{"id":51092,"date":"2024-06-29T19:55:06","date_gmt":"2024-06-29T11:55:06","guid":{"rendered":"https:\/\/swarma.org\/?p=51092"},"modified":"2024-06-29T19:55:06","modified_gmt":"2024-06-29T11:55:06","slug":"%e5%86%99%e7%bb%99%e7%89%a9%e7%90%86%e5%ad%a6%e5%ae%b6%e7%9a%84%e7%94%9f%e6%88%90%e6%a8%a1%e5%9e%8b","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=51092","title":{"rendered":"\u5199\u7ed9\u7269\u7406\u5b66\u5bb6\u7684\u751f\u6210\u6a21\u578b"},"content":{"rendered":"
\n
\n
\n
\n
\n

<\/p>\n<\/section>\n

\n
\n
\n
\n
\n
\n

<\/section>\n<\/section>\n
\n
\n

\u5bfc\u8bed<\/strong><\/p>\n<\/section>\n<\/section>\n

\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
\n
\n
\u79d1\u5b66\u7814\u7a76\u7684\u672c\u8d28\u5728\u4e8e\u521b\u9020\u3002\u751f\u6210\u5f0f\u4eba\u5de5\u667a\u80fd\u4e3a\u66f4\u6709\u521b\u610f\u7684\u79d1\u5b66\u63a2\u7d22\u6253\u5f00\u4e86\u65e0\u5c3d\u7684\u60f3\u8c61\u7a7a\u95f4\u3002\u4f5c\u4e3a\u751f\u6210\u5f0f\u4eba\u5de5\u667a\u80fd\u7684\u6838\u5fc3\uff0c\u751f\u6210\u6a21\u578b\u5b66\u4e60\u6570\u636e\u6837\u672c\u80cc\u540e\u7684\u6982\u7387\u5206\u5e03\uff0c\u5e76\u636e\u6b64\u968f\u673a\u91c7\u6837\u751f\u6210\u65b0\u7684\u6837\u672c\u3002\u751f\u6210\u6a21\u578b\u548c\u7edf\u8ba1\u7269\u7406\u5728\u672c\u8d28\u4e0a\u662f\u540c\u4e00\u679a\u786c\u5e01\u7684\u4e24\u9762\u3002\u6587\u7ae0\u4ece\u7269\u7406\u7684\u89c6\u89d2\u4ecb\u7ecd\u6269\u6563\u6a21\u578b\u3001\u81ea\u56de\u5f52\u6a21\u578b\u3001\u6d41\u6a21\u578b\u3001\u53d8\u5206\u81ea\u7f16\u7801\u5668\u7b49\u73b0\u4ee3\u751f\u6210\u6a21\u578b\u3002\u751f\u6210\u6a21\u578b\u5728\u539f\u5b50\u5c3a\u5ea6\u7269\u8d28\u7ed3\u6784\u7684\u751f\u6210\u4e0e\u8bbe\u8ba1\u4e2d\u5c55\u73b0\u51fa\u5de8\u5927\u7684\u6f5c\u529b\u3002\u4e0d\u4ec5\u5982\u6b64\uff0c\u57fa\u4e8e\u548c\u7edf\u8ba1\u7269\u7406\u7684\u5185\u5728\u8054\u7cfb\uff0c\u751f\u6210\u6a21\u578b\u5bf9\u4e8e\u4f18\u5316\u201c\u5927\u81ea\u7136\u7684\u635f\u5931\u51fd\u6570\u201d\u2014\u2014\u53d8\u5206\u81ea\u7531\u80fd\u5177\u6709\u72ec\u7279\u7684\u4f18\u52bf\uff0c\u8fd9\u4e3a\u6c42\u89e3\u56f0\u96be\u7684\u7edf\u8ba1\u7269\u7406\u548c\u91cf\u5b50\u591a\u4f53\u95ee\u9898\u63d0\u4f9b\u4e86\u65b0\u7684\u53ef\u80fd\u3002\u540c\u65f6\uff0c\u7269\u7406\u5b66\u7684\u6d1e\u5bdf\u4e5f\u5728\u63a8\u52a8\u751f\u6210\u6a21\u578b\u7684\u53d1\u5c55\u548c\u521b\u65b0\u3002\u901a\u8fc7\u501f\u9274\u7269\u7406\u5b66\u539f\u7406\u548c\u65b9\u6cd5\uff0c\u8fd8\u53ef\u4ee5\u8bbe\u8ba1\u51fa\u66f4\u52a0\u9ad8\u6548\u3001\u66f4\u52a0\u7edf\u4e00\u7684\u751f\u6210\u6a21\u578b\uff0c\u4ee5\u5e94\u5bf9\u4eba\u5de5\u667a\u80fd\u9886\u57df\u4e2d\u7684\u6311\u6218\u3002<\/span><\/strong><\/strong><\/strong><\/span><\/strong><\/section>\n

<\/section>\n
\u7814\u7a76\u9886\u57df\uff1a\u751f\u6210\u6a21\u578b\uff0c\u7edf\u8ba1\u7269\u7406\uff0c\u76f8\u5bf9\u71b5\uff0c\u6700\u5927\u4f3c\u7136\u4f30\u8ba1\uff0c\u53d8\u5206\u81ea\u7531\u80fd<\/strong><\/strong><\/span><\/strong>
<\/section>\n<\/section>\n
\n
<\/strong><\/section>\n<\/section>\n
\n
<\/strong><\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
\n
\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
\n
<\/section>\n<\/section>\n
\u738b\u78ca(\u4e2d\u56fd\u79d1\u5b66\u9662\u7269\u7406\u7814\u7a76\u6240)\u3001\u5f20\u6f58(\u4e2d\u56fd\u79d1\u5b66\u9662\u7406\u8bba\u7269\u7406\u7814\u7a76\u6240)<\/span> <\/span>| \u4f5c\u8005<\/span><\/strong><\/section>\n
\u300a\u7269\u7406\u300b2024\u5e74\u7b2c6\u671f<\/span> <\/span>| \u6765\u6e90<\/span><\/strong><\/span><\/strong><\/section>\n

<\/span><\/strong><\/span><\/strong><\/section>\n<\/section>\n
\n

\n
\n
\n
\n
\n

<\/section>\n

<\/section>\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n
\n

1. \u5f15\u8a00<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n

\u8d39\u66fc\u5728\u4ed6\u7684\u9ed1\u677f\u4e0a\u7559\u4e0b\u4e00\u53e5\u8bdd\uff1a\u201cwhat I can not create\uff0cI do not understand\u201d[1]\u3002\u4e09\u5341\u5e74\u540e\uff0c\u8fd9\u53e5\u8bdd\u88ab\u5982\u4eca\u5927\u7ea2\u5927\u7d2b\u7684OpenAI\u5f53\u4f5c\u4fe1\u6761\u6302\u5728\u7f51\u7ad9\u4e0a[2]\u3002\u786e\u5b9e\uff0c\u65e0\u8bba\u662f\u5728\u7269\u7406\u5b66\u8fd8\u662f\u4eba\u5de5\u667a\u80fd\u7684\u7814\u7a76\u4e2d\uff0c\u6709\u80fd\u529b\u521b\u9020\u5f80\u5f80\u624d\u610f\u5473\u7740\u6700\u9ad8\u5c42\u6b21\u7684\u7406\u89e3\u3002<\/span><\/p>\n


<\/p>\n

\u4ec0\u4e48\u662f\u521b\u9020\uff1f\u751f\u6210\u5f0f\u4eba\u5de5\u667a\u80fd<\/span> (Generative AI) <\/span>\u5bf9\u6b64\u7684\u56de\u7b54\u662f\uff1a\u5b66\u4e60\u6570\u636e\u6837\u672c\u80cc\u540e\u7684\u6982\u7387\u5206\u5e03\uff0c\u5e76\u901a\u8fc7\u968f\u673a\u91c7\u6837\u751f\u6210\u65b0\u7684\u6837\u672c\u3002\u8fd9\u4e24\u5e74\uff0c\u4eba\u4eec\u7528\u4eba\u5de5\u667a\u80fd\u4ea7\u54c1\u521b\u9020\u4e86\u65e0\u6570\u4ee4\u4eba\u60ca\u8273\u7684\u753b\u4f5c\u3001\u5f15\u4eba\u5165\u80dc\u7684\u6545\u4e8b\u3001\u52a8\u4eba\u5fc3\u5f26\u7684\u97f3\u4e50\u3002\u5f53\u7136\uff0c\u8fd8\u6709\u5e7f\u544a\u6587\u6848\u3001\u65b0\u95fb\u62a5\u9053\u3001\u5ba1\u7a3f\u62a5\u544a\u3001\u5546\u4e1a\u8ba1\u5212\u4e66\u3001\u63a8\u8350\u4fe1\u7b49\u7b49<\/span> (\u4f8b\u5982\u8fd9\u53e5\u8bdd\u672c\u8eab)<\/span>\u3002\u4eba\u5de5\u667a\u80fd\u521b\u9020\u7684\u6e90\u6cc9\u662f\u6570\u636e\u672c\u8eab\uff0c\u800c\u4eba\u5de5\u667a\u80fd\u521b\u9020\u7684\u5f15\u64ce\u5219\u662f\u201c\u751f\u6210\u6a21\u578b\u201d\uff1a\u4e00\u79cd\u7528\u4e8e\u8868\u8fbe\u3001\u5b66\u4e60\u548c\u91c7\u6837\u6570\u636e\u80cc\u540e\u7684\u6982\u7387\u5206\u5e03\u7684\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u3002\u751f\u6210\u6a21\u578b\u548c\u7edf\u8ba1\u7269\u7406\u7684\u5173\u7cfb\u975e\u5e38\u7d27\u5bc6\u3002\u4e00\u65e6\u4e86\u89e3\u751f\u6210\u6a21\u578b\u7684\u7269\u7406\u5b66\u57fa\u56e0\uff0c\u5c31\u6bd4\u8f83\u5bb9\u6613\u7406\u89e3\u548c\u6539\u9020\u5b83\u4eec\uff0c\u751a\u81f3\u53d1\u660e\u65b0\u7684\u751f\u6210\u6a21\u578b\u3002\u672c\u6587\u4ece\u7269\u7406\u5b66\u7684\u89d2\u5ea6\u4ecb\u7ecd\u51e0\u7c7b\u5e38\u89c1\u7684\u751f\u6210\u6a21\u578b\uff0c\u5e76\u4e3e\u4f8b\u8bf4\u660e\u5b83\u4eec\u5728\u79d1\u5b66\u7814\u7a76\u4e2d\u7684\u5e94\u7528\u3002<\/span><\/p>\n


<\/p>\n

\u76f8\u5bf9\u4e8e\u6027\u8d28\u9884\u6d4b\u4e4b\u7c7b\u7684\u201c\u5224\u522b\u5f0f\u201d\u4efb\u52a1\uff0c\u201c\u751f\u6210\u5f0f\u201d\u4eba\u5de5\u667a\u80fd\u66f4\u96be\u3001\u66f4\u57fa\u7840\u3001\u4e5f\u66f4\u6709\u7528\u3002\u7528\u6570\u5b66\u8bed\u8a00\u63cf\u8ff0\uff0c\u6027\u8d28\u9884\u6d4b\u7684\u76ee\u7684\u662f\u62df\u5408\u51fd\u6570y<\/em>=f<\/em>(x<\/em><\/strong>)\u3002\u8fd9\u91ccx<\/em><\/strong>\u662f\u795e\u7ecf\u7f51\u7edc\u7684\u8f93\u5165\uff0c\u901a\u5e38\u662f\u4ee3\u8868\u5fae\u89c2\u7ed3\u6784\u7684\u9ad8\u7ef4\u53d8\u91cf\u3002y<\/em>\u662f\u8f93\u51fa\uff0c\u901a\u5e38\u662f\u4ee3\u8868\u5b8f\u89c2\u6027\u8d28\u7684\u4f4e\u7ef4\u53d8\u91cf\u3002\u5728\u6027\u8d28\u9884\u6d4b\u4e4b\u5916\uff0c\u4eba\u4eec\u5f80\u5f80\u8fd8\u66f4\u5173\u5fc3\u4ece\u5b8f\u89c2\u6027\u8d28\u5230\u5fae\u89c2\u7ed3\u6784\u7684\u53cd\u5411\u8bbe\u8ba1\u95ee\u9898\u3002\u7531\u4e8e\u4ece\u7ed3\u6784\u5230\u6027\u8d28\u7684\u51fd\u6570\u4e0d\u53ef\u9006\uff0c\u7b80\u5355\u5730\u5bfb\u627e\u5b83\u7684\u53cd\u51fd\u6570\u5f80\u5f80\u4e0d\u80fd\u6210\u529f\u3002\u6982\u7387\u5efa\u6a21\u63d0\u4f9b\u4e86\u4e00\u4e2a\u6709\u7528\u7684\u89c6\u89d2\u3002\u8fd9\u65f6\uff0c\u6027\u8d28\u9884\u6d4b\u5c31\u662f\u8981\u5b66\u4e60\u6761\u4ef6\u6982\u7387\u5206\u5e03p<\/em>(<\/span>y<\/em>|<\/span>x<\/em><\/strong>)<\/span>\u3002\u800c\u53cd\u5411\u8bbe\u8ba1\u610f\u5473\u7740\u7ed9\u5b9a\u5b8f\u89c2\u6027\u8d28y<\/em>\uff0c\u4ece\u6761\u4ef6\u6982\u7387p<\/em>(x<\/em><\/strong>|y<\/em>)\u4e2d\u91c7\u6837\u751f\u6210\u65b0\u7684\u5fae\u89c2\u6784\u578bx<\/em><\/strong>\u3002\u8d1d\u53f6\u65af\u516c\u5f0f\u544a\u8bc9\u6211\u4eecp<\/em>(x<\/em><\/strong>|y<\/em>)\u221dp<\/em>(x<\/em><\/strong>)p<\/em>(y<\/em>|x<\/em><\/strong>)\u3002\u53ef\u89c1\uff0c\u628a\u63e1\u5fae\u89c2\u6784\u578b\u7684\u6982\u7387\u5206\u5e03p<\/em><\/span>(x<\/em><\/strong>)\u662f\u201c\u751f\u6210\u5f0f\u201d\u4efb\u52a1\u533a\u522b\u4e8e\u201c\u5224\u522b\u5f0f\u201d\u4efb\u52a1\u7684\u5173\u952e\u3002<\/span><\/p>\n


<\/p>\n

\u56fe1\u5f62\u8c61\u5730\u5c55\u793a\u4e86\u751f\u6210\u6a21\u578b\u5728\u505a\u4ec0\u4e48\u3002\u56fe1(a)\u4e2d\u7684\u84dd\u8272\u70b9\u4ee3\u8868\u6570\u636e\u6837\u672c\uff0c\u751f\u6210\u6a21\u578b\u9700\u8981\u5b66\u4f1a\u6570\u636e\u80cc\u540e\u7684\u6982\u7387\u5206\u5e03\uff0c\u5e76\u636e\u6b64\u751f\u6210\u65b0\u7684\u6837\u672c\u3002\u751f\u6210\u6a21\u578b\u80fd\u591f\u5904\u7406\u7684\u6570\u636e\u7c7b\u578b\u65e0\u6240\u4e0d\u5305\u3002\u5982\u56fe1(b)\u6240\u793a\uff0c\u56fe\u50cf\u751f\u6210\u6a21\u578b\u8868\u8fbe\u4e86\u50cf\u7d20\u53d6\u503c\u7684\u6982\u7387\u5206\u5e03\uff0c\u800c\u6750\u6599\u751f\u6210\u6a21\u578b\u8868\u8fbe\u4e86\u539f\u5b50\u7c7b\u578b\u548c\u5750\u6807\u7684\u8054\u5408\u6982\u7387\u5206\u5e03\u3002\u53ef\u4ee5\u60f3\u8c61\uff0c\u65e0\u8bba\u662f\u6240\u6709\u50cf\u7d20\u53d6\u503c\u6240\u6784\u6210\u7684\u56fe\u50cf\u7a7a\u95f4\uff0c\u8fd8\u662f\u6240\u6709\u539f\u5b50\u79cd\u7c7b\u548c\u6392\u5e03\u6240\u6784\u6210\u7684\u6750\u6599\u7a7a\u95f4\uff0c\u90fd\u5de8\u5927\u65e0\u6bd4\u3002\u800c\u4eba\u4eec\u771f\u6b63\u5173\u6ce8\u7684\u81ea\u7136\u56fe\u7247\u548c\u7a33\u5b9a\u6750\u6599\uff0c\u4ec5\u4ec5\u5360\u636e\u8fd9\u4e9b\u7a7a\u95f4\u4e2d\u4e00\u4e2a\u5c0f\u89d2\u843d\u3002\u751f\u6210\u6a21\u578b\u9700\u8981\u5c3d\u91cf\u63d0\u53d6\u6570\u636e\u6837\u672c\u4e2d\u7684\u7edf\u8ba1\u89c4\u5f8b\uff0c\u624d\u80fd\u751f\u6210\u6d51\u7136\u5929\u6210\u7684\u65b0\u56fe\u7247\u548c\u65b0\u6750\u6599\u3002
<\/span><\/p>\n


<\/span><\/p>\n

<\/p>\n

\u56fe1 (a)\u751f\u6210\u6a21\u578b\u5b66\u4e60\u6570\u636e\u80cc\u540e\u7684\u6982\u7387\u5206\u5e03\uff0c\u5e76\u636e\u6b64\u91c7\u6837\u751f\u6210\u65b0\u7684\u6837\u672c\uff1b(b)\u5728\u50cf\u7d20\u7a7a\u95f4\uff0c\u4e0d\u540c\u7c7b\u522b\u7684\u56fe\u7247\u5904\u4e8e\u6982\u7387\u5206\u5e03\u7684\u4e0d\u540c\u6a21\u5f0f\u3002\u7c7b\u4f3c\u5730\uff0c\u91d1\u5c5e\u4e0e\u7edd\u7f18\u4f53\u4e2d\u7684\u539f\u5b50\u6392\u5e03\u4e5f\u5904\u4e8e\u6676\u4f53\u751f\u6210\u6a21\u578b\u6982\u7387\u5206\u5e03\u7684\u4e0d\u540c\u6a21\u5f0f<\/span><\/section>\n


<\/p>\n


<\/section>\n

\n
\n
\n
\n
\n

<\/section>\n

<\/section>\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n
\n

2. \u81ea\u7136\u754c\u4e2d\u7684\u6982\u7387\u5206\u5e03<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n
\u81ea\u73bb\u5c14\u5179\u66fc\u4ee5\u6765\uff0c\u7269\u7406\u5b66\u5bf9\u4e8e\u81ea\u7136\u754c\u7684\u63cf\u8ff0\u5c31\u544a\u522b\u4e86\u51b3\u5b9a\u8bba\u3002\u5fae\u89c2\u4e16\u754c\u5145\u6ee1\u4e86\u968f\u673a\u6027\uff0c\u7406\u89e3\u5b83\u81ea\u7136\u9700\u8981\u638c\u63e1\u5fae\u89c2\u53d8\u91cf\u7684\u8054\u5408\u6982\u7387\u5206\u5e03\u3002\u4f8b\u5982\uff0c\u6c34\u548c\u51b0\u7531\u540c\u6837\u7684\u6c34\u5206\u5b50\u6240\u7ec4\u6210\uff0c\u5728\u57fa\u672c\u7ec4\u6210\u5355\u5143\u4e0a\u6ca1\u6709\u533a\u522b\u3002\u4f46\u7531\u4e8e\u5728\u4e0d\u540c\u6e29\u5ea6\u4e0b\u6c34\u5206\u5b50\u6784\u8c61x<\/em><\/strong>\u7684\u8054\u5408\u6982\u7387\u5206\u5e03p<\/em>(x<\/em><\/strong>)\u662f\u4e0d\u540c\u7684\uff0c\u56e0\u6b64\u5728\u5b8f\u89c2\u4e0a\u5c55\u73b0\u51fa\u4e0d\u540c\u7684\u7269\u7406\u6027\u8d28\u3002\u53e6\u4e00\u4e2a\u4f8b\u5b50\u662f\u7edf\u8ba1\u7269\u7406\u4e2d\u7684\u7ecf\u5178\u4f0a\u8f9b\u6a21\u578b\uff0c\u5176\u4e2d\u7684\u81ea\u65cb\u6784\u578b\u670d\u4ece\u73bb\u5c14\u5179\u66fc\u5206\u5e03<\/span>\uff0c\u5176\u4e2d<\/span>E<\/em>(<\/span>x<\/em><\/strong>)\u662f\u4f0a\u8f9b\u6784\u578b<\/span>x<\/strong><\/em>\u7684\u80fd\u91cf\uff0c\u914d\u5206\u51fd\u6570<\/span>Z<\/em>\u662f\u6982\u7387\u5206\u5e03\u7684\u5f52\u4e00\u5316\u56e0\u5b50\u3002\u4e0d\u540c\u7684\u6e29\u5ea61\/<\/span>\u03b2<\/em>\u4f1a\u5bfc\u81f4\u4e0d\u540c\u7684\u73bb\u5c14\u5179\u66fc\u5206\u5e03\uff0c\u751a\u81f3\u7ed9\u51fa\u622a\u7136\u4e0d\u540c\u7684\u78c1\u5316\u5f3a\u5ea6\u3001\u6bd4\u70ed\u7b49\u5b8f\u89c2\u7269\u7406\u91cf\u3002<\/span><\/span><\/section>\n

<\/span><\/section>\n
\u4e00\u822c\u60c5\u51b5\u4e0b\uff0c\u60f3\u8981\u4e25\u683c\u8ba1\u7b97\u7edf\u8ba1\u7269\u7406\u95ee\u9898\u4e2d\u5fae\u89c2\u53d8\u91cf\u7684\u6982\u7387\u5206\u5e03\u662f\u975e\u5e38\u56f0\u96be\u7684\uff0c\u56e0\u4e3a\u53d8\u91cf\u6240\u5904\u7684\u6982\u7387\u7a7a\u95f4\u592a\u5927\u4e86\uff0c\u5f52\u4e00\u5316\u56e0\u5b50\u5f88\u96be\u8ba1\u7b97\u3002\u4ee5\u5305\u542bn<\/em>\u4e2a\u81ea\u65cb\u7684\u4f0a\u8f9b\u6a21\u578b\u4e3a\u4f8b\uff0c\u76f4\u63a5\u8ba1\u7b97\u914d\u5206\u51fd\u6570\u9700\u8981\u505a2n<\/sup><\/em>\u6b21\u52a0\u6cd5\u3002\u54ea\u6015\u5728\u5f88\u5c11\u7684\u53d8\u91cf\u6570\u76een<\/em>\u4e0b\uff0c\u90fd\u9700\u8981\u5f88\u5927\u7684\u8ba1\u7b97\u91cf\u624d\u80fd\u5b8c\u6210\uff1a\u5229\u7528\u7b14\u8bb0\u672c\u7535\u8111\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u5f97\u5230n<\/em>=30\u7684\u914d\u5206\u51fd\u6570\uff0c\u4f7f\u7528\u8ba1\u7b97\u96c6\u7fa4\u53ef\u4ee5\u7b97\u5230n<\/em>=40\u4e2a\u4f0a\u8f9b\u81ea\u65cb\uff0c\u5f53n<\/em>\u5927\u4e8e60\u65f6\uff0c\u5373\u4f7f\u7528\u8d85\u7ea7\u8ba1\u7b97\u673a\u4e5f\u65e0\u6cd5\u76f4\u63a5\u4e25\u683c\u8ba1\u7b97\u914d\u5206\u51fd\u6570\uff0c\u56e0\u6b64\u4e5f\u5c31\u4e0d\u77e5\u9053\u67d0\u4e2a\u81ea\u65cb\u6784\u578b\u7684\u6982\u7387\u53d6\u503c\u3002\u5728\u673a\u5668\u5b66\u4e60\u5e94\u7528\u4e2d\uff0c\u6211\u4eec\u4e5f\u9762\u4e34\u7c7b\u4f3c\u7684\u95ee\u9898\uff1a\u4e00\u5f20\u56fe\u7247\u3001\u4e00\u6bb5\u6587\u672c\u3001\u4e00\u76d8\u68cb\u5c40\u90fd\u53ef\u4ee5\u7c7b\u6bd4\u4e8e\u4f0a\u8f9b\u6a21\u578b\u7684\u5fae\u89c2\u6784\u578b\u3002\u5b83\u4eec\u80cc\u540e\u90fd\u6709\u5404\u81ea\u5173\u4e8e\u50cf\u7d20\u3001\u8bcd\u548c\u68cb\u5b50\u4f4d\u7f6e\u7684\u8054\u5408\u6982\u7387\u5206\u5e03\uff0c\u800c\u6240\u6709\u8fd9\u4e9b\u6982\u7387\u5206\u5e03\u90fd\u5b58\u5728\u4e8e\u6307\u6570\u9ad8\u7ef4\u7684\u7a7a\u95f4\u4e2d\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u53e6\u5916\u4e00\u4e2a\u4e0d\u592a\u663e\u7136\uff0c\u4f46\u975e\u5e38\u91cd\u8981\u7684\u8054\u7cfb\u662f\u7edf\u8ba1\u7269\u7406\u4e0e\u8d1d\u53f6\u65af\u63a8\u65ad\u7684\u5bf9\u5e94\u5173\u7cfb\u3002\u5728\u8d1d\u53f6\u65af\u63a8\u65ad\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u7528\u4e00\u4e2a\u6a21\u578b\u63cf\u8ff0\u4e00\u7ec4\u89c2\u6d4b\u6570\u636e<\/span>\u3002\u8fd9\u91cc\u6240\u8c13\u201c\u6a21\u578b\u201d\u662f\u6307\u7ed9\u5b9a\u53c2\u6570\u03b8<\/em><\/strong>\u9884\u6d4b\u6570\u636e\u7684\u6761\u4ef6\u6982\u7387p<\/em>(<\/span>|\u03b8<\/em><\/strong>)\uff0c\u800c\u6240\u8c13\u201c\u63a8\u65ad\u201d\u5c31\u662f\u8981\u786e\u5b9a\u5982\u4f55\u6839\u636e\u89c2\u6d4b\u6570\u636e\u9009\u53d6\u6a21\u578b\u53c2\u6570\u3002\u8d1d\u53f6\u65af\u63a8\u65ad\u8003\u8651\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u6570\u636e\u548c\u53c2\u6570\u7684\u5148\u9a8c\u6982\u7387\u5206\u5e03p<\/em>(\u03b8<\/em><\/strong>)\uff0c\u4ece\u201c\u540e\u9a8c\u6982\u7387\u201d<\/span>\u4e2d\u9009\u62e9\u53c2\u6570\u3002\u7a0d\u5fae\u6539\u5199\u4e00\u4e0b\u540e\u9a8c\u6982\u7387\u7684\u8868\u8fbe\u5f0f\uff0c\u53ef\u4ee5\u770b\u5230\u8d1d\u53f6\u65af\u63a8\u65ad\u548c\u7edf\u8ba1\u7269\u7406\u4e4b\u95f4\u7684\u5bf9\u5e94\u5173\u7cfb\uff0c\u89c1\u88681\u3002\u5176\u4e2d\uff0c\u540e\u9a8c\u6982\u7387\u7684\u5f52\u4e00\u5316\u56e0\u5b50p<\/em>(<\/span>)\u5bf9\u5e94\u4e8e\u914d\u5206\u51fd\u6570Z<\/em>\uff0c\u5728\u8d1d\u53f6\u65af\u63a8\u65ad\u4e2d\u88ab\u79f0\u4e3a\u8fb9\u9645\u4f3c\u7136\uff0c\u5b83\u63cf\u8ff0\u4e86\u6a21\u578b\u5bf9\u6570\u636e\u7684\u603b\u4f53\u523b\u753b\u80fd\u529b\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u88681 \u8d1d\u53f6\u65af\u63a8\u65ad\u4e0e\u7edf\u8ba1\u7269\u7406\u4e4b\u95f4\u7684\u5b57\u5178<\/span><\/section>\n
<\/section>\n

<\/span><\/section>\n
\u4e0a\u9762\u5217\u4e3e\u7684\u5bf9\u5e94\u5173\u7cfb\u4e5f\u6697\u793a\u4e86\u673a\u5668\u5b66\u4e60\u4e2d\u6d89\u53ca\u7684\u4e0d\u5c11\u95ee\u9898\u90fd\u5177\u6709\u548c\u7edf\u8ba1\u7269\u7406\u95ee\u9898\u76f8\u4f3c\u7684\u8ba1\u7b97\u96be\u5ea6\uff1a\u8ba1\u7b97\u9ad8\u7ef4\u6982\u7387\u5206\u5e03\u51fd\u6570\u7684\u5f52\u4e00\u5316\u56e0\u5b50\u6d89\u53ca\u5230\u7406\u8bba\u8ba1\u7b97\u673a\u79d1\u5b66\u4e2d\u6240\u8c13\u201c#P\u96be\u201d\u7684\u4e00\u7c7b\u8ba1\u6570\u95ee\u9898\uff0c\u4e00\u822c\u88ab\u8ba4\u4e3a\u4e0d\u5b58\u5728\u5feb\u901f<\/span> (\u591a\u9879\u5f0f\u65f6\u95f4\u590d\u6742\u5ea6)<\/span> \u7684\u6c42\u89e3\u7b97\u6cd5\u3002\u4e0b\u6587\u4ecb\u7ecd\u7684\u51e0\u79cd\u73b0\u4ee3\u751f\u6210\u6a21\u578b\u201c\u5404\u663e\u795e\u901a\u201d\uff0c\u5de7\u5999\u5730\u7ed5\u8fc7\u4e86\u8fd9\u4e2a\u96be\u9898\u3002\u7ed3\u5408Box 1\u4e2d\u6240\u4ecb\u7ecd\u7684\u8bad\u7ec3\u76ee\u6807\u51fd\u6570\uff0c\u751f\u6210\u6a21\u578b\u4e3a\u9ad8\u7ef4\u53d8\u91cf\u7684\u6982\u7387\u5efa\u6a21\u548c\u53d8\u5206\u8ba1\u7b97\u6253\u5f00\u4e86\u65b0\u7684\u53ef\u80fd\u3002<\/span><\/section>\n

<\/span><\/section>\n

<\/section>\n
\n
\n
\n
\n

BOX 1<\/strong> <\/strong><\/span><\/p>\n<\/section>\n<\/section>\n

\n
\n
\u76f8\u5bf9\u71b5\u7684AB\u9762<\/strong><\/span><\/section>\n

\u76f8\u5bf9\u71b5\u662f\u4fe1\u606f\u8bba\u7684\u4e00\u4e2a\u57fa\u672c\u91cf\uff0c\u4e5f\u88ab\u79f0\u4e3aKullback\u2014Leibler\u6563\u5ea6\u3002\u5b83\u5ea6\u91cf\u4e86\u6982\u7387\u5206\u5e03\u4e4b\u95f4\u7684\u76f8\u4f3c\u5ea6\u3002\u5bf9\u4e8e\u4e24\u4e2a\u5f52\u4e00\u5316\u7684\u6982\u7387\u5206\u5e03q<\/em>\u548cp<\/em>\uff0c\u76f8\u5bf9\u71b5\u603b\u662f\u975e\u8d1f\u7684[3]\uff1a<\/span><\/p>\n


<\/span><\/p>\n

<\/p>\n


<\/span><\/p>\n

\u5176\u4e2d\u7b49\u53f7\u4ec5\u5728\u4e24\u4e2a\u6982\u7387\u5206\u5e03\u76f8\u7b49\u65f6\u53d6\u5230\u3002\u56e0\u6b64\uff0c\u76f8\u5bf9\u71b5\u5e38\u5e38\u88ab\u7528\u4f5c\u8bad\u7ec3\u751f\u6210\u6a21\u578b\u7684\u76ee\u6807\u51fd\u6570\u3002\u901a\u8fc7\u6700\u5c0f\u5316\u751f\u6210\u6a21\u578b\u6240\u8868\u8fbe\u7684\u6982\u7387\u5206\u5e03\u548c\u76ee\u6807\u6982\u7387\u5206\u5e03\u4e4b\u95f4\u7684\u76f8\u5bf9\u71b5\uff0c\u53ef\u4ee5\u8ba9\u751f\u6210\u6a21\u578b\u5b66\u4f1a\u76ee\u6807\u6982\u7387\u5206\u5e03\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u4e3a\u4ec0\u4e48\u8981\u9009\u62e9\u76f8\u5bf9\u71b5\u8fd9\u4e2a\u770b\u8d77\u6765\u5947\u602a\u7684\u5ea6\u91cf\uff0c\u800c\u4e0d\u76f4\u63a5\u4f7f\u7528\u7c7b\u4f3c\u4e8e<\/span>\u8fd9\u6837\u7684\u5747\u65b9\u5dee\u5ea6\u91cf\uff1f\u4e3b\u8981\u6709\u4e24\u4e2a\u539f\u56e0\uff1a\u7b2c\u4e00\uff0c\u6982\u7387\u5206\u5e03<\/span>p<\/em>(<\/span>x<\/em><\/strong>)\u548c<\/span>q<\/em>(<\/span>x<\/em><\/strong>)<\/span>\u5728\u6570\u91cf\u7ea7\u4e0a\u53ef\u80fd\u5dee\u522b\u5de8\u5927\uff0c\u5747\u65b9\u5dee\u8ddd\u79bb\u4e0d\u80fd\u5145\u5206\u4f53\u73b0\u8fd9\u70b9\u5dee\u522b\uff0c\u800c\u76f8\u5bf9\u71b5\u4e2d\u6bd4\u8f83\u6982\u7387\u51fd\u6570\u7684\u5bf9\u6570\u53ef\u4ee5\u66f4\u597d\u5730\u5904\u7406\u8fd9\u79cd\u6570\u91cf\u7ea7\u5dee\u5f02\uff1b\u7b2c\u4e8c\uff0c\u5176\u5b9e\u4e0d\u503c\u5f97\u5728\u4e24\u4e2a\u6982\u7387\u5206\u5e03\u90fd\u53d6\u503c\u6781\u5176\u5c0f\u7684\u533a\u57df\u6bd4\u8f83\u5b83\u4eec\u7684\u5dee\u5f02\uff0c\u56e0\u6b64\uff0c\u76f8\u5bf9\u71b5\u7684\u5b9a\u4e49\u4e2d\u6309\u7167\u6982\u7387<\/span>q<\/em>(<\/span>x<\/em><\/strong>)\u52a0\u6743\u8ba1\u7b97\uff0c\u5373\u96c6\u4e2d\u68c0\u67e5\u5bf9\u4e8e\u6982\u7387<\/span>q<\/em>(<\/span>x<\/em><\/strong>)<\/span>\u800c\u8a00\u6709\u610f\u4e49\u7684\u7a7a\u95f4\u4e2d\u4e24\u4e2a\u6982\u7387\u5206\u5e03\u5bf9\u6570\u7684\u5dee\u522b\u3002<\/span><\/span><\/p>\n


<\/span><\/p>\n

\u4ece\u5b9a\u4e49(1)\u53ef\u89c1\uff0c\u76f8\u5bf9\u71b5\u5bf9\u4e8e\u6982\u7387\u5206\u5e03q<\/em>\u548cp<\/em>\u7684\u4e92\u6362\u5e76\u4e0d\u662f\u5bf9\u79f0\u7684\u3002\u76f8\u5bf9\u71b5\u7684AB\u9762\u521a\u597d\u5bf9\u5e94\u4e86\u751f\u6210\u6a21\u578b\u5728\u6570\u636e\u5efa\u6a21\u548c\u7406\u8bba\u8ba1\u7b97\u4e2d\u7684\u4e24\u79cd\u5e94\u7528\uff0c\u89c1\u4e0b\u8868\u3002\u9996\u5148\uff0c\u6700\u5c0f\u5316\u6570\u636e\u96c6<\/span>\u6240\u4ee3\u8868\u7684\u7ecf\u9a8c\u6982\u7387\u5206\u5e03\u548c\u6a21\u578b\u5206\u5e03\u4e4b\u95f4\u7684\u76f8\u5bf9\u71b5\uff0c\u7b49\u4ef7\u4e8e\u6700\u5c0f\u5316\u4ee5\u4e0b\u7684\u76ee\u6807\u51fd\u6570\uff1a<\/span><\/p>\n


<\/span><\/p>\n

<\/p>\n


<\/span><\/p>\n

\u56e0\u4e3aln p<\/em>(<\/span>x<\/em><\/strong>)<\/span>\u5728\u7edf\u8ba1\u5b66\u4e2d\u88ab\u79f0\u4e3a\u5bf9\u6570\u4f3c\u7136\u51fd\u6570\uff0c\u6700\u5c0f\u5316(2)\u5f0f\u4e5f\u88ab\u79f0\u4e3a\u6700\u5927\u4f3c\u7136\u4f30\u8ba1(maximum likelihood estimation)\u3002\u6ce8\u610f\uff0c\u8bad\u7ec3\u6570\u636e\u4ec5\u4ec5\u662f\u76ee\u6807\u6982\u7387\u5206\u5e03\u4e2d\u6709\u4ee3\u8868\u6027\u7684\u6837\u672c\uff0c\u800c\u4e0d\u662f\u76ee\u6807\u5206\u5e03\u672c\u8eab\u3002\u56e0\u6b64\uff0c\u8fc7\u5206\u5730\u4f18\u5316(2)\u5f0f\u4f1a\u5bfc\u81f4\u8fc7\u62df\u5408\u73b0\u8c61\u3002\u4ee5\u56fe1(a)\u4e3a\u4f8b\uff0c\u5982\u679c\u6a21\u578b\u5b66\u5230\u7684\u6982\u7387\u5206\u5e03\u4ec5\u4ec5\u5728\u84dd\u8272\u6570\u636e\u70b9\u4e0a\u975e\u96f6\uff0c\u5b83\u5c31\u53ea\u4f1a\u6b7b\u8bb0\u786c\u80cc\u8bad\u7ec3\u6570\u636e\uff0c\u800c\u4e0d\u80fd\u518d\u751f\u6210\u65b0\u7684\u6837\u672c\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u5176\u6b21\uff0c\u5728\u7edf\u8ba1\u7269\u7406\u7814\u7a76\u4e2d\u4eba\u4eec\u5f80\u5f80\u77e5\u9053\u4f53\u7cfb\u7684\u80fd\u91cf\u51fd\u6570E<\/em>(x<\/em><\/strong>)\uff0c\u800c\u9700\u8981\u5f97\u5230\u7684\u662f\u670d\u4ece\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u7684\u6837\u672cx<\/em><\/strong>\u4ee5\u53ca\u914d\u5206\u51fd\u6570Z<\/em>\u3002\u8fd9\u79cd\u573a\u666f\u548c\u6570\u636e\u9a71\u52a8\u7684\u6700\u5927\u4f3c\u7136\u4f30\u8ba1\u6070\u6070\u76f8\u53cd\u3002\u6b64\u65f6\uff0c\u53ef\u4ee5\u5c06\u6a21\u578b\u5206\u5e03p<\/em>(x<\/em><\/strong>)\u5f53\u4f5c\u53d8\u5206\u6982\u7387\u5206\u5e03\uff0c\u5e76\u6700\u5c0f\u5316\u5b83\u548c\u7269\u7406\u7cfb\u7edf\u7684\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u4e4b\u95f4\u7684\u76f8\u5bf9\u71b5\u3002\u8fd9\u7b49\u4ef7\u4e8e\u53d8\u5206\u81ea\u7531\u80fd\uff1a<\/span><\/p>\n


<\/span><\/p>\n

<\/p>\n


<\/span><\/p>\n

\u5176\u4e2d\u4e0d\u7b49\u53f7\u6765\u81ea\u4e8e\u76f8\u5bf9\u71b5\u7684\u975e\u8d1f\u6027<\/span>\u3002(3)\u5f0f\u4e2d\u4e24\u9879\u7684\u7269\u7406\u542b\u4e49\u5206\u522b\u662f\u53d8\u5206\u6982\u7387\u5206\u5e03\u7684\u71b5\u548c\u80fd\u91cf\u671f\u671b\u503c\u3002\u5f53\u4e0d\u7b49\u5f0f\u53d6\u7b49\u53f7\u65f6\uff0c\u53d8\u5206\u6982\u7387\u5206\u5e03\u7b49\u4e8e\u771f\u5b9e\u7684\u73bb\u5c14\u5179\u66fc\u5206\u5e03\uff0c\u53d8\u5206\u81ea\u7531\u80fd\u8ba1\u7b97\u4e5f\u5c31\u4e25\u683c\u5730\u89e3\u51b3\u4e86\u95ee\u9898\u3002\u6ce8\u610f\u5230\u53d8\u5206\u8ba1\u7b97\u5e76\u4e0d\u4f9d\u8d56\u4e8e\u4e8b\u5148\u51c6\u5907\u597d\u7684\u8bad\u7ec3\u6837\u672c\uff0c\u56e0\u4e3a\u6837\u672c\u53ef\u4ee5\u4ece\u751f\u6210\u6a21\u578b\u6982\u7387\u5206\u5e03<\/span>p<\/em>(<\/span>x<\/em><\/strong>)\u4e2d\u91c7\u6837\u5f97\u6765\u3002\u6b64\u5916\uff0c\u53d8\u5206\u8ba1\u7b97\u4e5f\u4e0d\u9700\u8981\u62c5\u5fc3\u8fc7\u62df\u5408\uff0c\u53d8\u5206\u81ea\u7531\u80fd\u8fd9\u4e2a\u76ee\u6807\u51fd\u6570\u503c\u8d8a\u4f4e\u8d8a\u597d<\/span><\/span>\u3002<\/span><\/span><\/p>\n


<\/span><\/p>\n

\u751f\u6210\u6a21\u578b\u7684\u6700\u5927\u4f3c\u7136\u4f30\u8ba1\u548c\u53d8\u5206\u81ea\u7531\u80fd\u8ba1\u7b97\u662f\u540c\u4e00\u679a\u786c\u5e01\u7684\u4e24\u9762<\/span><\/p>\n

<\/p>\n


<\/p>\n<\/section>\n

\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

<\/span><\/section>\n

<\/section>\n

\n
\n
\n
\n
\n

<\/section>\n

<\/section>\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n
\n

3. \u751f\u6210\u6a21\u578b\u901f\u89c8<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n
\u6211\u4eec\u4ece\u7269\u7406\u5b66\u7684\u89c6\u89d2\u4ecb\u7ecd\u56fe2\u6240\u793a\u7684\u51e0\u7c7b\u5e38\u89c1\u7684\u751f\u6210\u6a21\u578b\u3002\u8bfb\u8005\u5982\u679c\u60f3\u8981\u66f4\u52a0\u5168\u9762\u5730\u4e86\u89e3\u751f\u6210\u6a21\u578b\uff0c\u53ef\u4ee5\u53c2\u8003\u8fd1\u671f\u51fa\u7248\u7684\u6559\u79d1\u4e66[4\u20146]\u3002<\/span><\/section>\n

<\/section>\n

\u56fe2 \u56db\u7c7b\u751f\u6210\u6a21\u578b\u548c\u5b83\u4eec\u80cc\u540e\u5173\u952e\u7684\u6570\u5b66\u516c\u5f0f   (a)\u6269\u6563\u6a21\u578b\uff1a\u6717\u4e4b\u4e07\u65b9\u7a0b\uff1b(b)\u81ea\u56de\u5f52\u6a21\u578b\uff1a\u6761\u4ef6\u6982\u7387\u5206\u89e3\uff1b(c)\u6d41\u6a21\u578b\uff1a\u53d8\u91cf\u66ff\u6362\uff1b(d)\u53d8\u5206\u81ea\u7f16\u7801\u5668\uff1a\u53d8\u5206\u8d1d\u53f6\u65af\u63a8\u65ad<\/span><\/p>\n


<\/strong><\/p>\n

3.1 \u73bb\u5c14\u5179\u66fc\u673a\u548c\u6269\u6563\u6a21\u578b<\/span><\/strong><\/span><\/p>\n


<\/strong><\/p>\n

\u73bb\u5c14\u5179\u66fc\u673a\u662f\u4e00\u79cd\u7ecf\u5178\u7684\u3001\u7531\u7edf\u8ba1\u7269\u7406\u542f\u53d1\u7684\u751f\u6210\u6a21\u578b[7]\u3002\u5b83\u5c06\u6a21\u578b\u5206\u5e03\u8868\u8fbe\u4e3a\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u7684\u5f62\u5f0f<\/span> (\u4e0d\u59a8\u4ee4\u03b2<\/em>=1) <\/span>\uff1a <\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n

<\/span><\/section>\n
\u8fd9\u79cd\u5f62\u5f0f\u81ea\u7136\u5730\u5c06\u7edf\u8ba1\u7269\u7406\u7406\u8bba\u548c\u8ba1\u7b97\u65b9\u6cd5\u5f15\u5165\u6982\u7387\u5efa\u6a21\u3002\u5728\u7edf\u8ba1\u7269\u7406\u4e2d\uff0c\u53cd\u4f0a\u8f9b\u95ee\u9898\u4e5f\u662f\u8981\u4ece\u6784\u578b\u6837\u672c\u53cd\u63a8\u80fd\u91cf\u51fd\u6570\u7684\u5f62\u5f0f[8]<\/sup>\u3002\u4f8b\u5982\uff0c\u5728\u4f4e\u6e29\u4e0b\u94c1\u78c1\u8026\u5408\u7684\u4f0a\u8f9b\u6a21\u578b\u81ea\u65cb\u5168\u4e0a\u548c\u5168\u4e0b\u4e24\u4e2a\u4f4e\u80fd\u6784\u578b\u6700\u5bb9\u6613\u88ab\u91c7\u6837\u5230\uff0c\u8fd9\u5c31\u50cf\u662f\u94c1\u78c1\u4f0a\u8f9b\u6a21\u578b\u53ef\u4ee5\u201c\u8bb0\u4f4f\u201d\u5168\u9ed1\u548c\u5168\u767d\u7684\u56fe\u7247\u3002\u5982\u679c\u8c03\u8282\u4f0a\u8f9b\u6a21\u578b\u7684\u8026\u5408\u53c2\u6570\u5f97\u5230\u66f4\u591a\u7684\u4f4e\u80fd\u6784\u578b\uff0c\u5c31\u4f1a\u201c\u8bb0\u4f4f\u201d\u66f4\u591a\u7684\u56fe\u7247\uff0c\u4ece\u800c\u5b66\u4f1a\u66f4\u52a0\u590d\u6742\u7684\u6570\u636e\u6982\u7387\u5206\u5e03\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u73bb\u5c14\u5179\u66fc\u673a\u867d\u7136\u8ddf\u7269\u7406\u5b66\u5173\u7cfb\u7d27\u5bc6\uff0c\u4f46\u5e76\u4e0d\u662f\u4e00\u79cd\u597d\u7528\u7684\u751f\u6210\u6a21\u578b\u3002\u9996\u5148\uff0c\u6ce8\u610f\u5230(4)\u5f0f\u5206\u6bcd\u7684\u5f52\u4e00\u5316\u56e0\u5b50Z<\/em>\uff0c\u5373\u914d\u5206\u51fd\u6570\uff0c\u5728\u4e00\u822c\u60c5\u51b5\u4e0b\u662f\u96be\u4ee5\u8ba1\u7b97\u7684\u3002\u8fd9\u5c31\u7ed9\u73bb\u5c14\u5179\u66fc\u673a\u7684\u5b66\u4e60\u51fa\u4e86\u4e2a\u96be\u9898\u3002\u6b64\u5916\uff0c\u5c31\u7b97\u6211\u4eec\u80fd\u5b66\u5230\u51c6\u786e\u7684\u80fd\u91cf\u51fd\u6570\uff0c\u4ece\u6240\u5bf9\u5e94\u7684\u73bb\u5c14\u5179\u66fc\u5206\u5e03\u4e2d\u91c7\u6837\u4e5f\u5f80\u5f80\u662f\u56f0\u96be\u7684\u3002\u5728\u8fd9\u70b9\u4e0a\uff0c\u751f\u6210\u6a21\u578b\u91c7\u6837\u548c\u7edf\u8ba1\u7269\u7406\u8ba1\u7b97\u6a21\u62df\u7684\u7ecf\u9a8c\u662f\u4e00\u81f4\u7684\u3002\u4f8b\u5982\uff0c\u57fa\u4e8e\u80fd\u91cf\u51fd\u6570\u968f\u673a\u91c7\u6837\u53ef\u80fd\u4f1a\u9762\u4e34\u5f1b\u8c6b\u65f6\u95f4\u957f\u3001\u904d\u5386\u6027\u5dee\u7684\u95ee\u9898\uff0c\u8868\u73b0\u4e3a\u6837\u672c\u957f\u65f6\u95f4\u5361\u5728\u56fe1(b)\u6240\u793a\u7684\u67d0\u4e2a\u5206\u5e03\u6a21\u5f0f\u4e2d\u51fa\u4e0d\u6765\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u6269\u6563\u6a21\u578b\u907f\u514d\u4e86\u73bb\u5c14\u5179\u66fc\u673a\u5b66\u4e60\u548c\u91c7\u6837\u4e2d\u7684\u4e24\u4e2a\u96be\u9898\u3002\u9996\u5148\uff0c\u8003\u8651\u5bf9\u6570\u4f3c\u7136\u51fd\u6570\u5bf9\u4e8e\u8fde\u7eed\u6570\u636e\u7684\u68af\u5ea6\uff0c\u53ef\u4ee5\u7ed5\u5f00\u96be\u4ee5\u8ba1\u7b97\u7684\u914d\u5206\u51fd\u6570\uff1a<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n

<\/span><\/section>\n
\u8fd9\u4e2a\u91cf\u5728\u7edf\u8ba1\u5b66\u4e2d\u88ab\u79f0\u4e3a\u201c\u5f97\u5206\u51fd\u6570\u201d<\/span> (score function) <\/span>\uff0c\u5b83\u7684\u7269\u7406\u542b\u4e49\u5176\u5b9e\u5c31\u662f\u529b\u3002\u5728\u4ec5\u4ec5\u7ed9\u5b9a\u6570\u636e\u6837\u672c\u7684\u60c5\u51b5\u4e0b\uff0c\u4e00\u79cd\u5de7\u5999\u7684\u4f30\u8ba1\u5f97\u5206\u51fd\u6570\u7684\u529e\u6cd5\u662f\u5bf9\u6570\u636e\u7565\u52a0\u6270\u52a8\uff0c\u7136\u540e\u8ba1\u7b97\u6062\u590d\u529b\u3002\u56e0\u6b64\uff0c\u5229\u7528\u795e\u7ecf\u7f51\u7edc\u53bb\u5b66\u4e60\u5f0f(5)\u88ab\u79f0\u4e3a\u53bb\u566a\u5f97\u5206\u5339\u914d<\/span> (denoising score matching) <\/span>[9]\u3002\u5176\u6b21\uff0c\u4e3a\u4e86\u7f13\u89e3\u91c7\u6837\u7684\u56f0\u96be\uff0c\u501f\u9274\u6a21\u62df\u9000\u706b\u7b97\u6cd5\u7684\u7cbe\u795e[10\uff0c11]\uff0c\u4f7f\u7528\u566a\u58f0\u5f3a\u5ea6\u9010\u6e10\u51cf\u5c0f\u7684\u9000\u706b\u6717\u4e4b\u4e07\u52a8\u529b\u5b66\u8fc7\u7a0b\u6765\u91c7\u6837\u3002\u4e3a\u6b64\uff0c\u5728\u8bad\u7ec3\u6a21\u578b\u7684\u8fc7\u7a0b\u4e2d\uff0c\u76f8<\/span>\u5e94\u5730\u4f7f\u7528\u5f3a\u5ea6\u9010\u6e10\u589e\u52a0\u7684\u566a\u58f0\u9010\u6b65\u6270\u52a8\u6570\u636e\uff0c\u5e76\u8bad\u7ec3\u795e\u7ecf\u7f51\u7edc\u5b66\u4e60\u4e0d\u540c\u566a\u58f0\u6c34\u5e73\u6240\u5bf9\u5e94\u7684\u5f97\u5206\u51fd\u6570\u3002\u56e0\u4e3a\u9000\u706b\u6717\u4e4b\u4e07\u65b9\u7a0b\u7684\u91c7\u6837\u8fc7\u7a0b\u76f8\u5f53\u4e8e\u7269\u7406\u4e0a\u7684\u53cd\u5411\u6269<\/span><\/span>\u6563[12]\uff0c<\/span>\u56e0\u6b64\u8fd9\u7c7b\u6a21\u578b\u4e5f\u88ab\u79f0\u4e3a\u6269\u6563\u6a21\u578b\u3002\u6700\u8fd1\u51e0\u5e74\uff0c\u6269\u6563\u6a21\u578b\u5728\u56fe\u50cf\u3001\u89c6\u9891\u548c\u5206\u5b50\u7ed3\u6784\u7684\u751f\u6210\u4e2d\u5927\u653e\u5f02\u5f69\u3002\u4eceSora\u5230AlphaFold3\u4e2d\u90fd\u6709\u6269\u6563\u6a21\u578b\u7684\u5f71\u5b50\u3002<\/span><\/span><\/section>\n

<\/span><\/section>\n
\u7814\u7a76\u5fae\u89c2\u4e16\u754c\u7269\u8d28\u7ed3\u6784\u7684\u6807\u51c6\u624b\u6bb5\u4e4b\u4e00\u662f\u5206\u5b50\u52a8\u529b\u5b66\u6a21\u62df\uff0c\u5b83\u7684\u51fa\u53d1\u70b9\u662f\u7269\u7406\u4f53\u7cfb\u7684\u80fd\u91cf\u548c\u529b\u3002\u800c\u751f\u6210\u6a21\u578b\u5219\u7ed5\u8fc7\u4e86\u57fa\u4e8e\u7269\u7406\u539f\u7406\u7684\u8ba1\u7b97\u6a21\u62df\uff0c\u76f4\u63a5\u57fa\u4e8e\u81ea\u7136\u754c\u5df2\u6709\u6570\u636e\u751f\u6210\u65b0\u7684\u5fae\u89c2\u7269\u8d28\u7ed3\u6784\u3002\u6709\u610f\u601d\u7684\u662f\uff0c\u6269\u6563\u6a21\u578b\u7684\u751f\u6210\u8fc7\u7a0b\u548c\u5206\u5b50\u52a8\u529b\u5b66\u6a21\u62df\u795e\u4f3c\uff0c\u4f46\u53c8\u4e0d\u4e00\u6837\u3002\u56e0\u4e3a\u5f97\u5206\u51fd\u6570\u672a\u5fc5\u662f\u771f\u5b9e\u7684\u529b\uff0c\u6269\u6563\u6a21\u578b\u5728\u751f\u6210\u8fc7\u7a0b\u4e2d\u5141\u8bb8\u6284\u8fd1\u8def\uff0c\u7ecf\u8fc7\u975e\u7269\u7406\u7684\u4e2d\u95f4\u6784\u578b\u3002\u53cd\u800c\u57fa\u4e8e\u771f\u5b9e\u529b\u573a\u7684\u5206\u5b50\u6a21\u62df\u5f80\u5f80\u53d7\u9650\u4e8e\u5206\u5b50\u6784\u8c61\u7a7a\u95f4\u4e2d\u5d0e\u5c96\u7684\u52bf\u80fd\u9762\uff0c\u9762\u4e34\u91c7\u6837\u7684\u56f0\u96be\u3002<\/span><\/section>\n

<\/strong><\/section>\n
3.2 \u81ea\u56de\u5f52\u6a21\u578b<\/span><\/strong><\/span><\/section>\n

<\/span><\/section>\n
\u81ea\u56de\u5f52\u6a21\u578b\u5c06\u9ad8\u7ef4\u968f\u673a\u53d8\u91cfx<\/em><\/strong>\u7684\u8054\u5408\u6982\u7387\u5206\u5e03\u5206\u89e3\u6210\u4e00\u4e32\u4f4e\u7ef4\u53d8\u91cf\u7684\u6761\u4ef6\u6982\u7387\u7684\u8fde\u4e58\uff1a<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n

<\/span><\/section>\n
\u8fd9\u79cd\u5206\u89e3\u7684\u597d\u5904\u662f\u6bcf\u4e2a\u6761\u4ef6\u6982\u7387\u56e0\u5b50\u90fd\u662f\u4f4e\u7ef4\u7684\uff0c\u66f4\u5bb9\u6613\u5efa\u6a21\u548c\u8ba1\u7b97\u3002\u4f8b\u5982\uff0c\u4e00\u6bb5\u6587\u5b57x<\/em><\/strong>\u7684\u53ef\u80fd\u6027\u662f\u6307\u6570\u5927\u7684\uff0c\u800c\u6bcf\u4e2a\u8bcdxi<\/sub><\/em>\u7684\u53ef\u80fd\u6027\u4ec5\u4ec5\u662f\u8bcd\u6c47\u91cf\u90a3\u4e48\u5927\u3002\u53ea\u8981\u6bcf\u4e2a\u6761\u4ef6\u6982\u7387\u56e0\u5b50\u662f\u5f52\u4e00\u5316\u7684\uff0c\u5c31\u53ef\u4ee5\u4fdd\u8bc1\u8054\u5408\u6982\u7387\u5206\u5e03\u7684\u5f52\u4e00\u5316\u3002\u6b64\u5916\uff0c\u91c7\u6837\u8054\u5408\u6982\u7387\u751f\u6210\u65b0\u7684\u6587\u672c\u4e5f\u662f\u76f4\u63a5\u7684\uff1a\u53ef\u4ee5\u6309\u7167\u53d8\u91cf\u7684\u987a\u5e8f\u9010\u8bcd\u751f\u6210\uff0c\u6bcf\u6b65\u90fd\u57fa\u4e8e\u4e0a\u6587\u4fe1\u606f\u9884\u6d4b\u4e0b\u4e00\u4e2a\u8bcd\u7684\u6982\u7387\u3002\u56e0\u4e3a\u9884\u6d4b\u6761\u4ef6\u6982\u7387p<\/em>(y<\/em>|x<\/em><\/strong>)\u88ab\u79f0\u4f5c\u201c\u56de\u5f52\u201d\u4efb\u52a1\uff0c\u9010\u8bcd\u9884\u6d4b\u6574\u4e2a\u5e8f\u5217\u88ab\u79f0\u4f5c\u201c\u81ea\u201d\u56de\u5f52\u6a21\u578b\u3002\u539f\u5219\u4e0a\uff0c\u5f62\u5982(6)\u5f0f\u7684\u81ea\u56de\u5f52\u6982\u7387\u5206\u89e3\u5bf9\u4e8e\u4efb\u4f55\u53d8\u91cf\u987a\u5e8f\u90fd\u6210\u7acb\u3002\u4f46\u7531\u4e8e\u5728\u5b9e\u8df5\u4e2d\u901a\u5e38\u4f7f\u7528\u795e\u7ecf\u7f51\u7edc\u6765\u62df\u5408\u6761\u4ef6\u6982\u7387\uff0c\u5e76\u901a\u8fc7\u5171\u4eab\u4e0d\u540c\u6761\u4ef6\u6982\u7387\u56e0\u5b50\u7684\u795e\u7ecf\u7f51\u7edc\u53c2\u6570\u964d\u4f4e\u53c2\u6570\u91cf\uff0c\u4eba\u4eec\u5f80\u5f80\u5e0c\u671b\u8bbe\u8ba1\u4e00\u79cd\u53d8\u91cf\u987a\u5e8f\u4f7f\u5f97\u5206\u89e3\u540e\u7684\u6761\u4ef6\u6982\u7387\u5951\u5408\u6570\u636e\u7684\u771f\u5b9e\u7279\u5f81\uff0c\u4ece\u800c\u66f4\u5bb9\u6613\u5efa\u6a21\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u81ea\u56de\u5f52\u6a21\u578b\u5929\u7136\u9002\u5408\u8bed\u8a00\u6570\u636e\u5e8f\u5217\u6027\u7684\u7279\u70b9\uff0c\u6240\u4ee5\u5728\u81ea\u7136\u8bed\u8a00\u6982\u7387\u5efa\u6a21\u4e2d\u5e94\u7528\u5e7f\u6cdb\u3002\u8457\u540d\u7684GPT<\/span> (Generative Pre-Trained Transformer) <\/span>\u5c31\u662f\u8fd9\u6837\u4e00\u7c7b\u81ea\u56de\u5f52\u751f\u6210\u6a21\u578b\u3002\u5176\u4e2d\uff0cTransformer[13]\u662f\u4e00\u79cd\u5bf9\u6df1\u5ea6\u5b66\u4e60\u5f15\u64ce<\/span> (GPU\u548c\u53cd\u5411\u4f20\u64ad\u7b97\u6cd5) <\/span>\u90fd\u5f88\u53cb\u597d\u7684\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784\u3002\u5f53\u88ab\u7528\u4f5c\u81ea\u56de\u5f52\u8bed\u8a00\u6a21\u578b\u65f6\uff0cTransformer\u7684\u8f93\u5165\u662f\u8bed\u8a00\u5e8f\u5217\u4e2d\u6bcf\u4e00\u4e2a\u8bcd\u7684\u5411\u91cf\u8868\u793a\uff0c\u800c\u8f93\u51fa\u5219\u662f\u4e0b\u4e00\u4e2a\u8bcd\u7684\u6982\u7387\u8868\u3002\u5e76\u4e14\uff0c\u901a\u8fc7\u63a9\u7801\u64cd\u4f5c\u4f7f\u5f97\u8f93\u51fa\u76f8\u5bf9\u4e8e\u8f93\u5165\u7684\u96c5\u53ef\u6bd4\u77e9\u9635\u662f\u4e0b\u4e09\u89d2\u5f62\u7684\uff0c\u4ee5\u4fdd\u8bc1\u6a21\u578b\u6982\u7387\u7684\u81ea\u56de\u5f52\u6027\u8d28\u3002Transformer\u5584\u4e8e\u628a\u63e1\u8bed\u8a00\u6570\u636e\u4e2d\u7684\u957f\u7a0b\u5173\u8054\uff0c\u662f\u5f53\u4e0b\u4e3b\u6d41\u7684\u8bed\u8a00\u6a21\u578b\u67b6\u6784\u3002\u4e0d\u4ec5\u5982\u6b64\uff0c\u81ea\u56de\u5f52\u6a21\u578b\u7684\u5e94\u7528\u573a\u666f\u4e5f\u5b8c\u5168\u53ef\u4ee5\u662f\u56fe\u50cf\u3001\u68cb\u5c40\uff0c\u6216\u8005\u662f\u4f0a\u8f9b\u6a21\u578b\u3002\u53ea\u8981\u5bf9\u6570\u636e\u53d8\u91cf\u6307\u5b9a\u987a\u5e8f\uff0c\u5c31\u53ef\u4ee5\u7528\u81ea\u56de\u5f52\u6a21\u578b\u5bf9\u6570\u636e\u53d8\u91cf\u7684\u8054\u5408\u6982\u7387\u5efa\u6a21\uff0c\u4ece\u800c\u5229\u7528Trans\u2010former\u5f3a\u5927\u7684\u5b66\u4e60\u80fd\u529b\u903c\u8fd1\u6570\u636e\u7684\u8054\u5408\u6982\u7387\u5206\u5e03\uff0c\u5e76\u751f\u6210\u65b0\u7684\u6570\u636e\u6837\u672c\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u81ea\u56de\u5f52\u6a21\u578b\u7684\u7a0b\u5e8f\u5b9e\u73b0\u5e76\u4e0d\u590d\u6742\u3002\u4ec5\u4ec5\u53ea\u752860\u884c\u7684Python\u4ee3\u7801[14]\u5c31\u53ef\u4ee5\u5b8c\u5168\u590d\u73b0OpenAI\u5f00\u53d1\u7684GPT2\u8bed\u8a00\u6a21\u578b[15]\u7684\u5168\u90e8\u63a8\u65ad\u8ba1\u7b97\u3002Ond\u0159ej \u010cert\u00edk\u66fe\u662f\u7f8e\u56fd\u6d1b\u65af\u963f\u62c9\u83ab\u65af\u56fd\u5bb6\u5b9e\u9a8c\u5ba4\u91cc\u4e00\u540d\u4ece\u4e8b\u8ba1\u7b97\u7269\u7406\u7814\u7a76\u7684\u79d1\u5b66\u5bb6\uff0c\u4ed6\u770b\u5230\u4e86GPT2\u7684\u201c60\u884c\u201d\u4ee3\u7801\u5b9e\u73b0\u5fcd\u4e0d\u4f4f\u52a8\u624b\u8bd5\u4e86\u4e00\u628a\uff0c\u8fd8\u901a\u8fc7\u628a\u4ee3\u7801\u6539\u5199\u6210Fortran\u8bed\u8a00\u5b9e\u73b0\u4e86\u52a0\u901f\u3002\u5b8c\u6210\u8fd9\u4e9b\u5b9e\u9a8c\u4e4b\u540e\uff0c\u010cert\u00edk\u5174\u594b\u5730\u5728\u4ed6\u7684\u535a\u5ba2[16]\u4e2d\u5199\u9053\uff1a\u201cGPT2\u770b\u8d77\u6765\u5c31\u50cf\u4e00\u6bb5\u5178\u578b\u7684\u8ba1\u7b97\u7269\u7406\u4ee3\u7801\uff0c\u548c\u6211\u5728\u6574\u4e2a\u804c\u4e1a\u751f\u6daf\u4e2d\u5f00\u53d1\u548c\u7ef4\u62a4\u7684\u8bb8\u591a\u4ee3\u7801\u7c7b\u4f3c\u201d\u3002\u201c\u6e90\u7801\u9762\u524d\uff0c\u4e86\u65e0\u79d8\u5bc6\u201d[17]\uff0c\u8bf7\u611f\u5174\u8da3\u7684\u8bfb\u8005\u4e5f\u53bb\u9605\u8bfb\u3001\u8fd0\u884c\u3001\u8c03\u8bd5\u4e00\u6bb5\u81ea\u56de\u5f52\u8bed\u8a00\u6a21\u578b\u7684\u6e90\u4ee3\u7801\uff0c\u4e00\u5b9a\u4f1a\u8ba9\u4f60\u5bf9\u8bed\u8a00\u6a21\u578b\u4ea7\u751f\u4e0d\u4e00\u6837\u7684\u4f53\u4f1a\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5f53\u81ea\u56de\u5f52\u8bed\u8a00\u6a21\u578b\u8d8a\u53d8\u8d8a\u5927\u4e4b\u540e\uff0c\u4eba\u4eec\u89c2\u5bdf\u5230\u4e24\u9879\u6709\u8da3\u7684\u73b0\u8c61\uff1a\u201c\u80fd\u529b\u6d8c\u73b0\u201d\u548c\u201c\u6807\u5ea6\u7387\u201d\u3002\u9996\u5148\uff0c\u6a21\u578b\u4f3c\u4e4e\u5728\u67d0\u4e00\u89c4\u6a21\u7a81\u7136\u83b7\u5f97\u67d0\u79cd\u80fd\u529b[18]\u3002\u8fd9\u96be\u514d\u8ba9\u4eba\u4eec\u4ea7\u751f\u4e00\u4e9b\u6d6a\u6f2b\u7684\u8054\u60f3\uff0c\u4f8b\u5982\u5c06\u8bed\u8a00\u6a21\u578b\u7684\u80fd\u529b\u6d8c\u73b0\u4e0e\u76f8\u53d8\u73b0\u8c61\u8054\u7cfb\u8d77\u6765\uff0c\u6216\u8005\u62c5\u5fc3\u5c06\u6765\u6a21\u578b\u4e5f\u4f1a\u7a81\u7136\u83b7\u5f97\u4eba\u7c7b\u65e0\u6cd5\u638c\u63a7\u7684\u80fd\u529b\u3002\u6b64\u5916\uff0c\u4eba\u4eec\u89c2\u5bdf\u5230\u5f53\u6570\u636e\u3001\u6a21\u578b\u548c\u7b97\u529b\u540c\u6b65\u589e\u52a0\u65f6\uff0c\u8bad\u7ec3\u6240\u5f97\u5230\u7684\u5bf9\u6570\u4f3c\u7136\u76ee\u6807\u51fd\u6570\u6309\u7167\u5e42\u5f8b\u964d\u4f4e\u3002\u8fd9\u79cd\u6807\u5ea6\u884c\u4e3a\u8de8\u8d8a\u4e86\u51e0\u4e2a\u6570\u91cf\u7ea7\uff0c\u5e76\u4e14\u4e0d\u4f9d\u8d56\u4e8e\u81ea\u56de\u5f52\u8bed\u8a00\u6a21\u578b\u5177\u4f53\u5b9e\u73b0\u7ec6\u8282\u3002\u5f15\u7528\u8bba\u6587[19]\u7684\u539f\u8bdd\uff1a\u201c\u5982\u679c\u80fd\u627e\u5230\u4e00\u4e2a\u7406\u8bba\u6846\u67b6\uff0c\u53ef\u4ee5\u63a8\u5bfc\u51fa\u8fd9\u4e9b\u6807\u5ea6\u5173\u7cfb\uff0c\u90a3\u5c06\u662f\u4ee4\u4eba\u5174\u594b\u7684\uff01\u90a3\u5c31\u50cf\u662f\u4e3a\u6211\u4eec\u6240\u89c2\u5bdf\u5230\u7684\u2018\u70ed\u529b\u5b66\u2019\u884c\u4e3a\u627e\u5230\u4e86\u2018\u7edf\u8ba1\u529b\u5b66\u2019\u89e3\u91ca\u201d\u3002\u201c\u6d8c\u73b0\u73b0\u8c61\u201d\u548c\u201c\u6807\u5ea6\u7387\u201d\u8fd9\u4e24\u4e2a\u73b0\u8c61\u770b\u8d77\u6765\u76f8\u5411\u800c\u884c\uff0c\u4f46\u5b83\u4eec\u90fd\u6210\u4e3a\u4e86\u8ffd\u6c42\u201c\u5927\u201d\u8bed\u8a00\u6a21\u578b\u7684\u6838\u5fc3\u9a71\u52a8\u529b\u3002\u8c03\u548c\u5176\u4e2d\u77db\u76fe\u7684\u5173\u952e\u4f3c\u4e4e\u5728\u4e8e\u5efa\u7acb\u5927\u8bed\u8a00\u6a21\u578b\u80fd\u529b\u548c\u635f\u5931\u51fd\u6570\u4e4b\u95f4\u76f4\u63a5\u7684\u8054\u7cfb[20\uff0c21]\u3002\u65e0\u8bba\u5982\u4f55\uff0c\u5927\u8bed\u8a00\u6a21\u578b\u4e2d\u6240\u89c2\u5bdf\u5230\u7684\u201c\u80fd\u529b\u6d8c\u73b0\u201d\u548c\u201c\u6807\u5ea6\u7387\u201d\u662f\u503c\u5f97\u7269\u7406\u5b66\u5bb6\u601d\u8003\u7684\u95ee\u9898\u3002<\/span><\/section>\n

<\/strong><\/section>\n
3.3 \u6d41\u6a21\u578b<\/span><\/strong><\/span><\/section>\n

<\/section>\n
\u6d41\u6a21\u578b[22]\u901a\u8fc7\u53ef\u9006\u7684\u795e\u7ecf\u7f51\u7edc\u5b9e\u73b0\u6570\u636e\u5230\u9690\u53d8\u91cf\u7684\u6620\u5c04x<\/em><\/strong>\u2194z<\/em><\/strong>\uff0c\u4ece\u800c\u53c2\u6570\u5316\u6982\u7387\u5206\u5e03\uff1a<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n

<\/span><\/section>\n
\u8fd9\u91cc\u6e90\u5206\u5e03q<\/em>(z<\/em><\/strong>)\u901a\u5e38\u88ab\u9009\u53d6\u4e3a\u5f52\u4e00\u5316\u56e0\u5b50\u5e76\u4e14\u4fbf\u4e8e\u91c7\u6837\u7684\u7b80\u5355\u6982\u7387\u5206\u5e03\uff0c\u4f8b\u5982\u6b63\u6001\u5206\u5e03\u3002\u901a\u8fc7\u5bf9\u6e90\u5206\u5e03\u4e2d\u7684\u6837\u672c\u505a\u53d8\u6362\uff0c\u53ef\u4ee5\u76f4\u63a5\u751f\u6210\u670d\u4ece\u6d41\u6a21\u578b\u6982\u7387\u5206\u5e03\u7684\u6570\u636e\u6837\u672c\u3002\u795e\u7ecf\u7f51\u7edc\u53d8\u91cf\u66ff\u6362\u7684\u4f5c\u7528\u662f\u5728\u670d\u4ece\u6b63\u6001\u5206\u5e03\u7684\u6837\u672c\u4e2d\u5f15\u5165\u5173\u8054\u3002(7)\u5f0f\u4e2d\u7684\u96c5\u53ef\u6bd4\u884c\u5217\u5f0f\u4fdd\u8bc1\u4e86\u6d41\u6a21\u578b\u6982\u7387\u5206\u5e03\u7684\u5f52\u4e00\u5316\u3002<\/span><\/section>\n

<\/span><\/section>\n
OpenAI\u5f00\u53d1\u8fc7\u4e00\u4e2a\u7528\u4e8e\u56fe\u50cf\u751f\u6210\u7684\u6d41\u6a21\u578bGlow[23]\u3002\u9664\u4e86\u76f4\u63a5\u751f\u6210\u81ea\u7136\u7684\u4eba\u8138\u56fe\u7247\u4e4b\u5916\uff0cGlow\u6a21\u578b\u8fd8\u53ef\u4ee5\u751f\u6210\u4e24\u5f20\u4eba\u8138\u56fe\u7247\u4e4b\u95f4\u7684\u201c\u5e73\u5747\u4eba\u8138\u201d\u3002\u4e3a\u6b64\uff0c\u5148\u5c06\u4e24\u5f20\u56fe\u7247\u5206\u522b\u6620\u5c04\u5230\u9690\u53d8\u91cf\u7a7a\u95f4\uff0c\u518d\u5bf9\u9690\u53d8\u91cf\u63d2\u503c\uff0c\u6700\u540e\u5c06\u63d2\u503c\u7ed3\u679c\u6620\u5c04\u56de\u50cf\u7d20\u7a7a\u95f4\u5f97\u5230\u6700\u540e\u7ed3\u679c\u3002\u53ef\u4ee5\u60f3\u8c61\uff0c\u5982\u679c\u4e0d\u5229\u7528\u9690\u53d8\u91cf\u5206\u5e03\u7b80\u5355\u4fbf\u4e8e\u63d2\u503c\u7684\u7279\u70b9\uff0c\u800c\u662f\u76f4\u63a5\u5c06\u4e24\u5f20\u4eba\u8138\u56fe\u7247\u7684\u50cf\u7d20\u53d6\u5e73\u5747\uff0c\u5219\u4e0d\u80fd\u5f97\u5230\u4e00\u5f20\u81ea\u7136\u7684\u4eba\u8138\u56fe\u7247\u3002\u6d41\u6a21\u578b\u53ef\u4ee5\u8868\u8fbe\u6570\u5b66\u548c\u7269\u7406\u7814\u7a76\u4e2d\u5e38\u89c1\u7684\u5085\u91cc\u53f6\u53d8\u6362\u3001\u5c0f\u6ce2\u53d8\u6362\u3001\u6b63\u5219\u53d8\u6362\u7b49\u3002\u4e0d\u4ec5\u5982\u6b64\uff0c\u6d41\u6a21\u578b\u8fd8\u5c06\u8fd9\u4e9b\u53d8\u6362\u63a8\u5e7f\u5230\u4e86\u975e\u7ebf\u6027\u3001\u53ef\u5b66\u4e60\u7684\u60c5\u51b5\u3002\u4f8b\u5982\uff0c\u795e\u7ecf\u7f51\u7edc\u91cd\u6b63\u5316\u7fa4\u53d8\u6362[24]\u548c\u6b63\u5219\u53d8<\/span>\u6362[25]\u901a<\/span>\u8fc7\u5b66\u4e60\u6d41\u6a21\u578b\u6765\u8bc6\u522b\u591a\u4f53\u7269\u7406\u7cfb\u7edf\u4e2d\u975e\u7ebf\u6027\u7684\u96c6\u4f53\u53d8\u91cf\u548c\u6162\u81ea\u7531\u5ea6\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u4e3a\u4e86\u8fdb\u4e00\u6b65\u63ed\u793a\u6d41\u6a21\u578b\u80cc\u540e\u7684\u7269\u7406\u5185\u6db5\uff0c\u53ef\u4ee5\u8003\u8651\u516c\u5f0f(7)\u7684\u8fde\u7eed\u65f6\u95f4\u6781\u9650\u3002\u8003\u8651\u7528\u65e0\u7a77\u5c0f\u7684\u53d8\u91cf\u66ff\u6362<\/span>\uff0c\u518d\u8003\u8651<\/span>\u03c4<\/span>\u21920\u7684\u8fde\u7eed\u65f6\u95f4\u6781\u9650\uff0c\u53ef\u4ee5\u5f97\u5230\u4e00\u4e2a\u5173\u4e8e\u542b\u65f6\u6982\u7387\u5bc6\u5ea6\u7684\u8fde\u7eed\u6027\u65b9<\/span><\/span>\u7a0b[26\uff0c27]<\/span>\uff1a<\/span><\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n

<\/span><\/section>\n
\u5176\u4e2d\u7684\u542b\u65f6\u6982\u7387\u5bc6\u5ea6\u5728\u8d77\u59cb\u548c\u7ec8\u6b62\u65f6\u523b\u5206\u522b\u5bf9\u5e94\u4e8e\u6e90\u5206\u5e03\u548c\u6a21\u578b\u6982\u7387\u5206\u5e03\u3002\u8fd9\u7ed9\u6df1\u5c42\u795e\u7ecf\u7f51\u7edc\u4e00\u4e2a\u7269\u7406\u56fe\u50cf\uff1a\u5b83\u662f\u521d\u6001\u6982\u7387\u5206\u5e03\u6d41\u5411\u672b\u6001\u6982\u7387\u5206\u5e03\u7684\u7ba1\u9053\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u8fde\u7eed\u89c6\u89d2\u8fd8\u66f4\u597d\u5730\u63ed\u793a\u4e86\u6d41\u6a21\u578b\u548c\u6269\u6563\u6a21\u578b\u7684\u5173\u7cfb\u3002\u524d\u6587\u63d0\u5230\uff0c\u6269\u6563\u6a21\u578b\u7684\u751f\u6210\u8fc7\u7a0b\u7528\u5230\u4e86\u9000\u706b\u6717\u4e4b\u4e07\u65b9\u7a0b\uff0c\u5176\u6982\u7387\u5bc6\u5ea6\u6f14\u5316\u9075\u5faa\u798f\u514b\u2014\u666e\u6717\u514b\u65b9\u7a0b<\/span> \u5176\u4e2df <\/em><\/strong>\u662f(5)\u5f0f\u4e2d\u4ecb\u7ecd\u7684\u5f97\u5206\u51fd\u6570\u3002\u53ea\u8981\u4ee4(8)\u5f0f\u4e2d\u7684<\/span><\/span>[28\uff0c29]\uff0c\u5c31\u80fd\u53d1\u73b0\u4e24\u7c7b\u6a21\u578b\u5177\u6709\u7edf\u4e00\u7684\u6570\u5b66\u5f62\u5f0f\u3002\u8fd9\u8bf4\u660e\u5176\u5b9e\u4efb\u4f55\u6269\u6563\u6a21\u578b\u80cc\u540e\u90fd\u9690\u85cf\u4e86\u4e00\u4e2a\u6d41\u6a21\u578b\u3002\u56e0\u6b64\uff0c\u54ea\u6015\u662f\u5728\u6269\u6563\u6a21\u578b\u5982\u65e5\u4e2d\u5929\u7684\u65f6\u5019\uff0c\u4e5f\u6709\u4e00\u5c0f\u6ce2\u6d41\u6a21\u578b\u7684\u4fe1\u5f92\u575a\u4fe1\uff0c\u53ea\u8981\u627e\u5230\u6b63\u786e\u7684\u8bad\u7ec3\u65b9\u5f0f\uff0c\u6d41\u6a21\u578b\u53ef\u4ee5\u505a\u5f97\u4e00\u6837\u597d\uff0c\u751a\u81f3\u66f4\u597d\u3002\u7ec8\u4e8e\uff0c2022\u5e74\u7684\u79cb\u5929\uff0c\u51e0\u7bc7\u5de5\u4f5c[30\u201432]\u51e0\u4e4e\u540c\u65f6\u53d1\u73b0\u4e86\u4e00\u79cd\u65b0\u7684\u8bad\u7ec3\u8fde\u7eed\u65f6\u95f4\u6d41\u6a21\u578b\u7684\u65b9\u6cd5\uff1a\u6d41\u5339\u914d<\/span> (flow matching) <\/span>\u3002\u6d41\u5339\u914d\u65b9\u6cd5\u53d7\u5230\u4e86\u5f97\u5206\u5339\u914d\u65b9\u6cd5\u7684\u542f\u53d1\uff0c\u4f46\u662f\u5b83\u6240\u8bad\u7ec3\u5f97\u5230\u7684\u6d41\u6a21\u578b\u53ef\u4ee5\u6bd4\u6269\u6563\u6a21\u578b\u66f4\u52a0\u7b80\u6d01\u3001\u7075\u6d3b\u3001\u9ad8\u6548\uff0c\u5bf9\u4e8e\u8ffd\u6c42\u5b9a\u91cf\u7cbe\u786e\u7684\u79d1\u5b66\u95ee\u9898\u5c24\u4e3a\u6709\u7528\u3002\u4f8b\u5982\uff0c\u8ba1\u7b97\u4f53\u7cfb\u5728\u4e0d\u540c\u6784\u8c61\u4e0b\u7684\u81ea\u7531\u80fd\u5dee\u5728\u5f88\u591a\u7269\u7406\u3001\u5316\u5b66\u548c\u751f\u7269\u7684\u5e94\u7528\u4e2d\u90fd\u975e\u5e38\u5173\u952e\u3002\u4f46\u662f\u4f20\u7edf\u8ba1\u7b97\u65b9\u6cd5\u5f80\u5f80\u4f9d\u8d56\u4e8e\u4eba\u4e3a\u8bbe\u8ba1\u67d0\u79cd\u8def\u5f84\uff0c\u4f7f\u5f97\u5728\u8ba1\u7b97\u6a21\u62df\u8fc7\u7a0b\u4e2d\u6784\u8c61\u80fd\u591f\u8fde\u63a5\u8d77\u6765\u3002\u800c\u4f7f\u7528\u6d41\u5339\u914d\u65b9\u6cd5\u4f30\u8ba1\u6784\u8c61\u4e4b\u95f4\u7684\u81ea\u7531<\/span>\u80fd\u5dee[33]\uff0c\u4ec5<\/span>\u4ec5\u9700\u8981\u4e0d\u540c\u6784\u8c61\u4e0b\u5404\u81ea\u7684\u6570\u636e\u6837\u672c\uff0c\u5177\u6709\u5f88\u5f3a\u7684\u901a\u7528\u6027\u3002<\/span><\/section>\n

<\/strong><\/section>\n
3.4 \u53d8\u5206\u81ea\u7f16\u7801\u5668<\/span><\/strong><\/section>\n

<\/span><\/section>\n
\u81ea\u7f16\u7801\u5668\u7684\u57fa\u672c\u60f3\u6cd5\u662f\u628a\u6570\u636e\u9001\u8fdb\u4e00\u4e2a\u6709\u74f6\u9888\u7684\u795e\u7ecf\u7f51\u7edc\u5e76\u5c3d\u91cf\u91cd\u6784\u5b83\u4eec\u3002\u7ecf\u8fc7\u8bad\u7ec3\u540e\uff0c\u7f51\u7edc\u7684\u524d\u534a\u90e8\u5206\u662f\u4e00\u4e2a\u7f16\u7801\u5668\uff0c\u5b83\u5c06\u6570\u636ex<\/em><\/strong>\u8f6c\u6362\u6210\u9690\u53d8\u91cfz<\/em><\/strong>\u3002\u7f51\u7edc\u7684\u540e\u534a\u90e8\u5206\u662f\u4e00\u4e2a\u89e3\u7801\u5668\uff0c\u5b83\u5c06\u9690\u53d8\u91cfz<\/em><\/strong>\u53d8\u6362\u4e3a\u6570\u636ex<\/em><\/strong>\u3002\u795e\u7ecf\u7f51\u7edc\u4e2d\u5b58\u5728\u74f6\u9888\u901a\u5e38\u610f\u5473\u7740\u9690\u53d8\u91cf\u7684\u7ef4\u5ea6\u6bd4\u539f\u59cb\u6570\u636e\u66f4\u4f4e\uff0c\u8fd9\u4f1a\u8feb\u4f7f\u795e\u7ecf\u7f51\u7edc\u4e0d\u80fd\u591f\u7b80\u5355\u5730\u628a\u8f93\u5165\u590d\u5236\u5230\u8f93\u51fa\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u4e3a\u4e86\u8ba1\u7b97\u81ea\u7f16\u7801\u5668\u6240\u8868\u8fbe\u7684\u6982\u7387\uff0c\u9700\u8981\u5728\u6570\u636e\u548c\u9690\u53d8\u91cf\u7684\u8054\u5408\u6982\u7387\u5206\u5e03\u4e2d\u79ef\u6389\u9690\u53d8\u91cf\uff1a<\/span>\u3002\u53ef\u662f\uff0c\u5bf9\u4e8e\u9690\u53d8\u91cf\u79ef\u5206\u5e76\u4e0d\u597d\u7b97\uff0c\u8fd9\u548c\u8ba1\u7b97\u88681\u4e2d\u7684\u914d\u5206\u51fd\u6570\u548c\u8fb9\u9645\u4f3c\u7136\u7684\u96be\u5ea6\u7c7b\u4f3c\u3002\u5e78\u8fd0\u7684\u662f\uff0c\u6ce8\u610f\u5230\u4e0e(3)\u5f0f\u7c7b\u4f3c\u7684\u53d8\u5206\u81ea\u7531\u80fd\u539f\u7406\uff0c\u6211\u4eec\u6709\uff1a<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n

<\/span><\/section>\n
\u56e0\u6b64\uff0c\u53ef\u4ee5\u901a\u8fc7\u6700\u5c0f\u5316\u5f0f(9)\u6765\u8fd1\u4f3c\u5730\u6700\u5c0f\u5316\u8d1f\u5bf9\u6570\u4f3c\u7136\u51fd\u6570\u3002\u8fd9\u91cc\u53d8\u5206\u5206\u5e03q<\/em>(z<\/strong><\/em>|x<\/em><\/strong>)\u4ee3\u8868\u4e86\u4ece\u6570\u636ex<\/em><\/strong>\u63a8\u65ad\u9690\u53d8\u91cfz<\/em><\/strong>\u7684\u7f16\u7801\u5668\u3002\u4ec5\u5f53(9)\u5f0f\u53d6\u5230\u7b49\u53f7\u65f6\uff0cq<\/em>(<\/span>z<\/strong><\/em>|<\/span>x<\/em><\/strong>)<\/span>\u4e25\u683c\u7b49\u4e8e\u8d1d\u53f6\u65af\u540e\u9a8c\u6982\u7387p<\/em>(z<\/em><\/strong>|x<\/em><\/strong>)=<\/span>\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u8054\u5408\u6982\u7387\u5206\u5e03\u4e5f\u53ef\u4ee5\u5199\u6210<\/span>\u3002\u8fd9\u91ccp<\/em>(z<\/em><\/strong>)\u662f\u9690\u53d8\u91cf\u7684\u5148\u9a8c\u5206\u5e03\uff0c\u4e00\u822c\u88ab\u9009\u53d6\u4e3a\u7b80\u5355\u7684\u6982\u7387\u5206\u5e03\uff0c\u800cp<\/em>(x<\/em><\/strong>|z<\/em><\/strong>)\u662f\u89e3\u7801\u5668\uff0c\u76f8\u5f53\u4e8e\u4e00\u4e2a\u4ece\u4f4e\u7ef4\u9690\u53d8\u91cf\u7a7a\u95f4\u51fa\u53d1\u751f\u6210\u9ad8\u7ef4\u6570\u636e\u7684\u751f\u6210\u6a21\u578b\u3002(9)\u5f0f\u8fd9\u6837\u7684\u4e0d\u7b49\u5f0f\u662f\u53d8\u5206\u81ea\u7f16\u7801\u5668\u540d\u5b57\u4e2d\u201c\u53d8\u5206\u201d\u4e00\u8bcd\u7684\u6765\u6e90\u3002\u88682\u603b\u7ed3\u4e86\u53d8\u5206\u81ea\u7f16\u7801\u5668\u548c\u53d8\u5206\u81ea\u7531\u80fd(3)\u5f0f\u7684\u5bf9\u5e94\u5173\u7cfb\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u88682 \u53d8\u5206\u81ea\u7f16\u7801\u5668\u4e0e\u53d8\u5206\u81ea\u7531\u80fd\u4e4b\u95f4\u7684\u5bf9\u5e94\u5173\u7cfb<\/span><\/section>\n
<\/section>\n

<\/span><\/section>\n
\u53d8\u5206\u81ea\u7f16\u7801\u5668\u7684\u4f4e\u7ef4\u9690\u53d8\u91cf\u7a7a\u95f4\u7ed9\u4e0d\u5c11\u79d1\u5b66\u5e94\u7528\u63d0\u4f9b\u4e86\u4fbf\u5229\u3002\u4f8b\u5982\uff0c\u5c06\u5316\u5b66\u5206\u5b50\u7f16\u7801\u5230\u5316\u5b66\u9690\u53d8\u91cf\u7a7a<\/span>\u95f4[34]\uff0c<\/span>\u518d\u5229\u7528\u5bf9\u4e8e\u9690\u53d8\u91cf\u7684\u68af\u5ea6\u4e0b\u964d\u6765\u4f18\u5316\u5206\u5b50\u6027\u8d28\uff0c\u4e4b\u540e\u901a\u8fc7\u89e3\u7801\u5668\u76f4\u63a5\u751f\u6210\u5206\u5b50\u6784\u578b\u3002\u8fd9\u4e2a\u5de5\u4f5c\u542f\u53d1\u4e86\u5927\u91cf\u5173\u4e8e\u7269\u8d28\u5fae\u89c2\u7ed3\u6784\u7684\u751f\u6210\u6a21\u578b\u7814\u7a76\u3002<\/span><\/section>\n

<\/strong><\/section>\n
3.5 \u5c0f\u7ed3<\/span><\/strong><\/section>\n

<\/span><\/section>\n
\u751f\u6210\u6a21\u578b\u8fdc\u4e0d\u6b62\u4e0a\u9762\u4ecb\u7ecd\u7684\u8fd9\u4e9b\u3002\u4f8b\u5982\uff0c\u7b14\u8005\u8fd8\u66fe\u4e0e\u5408\u4f5c\u8005\u63d0\u51fa\u8fc7\u201c\u73bb\u6069\u673a\u201d\uff0c\u4e00\u79cd\u91cf\u5b50\u6ce2\u51fd\u6570\u6982\u7387\u8be0\u91ca\u6240\u542f\u53d1\u7684\u751f\u6210\u6a21\u578b\u3002\u5728\u751f\u6210\u6a21\u578b\u4e0d\u957f\u7684\u5386\u53f2\u4e2d\uff0c\u5e76\u4e0d\u7f3a\u4e4f\u201c\u60ca\u8273\u9006\u88ad\u201d\u7684\u4f20\u5947\u6545\u4e8b\u3002\u4e5f\u8bb8\u4e0b\u4e00\u4e2a\u201c\u7206\u6b3e\u201d\u7684\u751f\u6210\u6a21\u578b\u5c31\u6765\u81ea\u672c\u6587\u7684\u8bfb\u8005\u3002\u9664\u4e86\u63d0\u51fa\u65b0\u6a21\u578b\uff0c\u8d70\u5411\u7edf\u4e00\u4e5f\u662f\u751f\u6210\u6a21\u578b\u53d1\u5c55\u7684\u4e00\u5927\u8d8b\u52bf\u3002\u5176\u5b9e\uff0c\u4e0a\u9762\u4ecb\u7ecd\u7684\u6269\u6563\u6a21\u578b\u3001\u6d41\u6a21\u578b\u548c\u53d8\u5206\u81ea\u7f16\u7801\u5668\u53ef\u4ee5\u7edf\u4e00\u5730\u88ab\u770b\u4f5c\u662f\u4e00\u7c7b\u6a21\u578b\uff0c\u5176\u6838\u5fc3\u662f\u6982\u7387\u5bc6\u5ea6\u7684\u8f93\u8fd0<\/span> (transportation) <\/span>[35]\u3002\u56e0\u6b64\uff0c\u5f53\u4e0b\u6700\u6210\u529f\u7684\u751f\u6210\u6a21\u578b\u80cc\u540e\u7684\u673a\u5236\u53ea\u6709\u4e24\u79cd\uff1a\u8f93\u8fd0\u548c\u81ea\u56de\u5f52\u3002\u90fd\u662f\u8fd9\u4e24\u79cd\u751f\u6210\u673a\u5236\u80cc\u540e\u7684\u9053\u7406\u201c\u79ef\u8dec\u6b65\uff0c\u884c\u5343\u91cc\u201d\uff0c\u901a\u8fc7\u4e00\u6b65\u6b65\u7684\u8fed\u4ee3\u79ef\u7d2f\u751f\u6210\u6837\u672c\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u54ea\u79cd\u751f\u6210\u6a21\u578b\u6700\u5389\u5bb3\uff1f\u8fd9\u6709\u70b9\u50cf\u5728\u95ee\u8c01\u5728\u5175\u5668\u8c31\u4e0a\u6392\u540d\u7b2c\u4e00\u3002\u5728\u6570\u636e\u91cf\u4e0d\u591a\u65f6\uff0c\u4e00\u6761\u9996\u8981\u7684\u7ecf\u9a8c\u6cd5\u5219<\/span> (\u6709\u4f8b\u5916\uff01) <\/span>\u662f\u770b\u95ee\u9898\u7684\u7279\u70b9\uff1a\u8981\u5904\u7406\u7684\u662f\u79bb\u6563\u8fd8\u662f\u8fde\u7eed\u53d8\u91cf\uff1f\u6570\u636e\u662f\u5426\u5177\u6709\u660e\u663e\u7684\u5e8f\u5217\u5316\u7279\u5f81\uff1f\u4e00\u822c\u6765\u8bf4\uff0c\u81ea\u56de\u5f52\u6a21\u578b\u9002\u5408\u4e8e\u90a3\u4e9b\u5177\u6709\u5e8f\u5217\u5316\u8868\u793a\u7684\u79bb\u6563\u6570\u636e\uff0c\u800c\u57fa\u4e8e\u8f93\u8fd0\u7684\u6d41\u6a21\u578b\u548c\u6269\u6563\u6a21\u578b\u66f4\u9002\u5408\u4e8e\u7ed3\u6784\u5316\u7684\u8fde\u7eed\u6570\u636e\u3002\u5bf9\u4e8e\u66f4\u52a0\u590d\u6742\u7684\u60c5\u51b5\uff0c\u5219\u53ef\u80fd\u9700\u8981\u8003\u8651\u51e0\u79cd\u6a21\u578b\u7684\u7ec4\u5408\u3002\u4f46\u662f\uff0c\u5047\u5982\u6570\u636e\u91cf\u5145\u5206\u5927\uff0c\u5219\u8fdb\u5165\u4e86\u201c\u624b\u4e2d\u65e0\u5251\uff0c\u5fc3\u4e2d\u6709\u5251\u201d\u7684\u65b0\u5883\u754c\uff1a\u5177\u4f53\u7684\u6a21\u578b\u67b6\u6784\u5df2\u7ecf\u4e0d\u91cd\u8981\u4e86\uff0c\u91cd\u8981\u7684\u662f\u7528\u6765\u8bad\u7ec3\u6a21\u578b\u7684\u6570\u636e<\/span>\u672c\u8eab[36]<\/span>\u3002<\/span><\/section>\n


<\/p>\n


<\/p>\n

\n
\n
\n
\n
\n

<\/section>\n

<\/section>\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n
\n

4. \u5e94\u7528\u4e8e\u7269\u8d28\u79d1\u5b66\u7684\u751f\u6210\u6a21\u578b<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n
\u8bad\u7ec3\u751f\u6210\u6a21\u578b\u6240\u9700\u8981\u7684\u6570\u636e\u91cf\u901a\u5e38\u8fdc\u5927\u4e8e\u6a21\u578b\u7684\u53c2\u6570\u3002\u56e0\u6b64\uff0c\u751f\u6210\u6a21\u578b\u9700\u8981\u505a\u597d\u201c\u6709\u635f\u538b\u7f29\u201d\uff1a\u53d1\u73b0\u6570\u636e\u4e2d\u7684\u7edf\u8ba1\u89c4\u5f8b\uff0c\u4ece\u800c\u751f\u6210\u7b26\u5408\u89c4\u5f8b\u7684\u6837\u672c\u3002\u672c\u6587\u4ecb\u7ecd\u7684\u56db\u7c7b\u73b0\u4ee3\u751f\u6210\u6a21\u578b\u90fd\u53ef\u4ee5\u76f4\u63a5\u91c7\u6837\u3002\u5b83\u4eec\u751f\u6210\u6837\u672c\u7684\u65b9\u5f0f\u6709\u70b9\u7c7b\u4f3c\u4e8e\u7ecf\u9a8c\u76f4\u89c9\u5f0f\u7684\u5feb\u901f\u53cd\u5e94\uff0c\u751f\u6210\u901f\u5ea6\u548c\u6837\u672c\u5177\u4f53\u662f\u4ec0\u4e48\u65e0\u5173\u3002\u4e0d\u4ec5\u5982\u6b64\uff0c\u6269\u6563\u6a21\u578b\u3001\u6d41\u6a21\u578b\u548c\u81ea\u56de\u5f52\u6a21\u578b\u6240\u8868\u8fbe\u7684\u6982\u7387\u5206\u5e03\u90fd\u5f88\u5bb9\u6613\u5f52\u4e00\u5316\u3002\u8fd9\u610f\u5473\u7740\u5b83\u4eec\u90fd\u6709\u201c\u81ea\u77e5\u4e4b\u660e\u201d\uff1a\u4e0d\u4ec5\u53ef\u4ee5\u751f\u6210\u6837\u672c\uff0c\u8fd8\u53ef\u4ee5\u7528\u6a21\u578b\u8ba1\u7b97\u7684\u4f3c\u7136\u51fd\u6570\u7ed9\u6837\u672c\u6253\u5206\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u751f\u6210\u6a21\u578b\u7ed9\u79d1\u5b66\u7814\u7a76\u6253\u5f00\u4e86\u65b0\u7684\u53ef\u80fd\u3002\u4f46\u4e3a\u4e86\u5207\u5b9e\u89e3\u51b3\u9886\u57df\u75db\u70b9\u95ee\u9898\uff0c\u8fd8\u662f\u9700\u8981\u7d27\u7d27\u6263\u4f4f\u751f\u6210\u6a21\u578b\u7684\u7269\u7406\u5185\u6db5\uff0c\u53d1\u6325\u51fa\u5b83\u4eec\u5404\u81ea\u7684\u7279\u70b9\uff0c\u800c\u4e0d\u662f\u4ec5\u4ec5\u642c\u8fd0\u73b0\u6709\u7684\u7a0b\u5e8f\u6846\u67b6\u3002\u4e0b\u9762\u6211\u4eec\u4e3e\u4f8b\u8bf4\u660e\u3002<\/span><\/section>\n

<\/strong><\/section>\n
4.1 \u86cb\u767d\u548c\u6750\u6599\u751f\u6210<\/span><\/strong><\/span><\/section>\n

<\/span><\/section>\n
\u86cb\u767d\u8d28\u662f\u751f\u547d\u7684\u7269\u8d28\u57fa\u7840\uff0c\u6750\u6599\u662f\u4eba\u7c7b\u6587\u660e\u7684\u7269\u8d28\u57fa\u7840\u3002\u5728\u6211\u4eec\u751f\u6d3b\u7684\u5730\u7403\u4e0a\uff0c\u7ecf\u8fc7\u4ebf\u4e07\u5e74\u7684\u6f14\u5316\u548c\u6570\u5343\u5e74\u7684\u6587\u660e\uff0c\u4eba\u7c7b\u638c\u63e1\u4e86\u6570\u5341\u4e07\u79cd\u86cb\u767d\u548c\u65e0\u673a\u6676\u4f53\u6750\u6599\u7684\u7ed3\u6784\u3002\u4f46\u662f\uff0c\u5b83\u4eec\u53ea\u4ee3\u8868\u4e86\u975e\u5e38\u5c11\u7684\u53ef\u80fd\u6027\uff0c\u86cb\u767d\u548c\u6750\u6599\u7a7a\u95f4\u4e2d\u8fd8\u5b58\u5728\u5927\u91cf\u7684\u7ed3\u6784\u6709\u5f85\u4eba\u7c7b\u63a2\u7d22\u4e0e\u5408\u6210\uff0c\u5176\u4e2d\u4e5f\u8bb8\u5c31\u5305\u542b\u7740\u65b0\u7684\u7075\u4e39\u5999\u836f\u548c\u5148\u8fdb\u6750\u6599\u3002\u5229\u7528\u751f\u6210\u6a21\u578b\u5bf9\u539f\u5b50\u7ea7\u522b\u7684\u5fae\u89c2\u4e16\u754c\u5efa\u6a21\uff0c\u53ef\u4ee5\u7ed5\u8fc7\u4f20\u7edf\u53cd\u5411\u8bbe\u8ba1\u7684\u601d\u8def\uff0c\u76f4\u63a5\u751f\u6210\u65b0\u7684\u3001\u6709\u7528\u7684\u86cb\u767d\u548c\u6750\u6599\u7ed3\u6784\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u4f8b\u5982\uff0c\u56fe3(a)\u5c55\u793a\u4e86\u86cb\u767d\u751f\u6210\u6a21\u578bChro<\/span>ma[37]\u6839\u636e\u5bf9\u79f0\u7fa4\u3001\u5b50\u7ed3\u6784\u548c\u80bd\u94fe\u7684\u6574\u4f53\u5f62\u72b6\u751f\u6210\u7684\u86cb\u767d\u7ed3\u6784\u3002Chroma\u7684\u5de5\u4f5c\u539f\u7406\u548c\u56fe3(b)\u6240\u5c55\u793a\u7684\u4ece\u6587\u672c\u751f\u6210\u56fe\u50cf\u7684DaLLE-3\u6a21\u578b\u4e00\u6837\uff0c\u90fd\u662f\u4f7f\u7528\u6269\u6563\u6a21\u578b\u4ece\u6761\u4ef6\u6982\u7387p(x|y)\u4e2d\u91c7\u6837\u3002\u9664\u6b64\u4ee5\u5916\uff0c\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u86cb\u767d\u5176\u5b9e\u4e5f\u6709\u663e\u8457\u7684\u79bb\u6563\u548c\u5e8f\u5217\u5316\u7279\u5f81\uff1a\u5b83\u4eec\u662f\u6c28\u57fa\u9178\u5e8f\u5217\u5728\u4e09\u7ef4\u7a7a\u95f4\u6240\u5f62\u6210\u7684\u7279\u5b9a\u7ed3\u6784\u3002\u53ef\u4ee5\u4f7f\u7528\u81ea\u56de\u5f52\u8bed\u8a00\u6a21\u578b\u5b66\u4e60\u6c28\u57fa\u9178\u5e8f\u5217\u7684\u8bed\u8a00\u89c4\u5f8b[39]<\/span>\uff0c\u5e76\u901a\u8fc7\u6c28\u57fa\u9178\u201c\u9020\u53e5\u201d\u7684\u65b9\u5f0f\u751f\u6210\u65b0\u7684\u5e8f\u5217\u7ec4\u5408\u3002\u8fd9\u7c7b\u86cb\u767d\u8bed\u8a00\u6a21\u578b\u7ed3\u5408AlphaFold\u4e4b\u7c7b\u7684\u5de5\u5177\uff0c\u53ef\u4ee5\u8fdb\u4e00\u6b65\u4ece\u751f\u6210\u7684\u6c28\u57fa\u9178\u5e8f\u5217\u4e2d\u9884\u6d4b\u86cb\u767d\u7684\u4e09\u7ef4\u7ed3\u6784\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n

\u56fe3 (a)Chroma\u57fa\u4e8e\u5bf9\u79f0\u6027(i)\u3001\u5b50\u7ed3\u6784(ii)\u548c\u5f62\u72b6(iii)\u751f\u6210\u7684\u86cb\u767d\u7ed3\u6784[37]\uff1b(b)DaLLE-3\u57fa\u4e8e\u6587\u5b57\u63d0\u793a\u751f\u6210\u56fe\u7247[38]<\/span><\/p>\n


<\/span><\/section>\n
\u751f\u6210\u6a21\u578b\u5728\u6750\u6599\u7684\u63a2\u7d22\u4e0a\u4e5f\u5927\u6709\u7528\u6b66\u4e4b\u5730\u3002\u751f\u6210\u6a21\u578b\u538b\u7f29\u5185\u5316\u5df2\u77e5\u7684\u6676\u4f53\u6750\u6599\u6570\u636e\uff0c\u628a\u6570\u636e\u4e2d\u8574\u542b\u7684\u56fa\u4f53\u5316\u5b66\u77e5\u8bc6\u5b58\u50a8\u5728\u795e\u7ecf\u7f51\u7edc\u6743\u91cd\u4e2d\u3002\u4e00\u4e2a\u597d\u7684\u6676\u4f53\u751f\u6210\u6a21\u578b\u9996\u5148\u4f1a\u662f\u4e00\u4e2a\u6676\u4f53\u201c\u9274\u8d4f\u5bb6\u201d\uff0c\u5f53\u7528\u5b83\u770b\u5230\u65b0\u7684\u6676\u4f53\u7ed3\u6784\u65f6\uff0c\u795e\u7ecf\u7f51\u7edc\u6fc0\u6d3b\u53cd\u6620\u5728\u6750\u6599\u7a7a\u95f4\u4e2d\u7684\u8054\u60f3\u80fd\u529b\uff0c\u800c\u6a21\u578b\u8ba1\u7b97\u7684\u4f3c\u7136\u51fd\u6570\u4ee3\u8868\u4e86\u5173\u4e8e\u6676\u4f53\u7a33\u5b9a\u6027\u7684\u5316\u5b66\u76f4\u89c9\u3002\u4e0d\u4ec5\u5982\u6b64\uff0c\u5b83\u8fd8\u662f\u4e00\u4e2a\u6676\u4f53\u201c\u827a\u672f\u5bb6\u201d\u3002\u548c\u90a3\u4e9b\u751f\u6210\u6587\u672c\u3001\u56fe\u7247\u548c\u89c6\u9891\u7684\u4eba\u5de5\u667a\u80fd\u201c\u827a\u672f\u5bb6\u201d\u4e00\u6837\uff0c\u6676\u4f53\u751f\u6210\u6a21\u578b\u53ef\u4ee5\u76f4\u63a5\u751f\u6210\u81ea\u7136\u754c\u4e2d\u53ef\u4ee5\u5b58\u5728\uff0c\u4f46\u8fd8\u6ca1\u88ab\u53d1\u73b0\u7684\u6676\u4f53\u6750\u6599\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u6269\u6563\u6a21\u578b\u5929\u7136\u7b26\u5408\u6676\u4f53\u751f\u957f\u7684\u7269\u7406\u76f4\u89c9\uff1a\u5b83\u4f3c\u4e4e\u6a21\u62df\u4e86\u539f\u5b50\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u5f7c\u6b64\u76f8\u4e92\u4f5c\u7528\uff0c\u9010\u6e10\u6269\u6563\u5230\u6700\u7ec8\u7684\u4f4d\u7f6e\u7684\u8fc7\u7a0b\u3002\u56e0\u6b64\uff0c\u6269\u6563\u6a21\u578b\u662f\u76ee\u524d\u6676\u4f53\u751f\u6210\u7684\u4e3b\u6d41\u63a2\u7d22\u65b9<\/span>\u5411[40\u201442]\u3002\u9664\u6b64\u4ee5\u5916\uff0c\u4e5f\u6709\u4e00\u4e9b\u522b\u51fa\u5fc3\u88c1\u7684\u5de5\u4f5c\u4f7f\u7528\u81ea\u56de\u5f52Transformer\u76f4\u63a5\u751f\u6210\u6676\u4f53\u7684\u6587\u672c\u8868\u793a[43\uff0c44]\u3002\u8fd9\u79cd\u505a\u6cd5\u629b\u5f03\u4e86\u6676\u4f53\u7684\u4e09\u7ef4\u7ed3\u6784\u548c\u5bf9\u79f0\u6027\uff0c\u4f46\u662f\u5c45\u7136\u4e5f\u53ef\u4ee5\u751f\u6210\u50cf\u6a21\u50cf\u6837\u7684\u6676\u4f53\u6784\u578b\u3002\u4e5f\u8bb8\uff0c\u8fd9\u53c8\u662f\u6df1\u5ea6\u5b66\u4e60\u7ed9\u6211\u4eec\u4e0a\u7684\u201c\u82e6\u6da9\u7684\u4e00\u8bfe\u201d[45]\u3002\u65e0\u8bba\u5982\u4f55\uff0c\u7b14\u8005\u8ba4\u4e3a\u5982\u679c\u8003\u8651\u5230\u6676\u4f53\u7a7a\u95f4\u7fa4\u7684Wyckoff\u4f4d\u7f6e\u7684\u81ea\u7136\u6392\u5e8f\uff0c\u6676\u4f53\u6750\u6599\u53ef\u4ee5\u6709\u4e00\u79cd\u4e25\u8c28\u7684\u79bb\u6563\u5e8f\u5217\u5316\u8868\u793a[46]\u3002<\/span>\u5728\u8fd9\u79cd\u6676\u4f53\u8bed\u8a00\u4e2d\uff0c\u201c\u8bed\u5e8f\u201d\u7531\u7a7a\u95f4\u7fa4Wyckoff\u5360\u4f4d\u7684\u987a\u5e8f\u51b3\u5b9a\uff0c\u201c\u8bed\u6cd5\u201d\u5bf9\u5e94\u4e8e\u56fa\u4f53\u5316\u5b66\u89c4\u5f8b\uff0c\u201c\u540c\u4e49\u8bcd\u201d\u4ee3\u8868\u53ef\u4ee5\u4e92\u6362\u7684\u5143\u7d20\uff0c\u201c\u6210\u8bed\u201d\u5bf9\u5e94\u5e38\u89c1\u7684\u5316\u5b66\u914d\u4f4d\u3002\u4f7f\u7528\u6676\u4f53\u8bed\u8a00\u5199\u51fa\u7684\u4e00\u9996\u9996\u8bd7\uff0c\u6b63\u5bf9\u5e94\u7740\u81ea\u7136\u754c\u4e2d\u90a3\u4e9b\u6f02\u4eae\u7684\u6676\u4f53\u3002\u7b14\u8005\u76f8\u4fe1\uff0c\u878d\u5408\u7a7a\u95f4\u7fa4\u5bf9\u79f0\u6027\u7684\u6676\u4f53\u8bed\u8a00\u6a21\u578b\u8fd8\u6709\u5de8\u5927\u7684\u3001\u6709\u5f85\u6316\u6398\u7684\u6f5c\u529b\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u53e6\u5916\uff0c\u503c\u5f97\u63d0\u4e00\u4e0bGoogle DeepMind\u52a0\u901f\u6750\u6599\u53d1\u73b0\u7684\u5de5\u4f5c[47]\u548c\u672c\u6587\u4e3b\u9898\u201c\u751f\u6210\u6a21\u578b\u201d\u7684\u5173\u7cfb\u3002\u629b\u5f00\u5173\u4e8e\u7ed3\u679c\u7684\u4e00\u4e9b\u4e89\u8bae\u4e0d\u8c08[48]\uff0c\u8fd9\u4e2a\u5de5\u4f5c\u9996\u5148\u901a\u8fc7\u5143\u7d20\u66ff\u6362\u7b49\u624b\u6bb5\u4ea7\u751f\u5927\u91cf\u5907\u9009\u7ed3\u6784\uff0c\u518d\u5229\u7528\u673a\u5668\u5b66\u4e60\u52bf\u51fd\u6570<\/span> (\u8be6\u7ec6\u8ba8\u8bba\u89c1[49]) <\/span>\u5feb\u901f\u5f1b\u8c6b\u6676\u4f53\u7ed3\u6784\u5e76\u4f5c\u51fa\u80fd\u91cf\u8bc4\u4f30\u3002\u5176\u5b9e\uff0c\u673a\u5668\u5b66\u4e60\u52bf\u51fd\u6570\u4e5f\u53ef\u4ee5\u88ab\u770b\u4f5c\u662f\u4e00\u79cd\u751f\u6210\u6a21\u578b\uff1a\u5b83\u4eec\u662f\u57fa\u4e8e\u7269\u7406\u4f53\u7cfb\u80fd\u91cf\u51fd\u6570\u7684\u73bb\u5c14\u5179\u66fc\u673a((4)\u5f0f)\u3002\u4f46\u4e0d\u540c\u4e8e\u672c\u6587\u8ba8\u8bba\u7684\u65e0\u76d1\u7763\u5b66\u4e60\u65b9\u5f0f\uff0c\u673a\u5668\u5b66\u4e60\u52bf\u51fd\u6570\u901a\u5e38\u9700\u8981\u7b2c\u4e00\u6027\u539f\u7406\u8ba1\u7b97\u6240\u5f97\u7684\u80fd\u91cf\u548c\u529b\u4f5c\u4e3a\u8bad\u7ec3\u6807\u7b7e\u3002\u6b64\u5916\uff0c\u6b63\u5982\u524d\u6587\u5bf9\u6bd4\u6269\u6563\u6a21\u578b\u548c\u5206\u5b50\u52a8\u529b\u5b66\u91c7\u6837\u65f6\u6240\u8bf4\u7684\u90a3\u6837\uff0c\u57fa\u4e8e\u771f\u5b9e\u80fd\u91cf\u51fd\u6570\u7684\u201c\u751f\u6210\u6a21\u578b\u201d\u5f80\u5f80\u4e0d\u5bb9\u6613\u5728\u5d0e\u5c96\u7684\u52bf\u80fd\u7a7a\u95f4\u8d70\u5f97\u5f88\u8fdc\u3002\u800c\u672c\u6587\u4ecb\u7ecd\u7684\u51e0\u7c7b\u73b0\u4ee3\u751f\u6210\u6a21\u578b\u907f\u5f00\u4e86\u771f\u5b9e\u4f53\u7cfb\u7684\u80fd\u91cf\u51fd\u6570\u548c\u529b\u7684\u7ea6\u675f\uff0c\u53ef\u4ee5\u76f4\u63a5\u751f\u6210\u591a\u6837\u4e14\u7a33\u5b9a\u7684\u6676\u4f53\u7ed3\u6784\u3002\u751f\u6210\u6a21\u578b\u5c06\u662f\u672a\u6765\u63a2\u7d22\u6676\u4f53\u6750\u6599\u7a7a\u95f4\u7684\u91cd\u8981\u624b\u6bb5\u3002<\/span><\/section>\n

<\/strong><\/section>\n
4.2 \u53d8\u5206\u81ea\u7531\u80fd\u8ba1\u7b97<\/span><\/strong><\/span><\/section>\n

<\/strong><\/section>\n
\u516c\u5f0f(3)\u6240\u793a\u7684\u53d8\u5206\u81ea\u7531\u80fd\u539f\u7406\u5176\u5b9e\u65e9\u5c31\u4e3a\u4eba\u6240\u77e5\u3002\u5728\u7269\u7406\u6587\u732e\u4e2d\uff0c\u5b83\u5e38\u5e38\u88ab\u79f0\u4e3a\u5409\u5e03\u65af\u2014\u535a\u6208\u7559\u6ce2\u592b\u2014\u8d39\u66fc<\/span> (Gibbs\u2014Bogoliubov\u2014Feynman) <\/span>\u4e0d\u7b49\u5f0f\u3002\u5b83\u53cd\u6620\u4e86\u5927\u81ea\u7136\u5728\u6709\u9650\u6e29\u5ea6\u4e0b\u7684\u4e00\u79cd\u503e\u5411\uff1a\u5e73\u8861\u80fd\u91cf\u548c\u71b5\u4ece\u800c\u4f7f\u4f53\u7cfb\u7684\u81ea\u7531\u80fd\u6781\u5c0f\u3002\u7136\u800c\uff0c\u6709\u70b9\u8bbd\u523a\u7684\u662f\uff0c\u8bd5\u56fe\u5c06\u8fd9\u4e00\u57fa\u672c\u539f\u7406\u8f6c\u5316\u6210\u5b9e\u7528\u7684\u8ba1\u7b97\u65b9\u6cd5\u5374\u662f\u76f8\u5f53\u56f0\u96be\u7684\u3002\u56f0\u96be\u4e3b\u8981\u6e90\u4e8e\u70ed\u529b\u5b66\u71b5\u7684\u9ad8\u6602\u8ba1\u7b97\u4ee3\u4ef7\u2014\u2014\u8fd9\u80cc\u540e\u7684\u96be\u70b9\u8fd8\u662f\u5728\u4e8e\u6982\u7387\u5206\u5e03\u7684\u5f52\u4e00\u5316\u56e0\u5b50\u3002\u5728\u7edf\u8ba1\u7269\u7406\u8ba1\u7b97\u4e2d\uff0c\u4eba\u4eec\u5e38\u5e38\u505a\u51fa\u59a5\u534f\uff0c\u8bbe\u8ba1\u4e00\u4e9b\u7b80\u5355\u7684\u6982\u7387\u6765\u505a\u53d8\u5206\u8ba1\u7b97\uff0c\u4f8b\u5982\u5e73\u5747\u573a\u65b9\u6cd5\u6216\u8005\u8d1d\u7279<\/span> (Bethe) <\/span>\u8fd1\u4f3c\u3002\u8fd9\u4e9b\u59a5\u534f\u6781\u5927\u5730\u9650\u5236\u4e86\u53d8\u5206\u7a7a\u95f4\uff0c\u5e76\u4e0d\u80fd\u591f\u7cbe\u51c6\u5730\u6c42\u89e3\u95ee\u9898\u3002\u800c\u672c\u6587\u6240\u4ecb\u7ecd\u7684\u81ea\u56de\u5f52\u6a21\u578b\u548c\u6d41\u6a21\u578b\u53ef\u4ee5\u5929\u7136\u4fdd\u8bc1\u6982\u7387\u5206\u5e03\u5f52\u4e00\u5316\uff0c\u5e76\u4e14\u8fd8\u80fd\u76f4\u63a5\u91c7\u6837\u3002\u4f7f\u7528\u8fd9\u7c7b\u73b0\u4ee3\u7684\u751f\u6210\u6a21\u578b\u4f5c\u4e3a\u53d8\u5206\u6982\u7387\u5206\u5e03\uff0c\u7ec8\u4e8e\u53ef\u4ee5\u53d1\u6325\u51fa\u5409\u5e03\u65af\u2014\u535a\u6208\u7559\u6ce2\u592b\u2014\u8d39\u66fc\u4e0d\u7b49\u5f0f\u4e2d\u6240\u8574\u542b\u7684\u5a01\u529b[24\uff0c50\uff0c51]\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u9664\u4e86\u7ecf\u5178\u7684\u7edf\u8ba1\u7269\u7406\u95ee\u9898\u4e4b\u5916\uff0c\u57fa\u4e8e\u751f\u6210\u6a21\u578b\u7684\u53d8\u5206\u81ea\u7531\u80fd\u8ba1\u7b97\u4e5f\u4e3a\u89e3\u51b3\u91cf\u5b50\u591a\u4f53\u95ee\u9898\u63d0\u4f9b\u4e86\u5b9d\u8d35\u7684\u673a\u9047\u3002\u5bf9\u4e8e\u54c8\u5bc6\u987f\u91cf\u4e3aH\u7684\u91cf\u5b50\u591a\u4f53\u95ee\u9898\uff0c\u6700\u5c0f\u5316\u5bc6\u5ea6\u77e9\u9635\u7684\u76f8\u5bf9\u71b5\u53ef\u4ee5\u7ed9\u51fa\u548c(3)\u5f0f\u7c7b\u4f3c\u7684\u76ee\u6807\u51fd\u6570\uff1a<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n

<\/span><\/section>\n
\u8fd9\u91cc\u7684\u96be\u70b9\u662f\u53c2\u6570\u5316\u591a\u4f53\u5bc6\u5ea6\u77e9\u9635\uff0c\u5e76\u4e14\u8fd8\u8981\u4fdd\u8bc1(10)\u5f0f\u7b2c\u4e00\u9879\u7684\u70ed\u529b\u5b66\u71b5\u6613\u4e8e\u8ba1\u7b97\u3002\u901a\u8fc7\u7ec4\u5408\u4f7f\u7528\u51e0\u79cd\u73b0\u4ee3\u7684\u751f\u6210\u6a21\u578b\u53ef\u4ee5\u89e3\u51b3\u8fd9\u4e2a\u96be\u70b9\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u4e0b\u9762\u6211\u4eec\u4ee5\u7535\u5b50\u6c14\u4f4e\u6e29\u72b6\u6001\u65b9\u7a0b\u7814\u7a76\u4e3a\u4f8b\u5c55\u5f00\u5177\u4f53\u8ba8<\/span>\u8bba[52]\u3002\u7535<\/span>\u5b50\u6c14\u662f\u51dd\u805a\u6001\u7269\u7406\u7814\u7a76\u7684\u4e00\u4e2a\u57fa\u7840\u6a21\u578b\uff0c\u5b83\u4e00\u65b9\u9762\u662f\u6d4b\u8bd5\u5404\u79cd\u8ba1\u7b97\u65b9\u6cd5\u7684\u8bd5\u91d1\u77f3\uff0c\u53e6\u4e00\u65b9\u9762\uff0c\u5b83\u4e5f\u662f\u8d39\u7c73\u6db2\u4f53\u548c\u5bc6\u5ea6\u6cdb\u51fd\u7406\u8bba\u4e2d\u7684\u57fa\u7840\u6a21\u578b\u3002\u7535\u5b50\u6c14\u5bc6\u5ea6\u77e9\u9635\u7684\u4e00\u822c\u5f62\u5f0f\u662f<\/span>\uff0c\u5176\u4e2dk<\/strong><\/em>\u662f\u6807\u8bb0\u591a\u7535\u5b50\u80fd\u7ea7\u7684\u91cf\u5b50\u6570\uff0cp<\/em>(k<\/em><\/strong>)\u662f\u80fd\u7ea7\u5360\u636e\u7684\u7ecf\u5178\u6982\u7387\u5206\u5e03\u3002\u53ef\u4ee5\u4f7f\u7528\u81ea\u56de\u5f52\u6a21\u578b\u8868\u8fbe\u8fd9\u4e2a\u79bb\u6563\u53d8\u91cf\u7684\u8054\u5408\u6982\u7387\u5206\u5e03\uff0c\u5b83\u7684\u7269\u7406\u542b\u4e49\u5c31\u662f\u8d39\u7c73\u6db2\u4f53\u7684\u6717\u9053\u80fd\u91cf\u6cdb\u51fd\u3002\u53e6\u4e00\u65b9\u9762\uff0c<\/span>\u662f\u6b63\u4ea4\u5f52\u4e00\u7684\u591a\u7535\u5b50\u6ce2\u51fd\u6570\uff0c\u7c7b\u6bd4\u4e8e\u524d\u6587(7)\u5f0f\uff0c\u53ef\u4ee5\u7528\u201c\u5f00\u6839\u53f7\u201d\u7684\u6d41\u6a21\u578b\u53c2\u6570\u5316\u8fd9\u7c07\u591a\u4f53\u6ce2\u51fd\u6570\uff1a<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n

<\/span><\/span><\/section>\n
\u8fd9\u91cc\uff0cx<\/em><\/strong>\u548cz<\/em><\/strong>\u5206\u522b\u5bf9\u5e94\u7c92\u5b50\u5750\u6807\u548c\u51c6\u7c92\u5b50\u5750\u6807\u3002(11)\u5f0f\u4e2d\u5305\u542b\u7684\u795e\u7ecf\u7f51\u7edc\u53d8\u6362\u7684\u96c5\u53ef\u6bd4\u884c\u5217\u5f0f\u4fdd\u8bc1\u4e86\u6ce2\u51fd\u6570\u7684\u6b63\u4ea4\u5f52\u4e00\u5316\u3002\u8fd9\u7c7b\u53d8\u6362\u7684\u4e00\u4e2a\u76f8\u5173\u7684\u4f8b\u5b50\u662f\u8d39\u66fc\u548c\u4ed6\u7684\u5b66\u751f\u7814\u7a76\u6db2\u6c26\u65f6\u5f15\u5165\u7684\u6d04\u6d41<\/span> (backflow) <\/span>\u53d8\u6362[53]\uff1a<\/span>\u3002\u6d04\u6d41\u7684\u7269\u7406\u542b\u4e49\u662f\u5728\u76f8\u4e92\u4f5c\u7528\u4f53\u7cfb\u4e2d\uff0c\u7c92\u5b50\u62d6\u66f3\u5468\u56f4\u7684\u7c92\u5b50\u5f62\u6210\u4e86\u51c6\u7c92\u5b50\u3002\u7528\u51c6\u7c92\u5b50\u5750\u6807\u8868\u8fbe\u7684\u7b80\u5355\u6ce2\u51fd\u6570\uff0c\u5982\u679c\u5199\u56de\u5230\u7c92\u5b50\u5750\u6807\u5c31\u662f\u4e00\u4e2a\u5305\u542b\u4e86\u5173\u8054\u6548\u5e94\u7684\u591a\u4f53\u6ce2\u51fd\u6570\u3002\u4ece\u6df1\u5ea6\u5b66\u4e60\u7684\u89d2\u5ea6\u770b\uff0c\u6d04\u6d41\u53d8\u6362\u5bf9\u5e94\u4e8e\u4e00\u4e2a\u6b8b\u5dee\u795e\u7ecf\u7f51\u7edc[54]\u3002\u56e0\u6b64\uff0c\u5176\u5b9e\u53ef\u4ee5\u628a\u82e5\u5e72\u8fd9\u6837\u7684\u53d8\u6362\u4e32\u8054\u8d77\u6765\u5f62\u6210\u56fe4\u6240\u793a\u7684\u6df1\u5c42\u6b8b\u5dee\u795e\u7ecf\u7f51\u7edc\u3002\u53ef\u89c1\uff0c\u6d41\u6a21\u578b\u6293\u4f4f\u4e86\u8d39\u7c73\u6db2\u4f53\u7406\u8bba\u4e2d\u5173\u952e\u7684\u7edd\u70ed\u8fde\u7eed\u6027<\/span> (adiabatic continuity) <\/span>\u7684\u6982\u5ff5\uff0c\u800c\u51dd\u805a\u6001\u7269\u7406\u5b66\u5bb6\u8ba8\u8bba\u7684\u51c6\u7c92\u5b50\u5c31\u751f\u6d3b\u5728\u6d41\u6a21\u578b\u7684\u9690\u53d8\u91cf\u7a7a\u95f4\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n

\u56fe4 \u4f7f\u7528\u6df1\u5c42\u7684\u6b8b\u5dee\u795e\u7ecf\u7f51\u7edc\u5b9e\u73b0\u7c92\u5b50\u548c\u51c6\u7c92\u5b50\u5750\u6807\u4e4b\u95f4\u7684\u6d04\u6d41\u53d8\u6362\u3002\u4e3a\u4e86\u4fdd\u8bc1\u51c6\u7c92\u5b50\u7684\u7edf\u8ba1\u6027\u8d28\uff0c\u795e\u7ecf\u7f51\u7edc\u53d8\u6362\u9700\u8981\u6ee1\u8db3\u7f6e\u6362\u7b49\u53d8\u6027\u8d28\uff0c\u5373\u7c92\u5b50\u7f6e\u6362\u64cd\u4f5c\u548c\u795e\u7ecf\u7f51\u7edc\u53d8\u6362\u5bf9\u6613<\/span><\/p>\n


<\/span><\/section>\n
\u5728\u91cf\u5b50\u7edf\u8ba1\u4e2d\uff0c\u5bc6\u5ea6\u77e9\u9635\u63cf\u8ff0\u7684\u662f\u6df7\u5408\u6001\u3002\u76f8\u5bf9\u5e94\u5730\uff0c\u6211\u4eec\u4f7f\u7528\u81ea\u56de\u5f52\u6a21\u578b\u548c\u6d41\u6a21\u578b\u5206\u522b\u53c2\u6570\u5316\u4e86\u53d8\u5206\u5bc6\u5ea6\u77e9\u9635\u4e2d\u7684\u7ecf\u5178\u6982\u7387\u548c\u91cf\u5b50\u6ce2\u51fd\u6570\u3002\u8fd9\u79cd\u53c2\u6570\u5316\u65b9\u5f0f\u4e0d\u4ec5\u7b26\u5408\u7269\u7406\u7ea6\u675f\uff0c\u8fd8\u8574\u542b\u4e86\u4e30\u5bcc\u7684\u7269\u7406\u3002\u4e00\u65e6\u786e\u7acb\u4e86\u53c2\u6570\u5316\u7684\u53d8\u5206\u7a7a\u95f4\uff0c\u63a5\u4e0b\u6765\u5c31\u53ef\u4ee5\u901a\u8fc7\u6700\u5c0f\u5316\u53d8\u5206\u81ea\u7531\u80fd(10)\u5f0f\u8054\u5408\u4f18\u5316\u4e24\u4e2a\u751f\u6210\u6a21\u578b\uff0c\u4ece\u800c\u8fd1\u4f3c\u89e3\u51b3\u7535\u5b50\u6c14\u548c\u66f4\u52a0\u4e00\u822c\u7684\u91cf\u5b50\u591a\u4f53\u95ee\u9898\u3002\u57fa\u4e8e\u751f\u6210\u6a21\u578b\u7684\u53d8\u5206\u81ea\u7531\u80fd\u65b9\u6cd5\u5c06\u6c42\u89e3\u7269\u7406\u95ee\u9898\u8f6c\u5316\u4e3a\u5bf9\u81ea\u7136\u754c\u7684\u635f\u5931\u51fd\u6570\uff1a\u81ea\u7531\u80fd\u7684\u968f\u673a\u68af\u5ea6\u4f18\u5316\u3002\u8fd9\u6761\u7814\u7a76\u8def\u7ebf\u503c\u5f97\u5173\u6ce8\uff0c\u5176\u5b9e\u8fd8\u6709\u4e00\u4e2a\u6280\u672f\u5c42\u9762\u7684\u7406\u7531\uff0c\u968f\u673a\u68af\u5ea6\u4f18\u5316\u7b80\u5355\u6734\u5b9e\uff0c\u5374\u80fd\u5145\u5206\u53d1\u6325\u51fa\u6df1\u5ea6\u5b66\u4e60\u5f15\u64ce\uff1a\u5fae\u5206\u7f16\u7a0b<\/span>\u6846\u67b6[55]\u548c<\/span>\u4e13\u7528\u52a0\u901f\u786c\u4ef6\u7684\u5f3a\u5927\u8ba1\u7b97\u80fd\u529b\uff0c\u4ece\u800c\u642d\u4e0a\u4eba\u5de5\u667a\u80fd\u98de\u901f\u53d1\u5c55\u7684\u4fbf\u8f66\uff0c\u4e3a\u89e3\u51b3\u56f0\u96be\u7684\u7269\u7406\u95ee\u9898\u63d0\u4f9b\u65b0\u673a\u4f1a\u3002<\/span><\/section>\n


<\/p>\n


<\/p>\n

\n
\n
\n
\n
\n

<\/section>\n

<\/section>\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n
\n

5. \u7ed3\u8bed<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n
\u957f\u671f\u4ee5\u6765\u8ba1\u7b97\u673a\u6700\u663e\u8457\u7684\u7279\u70b9\u662f\u7b97\u5f97\u5feb\u3001\u7b97\u5f97\u51c6\u3002\u7136\u800c\u751f\u6210\u5f0f\u4eba\u5de5\u667a\u80fd\u8d4b\u4e88\u4e86\u8ba1\u7b97\u673a\u4ece\u7ecf\u9a8c\u4e2d\u5b66\u4e60\u201c\u76f4\u89c9\u201d\u7684\u80fd\u529b\uff0c\u751a\u81f3\u53ef\u4ee5\u7528\u6765\u201c\u521b\u9020\u201d\u65b0\u7684\u7ecf\u9a8c\u3002\u5b9a\u91cf\u63cf\u8ff0\u8fd9\u79cd\u201c\u76f4\u89c9\u201d\u548c\u201c\u521b\u9020\u201d\u7684\u6570\u5b66\u5de5\u5177\u548c\u7edf\u8ba1\u7269\u7406\u4e00\u6837\uff0c\u90fd\u662f\u81ea\u7136\u754c\u4e2d\u7684\u6982\u7387\u5206\u5e03\u3002\u88683\u4e3a\u6709\u7269\u7406\u80cc\u666f\u7684\u8bfb\u8005\u63d0\u4f9b\u4e86\u4e00\u4e2a\u5c0f\u5c0f\u7684\u5b57\u5178\u3002\u5e0c\u671b\u5b83\u548c\u672c\u6587\u6709\u52a9\u4e8e\u63ed\u5f00\u751f\u6210\u5f0f\u4eba\u5de5\u667a\u80fd\u7684\u795e\u79d8\u9762\u7eb1\u3002<\/span><\/section>\n

<\/section>\n
\u88683 \u751f\u6210\u6a21\u578b\u548c\u7edf\u8ba1\u7269\u7406\u8bfe\u9898\u4e4b\u95f4\u7684\u5b57\u5178<\/span><\/section>\n
<\/section>\n

<\/span><\/section>\n
\u751f\u6210\u6a21\u578b\u548c\u7269\u7406\u7814\u7a76\u8840\u8109\u76f8\u8fde\uff0c\u5b83\u4eec\u90fd\u5e0c\u671b\u638c\u63e1\u6570\u636e\u80cc\u540e\u7684\u89c4\u5f8b\uff0c\u5e76\u5229\u7528\u89c4\u5f8b\u63a2\u7d22\u672a\u77e5\u3002\u5f53\u6211\u4eec\u60ca\u53f9\u4e8e\u751f\u6210\u5f0f\u4eba\u5de5\u667a\u80fd\u795e\u5947\u7684\u80fd\u529b\u7684\u540c\u65f6\uff0c\u4e0d\u59a8\u4e5f\u5c06\u76ee\u5149\u6295\u5411\u6211\u4eec\u8d56\u4ee5\u751f\u5b58\u7684\u5b87\u5b99\uff0c\u5b83\u4e5f\u8bb8\u5c31\u662f\u4e00\u4e2a\u66f4\u5b8f\u5927\u7684\u751f\u6210\u6a21\u578b\uff1a\u4ece\u4e00\u4e2a\u5728\u9910\u5dfe\u7eb8\u4e0a\u5c31\u5199\u5f97\u4e0b\u7684\u4f5c\u7528\u91cf\u51fa\u53d1\uff0c\u4ea7\u751f\u4e86\u4e30\u5bcc\u591a\u5f69\u7684\u4e16\u95f4\u4e07\u7269\u3002\u7269\u7406\u5b66\u7814\u7a76\u7684\u76ee\u7684\u4e4b\u4e00\uff0c\u5c31\u662f\u57fa\u4e8e\u5b9e\u9a8c\u89c2\u5bdf\u6240\u5f97\u7684\u6570\u636e\u627e\u5230\u90a3\u4e2a\u4f5c\u7528\u91cf\u3002<\/span><\/section>\n

<\/span><\/section>\n
\n
\n
\u81f4\u8c22 <\/span>\u672c\u6587<\/span><\/span>\u7684\u5199\u4f5c\u53d7\u76ca\u4e8e\u4e0e\u5f20\u6797\u5cf0\u3001\u738b\u6db5\u3001\u5c24\u4ea6\u5e84\u3001\u5415\u5065\u3001\u674e\u70c1\u8f89\u3001\u8c22\u6d69\u3001\u5218\u91d1\u56fd\u3001\u5434\u5178\u3001\u8463\u99a8\u9633\u3001\u6b27\u4ed5\u521a\u7b49\u7684\u5408\u4f5c\u4e0e\u8ba8\u8bba\u3002<\/span><\/section>\n<\/section>\n<\/blockquote>\n


<\/p>\n

<\/span><\/p>\n<\/section>\n

\n
\n
\n
\n
\u53c2\u8003\u6587\u732e<\/span><\/strong><\/span><\/section>\n
\n
\n