fe1\u606f<\/p>\n<p>\u4eba\u7c7b\u770b\u6587\u5b57&#xff1a;\u300c\u4f60\u597d\u300d<br \/>\n\u673a\u5668\u770b\u6587\u5b57&#xff1a; [0.21,0.53,-0.12,\u2026\u9ad8\u7ef4\u6570\u7ec4]<\/p>\n<p>\u5927\u6a21\u578b\u6240\u6709\u667a\u80fd&#xff0c;\u5168\u90e8\u5efa\u7acb\u5728\u5411\u91cf\u4e4b\u4e0a\u3002<\/p>\n<li>\u5b9e\u6570\u5411\u91cf<\/li>\n<p>\u5927\u6a21\u578b\u5168\u90e8\u4f7f\u7528 \u5b9e\u6570\u5411\u91cf<\/p>\n<ul>\n<li>\u53ef\u6b63\u3001\u53ef\u8d1f\u3001\u53ef\u5c0f\u6570<\/li>\n<li>\u4ee3\u8868\u8bed\u4e49\u5f3a\u5f31\u3001\u7279\u5f81\u6743\u91cd<\/li>\n<li>\u7ef4\u5ea6\u53ef\u4ee5\u662f128\u3001256\u3001512\u30011024\u30014096<\/li>\n<\/ul>\n<p>\u9ad8\u7ef4\u5411\u91cf &#061; \u7cbe\u7ec6\u7684\u8bed\u4e49\u7279\u5f81<\/p>\n<li>\u5411\u91cf\u52a0\u51cf\u6cd5&#xff08;AI\u610f\u4e49&#xff1a;\u7279\u5f81\u878d\u5408\u3001\u7279\u5f81\u53e0\u52a0&#xff09;<\/li>\n<p>\u8bbe\u6709\u4e24\u4e2a\u540c\u7ef4\u5ea6\u5411\u91cf&#xff1a;<br \/>\n\\\\boldsymbol a &#061; [a_1,a_2],\\\\quad \\\\boldsymbol b &#061; [b_1,b_2]<\/p>\n<p>\u52a0\u6cd5&#xff08;\u7279\u5f81\u878d\u5408&#xff09;<\/p>\n<p>\\\\boldsymbol a&#043;\\\\boldsymbol b &#061; [a_1&#043;b_1,\\\\ a_2&#043;b_2]<br \/>\nAI\u610f\u4e49&#xff1a;\u4e24\u4e2a\u8bed\u4e49\u7279\u5f81\u53e0\u52a0\u3001\u4fe1\u606f\u878d\u5408<\/p>\n<p>\u51cf\u6cd5&#xff08;\u7279\u5f81\u5dee\u5f02&#xff09;<\/p>\n<p>\\\\boldsymbol a-\\\\boldsymbol b &#061; [a_1-b_1,\\\\ a_2-b_2]<br \/>\nAI\u610f\u4e49&#xff1a;\u4e24\u4e2a\u8bed\u4e49\u7684\u5dee\u8ddd\u3001\u504f\u5dee\u3001\u8bef\u5dee<\/p>\n<li>\u5411\u91cf\u6570\u4e58&#xff08;AI\u610f\u4e49&#xff1a;\u7279\u5f81\u7f29\u653e\u3001\u6743\u91cd\u5f3a\u5f31&#xff09;<\/li>\n<p>k\\\\cdot \\\\boldsymbol a &#061; [k\\\\cdot a_1,\\\\ k\\\\cdot a_2]<\/p>\n<ul>\n<li>k&gt;1&#xff1a;\u653e\u5927\u7279\u5f81<\/li>\n<li>0&lt;k&lt;1&#xff1a;\u5f31\u5316\u7279\u5f81<br \/>\n-&lt;0&#xff1a;\u53cd\u5411\u7279\u5f81<\/li>\n<\/ul>\n<p>\u5927\u6a21\u578b\u6fc0\u6d3b\u3001\u95e8\u63a7\u3001\u6743\u91cd\u5f3a\u5f31\u5168\u90e8\u662f\u6570\u4e58\u903b\u8f91<\/p>\n<p>\u56db\u3001Numpy\u624b\u5199\u5411\u91cf\u8fd0\u7b97\u5b9e\u6218&#xff08;\u53ef\u76f4\u63a5\u8fd0\u884c&#xff09;<\/p>\n<li>\u5bfc\u5165\u5e93\u3001\u5b9a\u4e49\u5411\u91cf<\/li>\n<p>python<\/p>\n<p>import numpy as np<\/p>\n<h2>\u5b9a\u4e49\u4e24\u4e2a\u4e8c\u7ef4\u5b9e\u6570\u5411\u91cf<\/h2>\n<p>a &#061; np.array([2.0, 3.0])<br \/>\nb &#061; np.array([1.0, -1.0])<\/p>\n<p>print(\u201c\u5411\u91cfa &#061;\u201d, a)<br \/>\nprint(\u201c\u5411\u91cfb &#061;\u201d, b)<\/p>\n<li>\u5411\u91cf\u52a0\u6cd5&#xff08;\u7279\u5f81\u878d\u5408&#xff09;<\/li>\n<p>python<\/p>\n<p>add_res &#061; a &#043; b<br \/>\nprint(\u201c\u5411\u91cf\u52a0\u6cd5 a&#043;b &#061;\u201d, add_res)<\/p>\n<li>\u5411\u91cf\u51cf\u6cd5&#xff08;\u7279\u5f81\u5dee\u5f02&#xff09;<\/li>\n<p>python<\/p>\n<p>sub_res &#061; a &#8211; b<br \/>\nprint(\u201c\u5411\u91cf\u51cf\u6cd5 a-b &#061;\u201d, sub_res)<\/p>\n<li>\u5411\u91cf\u6570\u4e58&#xff08;\u7279\u5f81\u7f29\u653e&#xff09;<\/li>\n<p>python<\/p>\n<p>k &#061; 2.5<br \/>\nmul_res &#061; k * a<br \/>\nprint(\u201c\u5411\u91cf\u6570\u4e58 k*a &#061;\u201d, mul_res)<\/p>\n<li>\u8fd0\u884c\u7ed3\u679c\u89e3\u91ca<\/li>\n<ul>\n<li>\u52a0\u6cd5&#xff1a;\u4e24\u4e2a\u4fe1\u606f\u53e0\u52a0&#xff0c;\u8bed\u4e49\u878d\u5408<\/li>\n<li>\u51cf\u6cd5&#xff1a;\u6355\u6349\u4e24\u4e2a\u5411\u91cf\u7684\u5dee\u522b<\/li>\n<li>\u6570\u4e58&#xff1a;\u63a7\u5236\u7279\u5f81\u5f3a\u5ea6\u5927\u5c0f<\/li>\n<\/ul>\n<p>\u4e94\u3001\u672c\u8bfe\u6838\u5fc3AI\u603b\u7ed3&#xff08;\u5fc5\u80cc&#xff09;<\/p>\n<li>\u5fae\u79ef\u5206\u8ba9\u6a21\u578b\u4f1a\u5b66\u4e60&#xff0c;\u7ebf\u6027\u4ee3\u6570\u8ba9\u6a21\u578b\u4f1a\u601d\u8003<\/li>\n<li>\u5411\u91cf\u662f\u5927\u6a21\u578b\u5b58\u50a8\u4e00\u5207\u77e5\u8bc6\u7684\u6700\u5c0f\u5355\u5143<\/li>\n<li>\u5411\u91cf\u52a0\u6cd5 &#061; \u4fe1\u606f\u878d\u5408<\/li>\n<li>\u5411\u91cf\u51cf\u6cd5 &#061; \u4fe1\u606f\u5dee\u5f02<\/li>\n<li>\u5411\u91cf\u6570\u4e58 &#061; \u7279\u5f81\u5f3a\u5f31\u7f29\u653e<\/li>\n<p>\u516d\u3001\u4e0b\u8282\u8bfe\u9884\u544a<\/p>\n<p>\u7b2c62\u8bfe&#xff1a;\u5411\u91cf\u6a21\u957f\u3001\u5411\u91cf\u8ddd\u79bb\u3001\u5411\u91cf\u5f52\u4e00\u5316\u3001\u4f59\u5f26\u76f8\u4f3c\u5ea6&#xff0c;\u5185\u79ef&#xff0c;\u6cdb\u6570&#xff0c;\u5939\u89d2\u3002<br \/>\n\u5f7b\u5e95\u770b\u61c2&#xff1a;<\/p>\n<ul>\n<li>\u8bed\u4e49\u76f8\u4f3c\u5ea6<\/li>\n<li>\u6587\u672c\u5339\u914d<\/li>\n<li>\u641c\u7d22\u53ec\u56de<\/li>\n<li>\u5927\u6a21\u578bEmbedding\u6bd4\u5bf9\u6838\u5fc3\u6570\u5b66<\/li>\n<\/ul>\n<p>\u672c\u4e13\u680f\u300aAI\u5927\u6a21\u578b\u4e0e\u6570\u5b66\u300b\u7b2c\u4e8c\u9636\u6bb5\u7ebf\u6027\u4ee3\u6570\u5168\u65b0\u5f00\u542f&#xff0c;\u4ece\u96f6\u7cfb\u7edf\u5403\u900f\u5927\u6a21\u578b\u7a7a\u95f4\u3001\u5411\u91cf\u3001\u77e9\u9635\u3001\u6ce8\u610f\u529b\u5e95\u5c42\u3002<br 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