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data-dominant-color=\"d0d0d0\" data-has-transparency=\"false\" style=\"--dominant-color: #d0d0d0;\" loading=\"lazy\" decoding=\"async\" class=\"not-transparent alignnone size-full wp-image-26903\" src=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/09\/c47748d05d9ba02ed517836d80096796bd1015.png\" width=\"1080\" height=\"297\" alt=\"\u56fe1\uff1a\u6bd4\u8f83\uff1a\u7ecf\u5178\u8fd1\u4f3c\u7406\u8bba\u4e0e\u6211\u4eec\u7684\u590d\u6742\u6027\u7406\u8bba\u6539\u8fdb\u3002\" title=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/09\/c47748d05d9ba02ed517836d80096796bd1015.png 1080w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/09\/c47748d05d9ba02ed517836d80096796bd1015-300x83.png 300w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/09\/c47748d05d9ba02ed517836d80096796bd1015-1024x282.png 1024w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/09\/c47748d05d9ba02ed517836d80096796bd1015-150x41.png 150w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/09\/c47748d05d9ba02ed517836d80096796bd1015-768x211.png 768w\" sizes=\"auto, (max-width: 1080px) 100vw, 1080px\" \/><span class=\"data-image-title\">\u56fe1\uff1a\u6bd4\u8f83\uff1a\u7ecf\u5178\u8fd1\u4f3c\u7406\u8bba\u4e0e\u6211\u4eec\u7684\u590d\u6742\u6027\u7406\u8bba\u6539\u8fdb\u3002<\/span><\/p>\n<p>\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u7535\u8def\u590d\u6742\u5ea6\u7406\u8bba\u5219\u4ece\u53e6\u4e00\u4e2a\u89d2\u5ea6\u523b\u753b\u8ba1\u7b97\u80fd\u529b\u3002\u5b83\u5c06\u7b97\u6cd5\u89c6\u4e3a\u7531\u57fa\u672c\u8fd0\u7b97\u5355\u5143\uff08\u95e8\uff09\u7ec4\u6210\u7684\u7535\u8def\uff0c\u7814\u7a76\u5728\u7ed9\u5b9a\u95e8\u96c6\u4e0b\u5b9e\u73b0\u67d0\u4e2a\u51fd\u6570\u6240\u9700\u7684\u6700\u5c0f\u7535\u8def\u89c4\u6a21\u4e0e\u6df1\u5ea6\u3002<\/p>\n<p>\u4e0d\u540c\u7c7b\u578b\u7684\u7535\u8def\u2014\u2014\u5e03\u5c14\u7535\u8def\uff08\u5904\u7406\u903b\u8f91\u8fd0\u7b97\uff09\u3001\u7b97\u672f\u7535\u8def\uff08\u5904\u7406\u52a0\u6cd5\u4e0e\u4e58\u6cd5\uff09\u3001\u70ed\u5e26\u7535\u8def\uff08\u5904\u7406\u6700\u5c0f\u503c\u4e0e\u52a0\u6cd5\uff09\u2014\u2014\u5bf9\u5e94\u7740\u4e0d\u540c\u7c7b\u522b\u7684\u63a8\u7406\u4efb\u52a1\u3002<\/p>\n<p>\u5728\u5f62\u5f0f\u5316\u8868\u793a\u4e0a\uff0c\u8fd9\u4e9b\u7535\u8def\u7684\u8ba1\u7b97\u8fc7\u7a0b\u53ef\u4ee5\u62bd\u8c61\u4e3a\u6709\u5411\u65e0\u73af\u56fe\uff08DAG\uff09\u3002DAG\u7684\u8282\u70b9\u4ee3\u8868\u8ba1\u7b97\u6b65\u9aa4\uff0c\u8fb9\u8868\u793a\u6570\u636e\u6d41\u52a8\u3002\u8f93\u5165\u8282\u70b9\u63a5\u6536\u539f\u59cb\u6570\u636e\uff0c\u8ba1\u7b97\u8282\u70b9\u6267\u884c\u57fa\u672c\u8fd0\u7b97\uff0c\u8f93\u51fa\u8282\u70b9\u7ed9\u51fa\u6700\u7ec8\u7ed3\u679c\u3002<\/p>\n<p>\u8fd9\u79cd\u7ed3\u6784\u5316\u8868\u793a\u4e0d\u4ec5\u63ed\u793a\u4e86\u7b97\u6cd5\u7684\u6267\u884c\u987a\u5e8f\uff0c\u4e5f\u4e3a\u5206\u6790\u63a8\u7406\u94fe\u6761\u63d0\u4f9b\u4e86\u5929\u7136\u7684\u5de5\u5177\u3002<\/p>\n<p>\u6709\u8da3\u7684\u662f\uff0c\u8fd9\u79cd\u201c\u63a8\u7406\u94fe\u201d\u4e0e\u5927\u8bed\u8a00\u6a21\u578b\u4e2d\u7684Chain-of-Thought\uff08CoT\uff09\u6982\u5ff5\u9ad8\u5ea6\u5951\u5408\u3002<\/p>\n<p>LLM\u5728\u591a\u6b65\u63a8\u7406\u65f6\uff0c\u4f1a\u751f\u6210\u4e00\u7cfb\u5217\u4e2d\u95f4\u63a8\u65ad\u6b65\u9aa4\uff0c\u9010\u6b65\u903c\u8fd1\u6700\u7ec8\u7b54\u6848\uff1b\u800c\u5728\u7535\u8def\u6a21\u578b\u4e2d\uff0c\u8fd9\u4e9b\u4e2d\u95f4\u6b65\u9aa4\u6b63\u5bf9\u5e94\u7740DAG\u4e2d\u7684\u8ba1\u7b97\u8282\u70b9\u3002\u7531\u6b64\uff0cLLM\u7684\u63a8\u7406\u94fe\u53ef\u4ee5\u88ab\u89c6\u4e3a\u4e00\u79cd\u7279\u6b8a\u7684\u7535\u8def\u6267\u884c\u8fc7\u7a0b\uff0c\u8fd9\u4e3a\u5c06AI\u63a8\u7406\u80fd\u529b\u6620\u5c04\u5230\u7535\u8def\u590d\u6742\u5ea6\u6846\u67b6\u4e2d\u63d0\u4f9b\u4e86\u7406\u8bba\u57fa\u7840\u3002<\/p>\n<p><img data-dominant-color=\"fafafb\" data-has-transparency=\"false\" style=\"--dominant-color: #fafafb;\" loading=\"lazy\" decoding=\"async\" class=\"not-transparent alignnone size-full wp-image-26904\" src=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/09\/a6756a0727bbd642dde559189cd5cc1a6fcfd8.png\" width=\"856\" height=\"634\" alt=\"\u56fe\u7247\" title=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/09\/a6756a0727bbd642dde559189cd5cc1a6fcfd8.png 856w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/09\/a6756a0727bbd642dde559189cd5cc1a6fcfd8-300x222.png 300w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/09\/a6756a0727bbd642dde559189cd5cc1a6fcfd8-150x111.png 150w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/09\/a6756a0727bbd642dde559189cd5cc1a6fcfd8-768x569.png 768w\" sizes=\"auto, (max-width: 856px) 100vw, 856px\" \/><span class=\"data-image-title\">\u56fe\u7247<\/span><\/p>\n<p>\u56fe2\uff1a\u4e3b\u8981\u7ed3\u679c\u603b\u7ed3\uff1a\u7ed9\u5b9a\u53ef\u8ba1\u7b97\u51fd\u6570\u4f5c\u4e3a\u7535\u8def\u7684\u4efb\u4f55\uff08\u8fd1\u4f3c\uff09\u8868\u793a\uff0c\u6211\u4eec\u7528\u4e00\u4e2a\u57fa\u672c\u7684ReLU\u795e\u7ecf\u7f51\u7edc\uff08\u4ece\u9884\u5148\u6307\u5b9a\u7684\u5b57\u5178\u4e2d\u9009\u62e9\uff09\u66ff\u6362\u6bcf\u4e2a\u8ba1\u7b97\u8282\u70b9\uff0c\u8be5\u7f51\u7edc\u6a21\u62df\u76f8\u5e94\u7684\u8ba1\u7b97\u3002<\/p>\n<p>\u901a\u8fc7\u5c06\u901a\u7528\u903c\u8fd1\u7406\u8bba\u4e0e\u7535\u8def\u590d\u6742\u5ea6\u7ed3\u5408\uff0c\u7814\u7a76\u56e2\u961f\u4e3a\u6211\u4eec\u63d0\u4f9b\u4e86\u4e00\u4e2a\u65b0\u7684\u89c6\u89d2\uff1a\u4e0d\u518d\u4ec5\u4ec5\u95ee\u201c\u795e\u7ecf\u7f51\u7edc\u80fd\u5426\u903c\u8fd1\u67d0\u4e2a\u51fd\u6570\u201d\uff0c\u800c\u662f\u95ee\u201c\u795e\u7ecf\u7f51\u7edc\u80fd\u5426\u9ad8\u6548\u5730\u6a21\u62df\u8ba1\u7b97\u8be5\u51fd\u6570\u7684\u7b97\u6cd5\u8fc7\u7a0b\u201d\u3002\u8fd9\u6b63\u662f\u91cf\u5316AI\u63a8\u7406\u6781\u9650\u7684\u5173\u952e\u6240\u5728\u3002<\/p>\n<h3>2.\u7814\u7a76\u65b9\u6cd5\u4e0e\u6838\u5fc3\u6784\u9020<\/h3>\n<p>\u8fd9\u9879\u7814\u7a76\u7684\u6838\u5fc3\uff0c\u662f\u4e00\u5957\u7814\u7a76\u56e2\u961f\u79f0\u4e4b\u4e3a\u201c\u7cfb\u7edf\u5316\u5143\u7b97\u6cd5\uff08Meta-Algorithm\uff09\u201d\u7684\u6784\u9020\u65b9\u6cd5\u3002\u5b83\u7684\u91ce\u5fc3\u5f88\u5927\u2014\u2014\u65e0\u8bba\u4f60\u624b\u91cc\u62ff\u7684\u662f\u5e03\u5c14\u7535\u8def\u3001\u7b97\u672f\u7535\u8def\u3001\u70ed\u5e26\u7535\u8def\uff0c\u8fd8\u662f\u6df7\u5408\u903b\u8f91\u4e0e\u7b97\u672f\u7684\u590d\u6742\u8ba1\u7b97\u56fe\uff0c\u8fd9\u4e2a\u65b9\u6cd5\u90fd\u80fd\u5c06\u5b83\u4e00\u6b65\u6b65\u201c\u7ffb\u8bd1\u201d\u6210\u4e00\u4e2a\u7b49\u4ef7\u7684\u00a0ReLU\u00a0\u524d\u9988\u795e\u7ecf\u7f51\u7edc\uff0c\u800c\u4e14\u662f\u7cbe\u786e\u6a21\u62df\uff0c\u4e0d\u662f\u8fd1\u4f3c\u3002<\/p>\n<p>\u5b9e\u73b0\u7684\u601d\u8def\u5f88\u76f4\u89c2\uff0c\u5148\u628a\u7b97\u6cd5\u62bd\u8c61\u6210\u4e00\u4e2a\u6709\u5411\u65e0\u73af\u56fe\uff08DAG\uff09\uff0c\u6bcf\u4e2a\u8282\u70b9\u5c31\u662f\u4e00\u4e2a\u201c\u95e8\u201d\uff08gate\uff09\uff0c\u6267\u884c\u67d0\u79cd\u57fa\u672c\u8fd0\u7b97\u3002\u7136\u540e\u9488\u5bf9\u6bcf\u79cd\u95e8\u7c7b\u578b\uff0c\u4e8b\u5148\u51c6\u5907\u4e00\u4e2a\u6807\u51c6\u5316\u7684\u00a0ReLU MLP\u6a21\u5757\u4f5c\u4e3a\u201c\u6a21\u62df\u5668\u201d\u3002<\/p>\n<p>\u63a5\u4e0b\u6765\uff0c\u901a\u8fc7\u4e00\u79cd\u88ab\u7814\u7a76\u56e2\u961f\u5f62\u8c61\u5730\u79f0\u4e3a\u201c\u7535\u8def\u624b\u672f\uff08Circuit Surgery\uff09\u201d\u7684\u64cd\u4f5c\uff0c\u628a\u539f\u7535\u8def\u4e2d\u7684\u8282\u70b9\u9010\u4e00\u66ff\u6362\u6210\u5bf9\u5e94\u7684\u00a0MLP\u00a0\u6a21\u5757\uff0c\u5e76\u91cd\u65b0\u63a5\u597d\u8f93\u5165\u8f93\u51fa\u7684\u8fde\u7ebf\u3002\u8fd9\u6837\uff0c\u539f\u7535\u8def\u7684\u8ba1\u7b97\u6d41\u7a0b\u5c31\u88ab\u65e0\u7f1d\u5d4c\u5165\u5230\u795e\u7ecf\u7f51\u7edc\u7684\u8ba1\u7b97\u56fe\u4e2d\u3002<\/p>\n<p>\u8fd9\u79cd\u201c\u624b\u672f\u201d\u6709\u51e0\u4e2a\u5173\u952e\u8981\u6c42\uff1a\u66ff\u6362\u540e\u7684\u7f51\u7edc\u5fc5\u987b\u4fdd\u6301\u539f\u6709\u7684\u8ba1\u7b97\u4f9d\u8d56\u5173\u7cfb\uff08Graph Structure Preservation\uff09\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u7f51\u7edc\u7684\u62d3\u6251\u7ed3\u6784\u8981\u548c\u539f\u7535\u8def\u7684\u00a0DAG\u00a0\u4e00\u4e00\u5bf9\u5e94\u3002<\/p>\n<p>\u540c\u65f6\uff0c\u7f51\u7edc\u7684\u89c4\u6a21\u2014\u2014\u4e5f\u5c31\u662f\u795e\u7ecf\u5143\u548c\u53c2\u6570\u7684\u6570\u91cf\u2014\u2014\u8981\u548c\u539f\u7535\u8def\u7684\u590d\u6742\u5ea6\u6210\u6bd4\u4f8b\uff08Complexity Mapping\uff09\uff0c\u5b9e\u73b0\u7a7a\u95f4\u590d\u6742\u5ea6\u4e0e\u65f6\u95f4\u590d\u6742\u5ea6\u7684\u76f4\u63a5\u6620\u5c04\u3002<\/p>\n<p>\u4e3a\u4e86\u8ba9\u8fd9\u79cd\u6620\u5c04\u5728\u771f\u5b9e\u8ba1\u7b97\u673a\u4e0a\u6210\u7acb\uff0c\u7814\u7a76\u56e2\u961f\u8fd8\u5f15\u5165\u4e86\u6570\u5b57\u8ba1\u7b97\u6a21\u578b\u7684\u7ec6\u8282\u3002\u73b0\u5b9e\u4e2d\u7684\u8ba1\u7b97\u4e0d\u662f\u5728\u8fde\u7eed\u5b9e\u6570\u57df\u4e0a\u8fdb\u884c\u7684\uff0c\u800c\u662f\u5728\u6709\u9650\u7cbe\u5ea6\u7684\u6570\u503c\u7f51\u683c\u4e0a\u8fd0\u7b97\u3002<\/p>\n<p>\u6280\u672f\u8bba\u6587\u4e2d\u660e\u786e\u4e86\u6a21\u8fd0\u7b97\uff08modular arithmetic\uff09\u548c\u820d\u5165\u673a\u5236\uff08rounding scheme\uff09\u7684\u5b9a\u4e49\uff0c\u5e76\u63d0\u51fa\u4e86\u201c\u673a\u5668\u7cbe\u5ea6\u4e0b\u7684\u51fd\u6570\u7b49\u4ef7\u6027\u201d\u2014\u2014\u5982\u679c\u4e24\u4e2a\u51fd\u6570\u5728\u7ed9\u5b9a\u7cbe\u5ea6\u7684\u6570\u503c\u7f51\u683c\u4e0a\u8f93\u51fa\u5b8c\u5168\u4e00\u81f4\uff0c\u5c31\u8ba4\u4e3a\u5b83\u4eec\u662f\u7b49\u4ef7\u7684\u3002\u8fd9\u4e3a\u540e\u7eed\u7684\u7cbe\u786e\u6a21\u62df\u63d0\u4f9b\u4e86\u4e25\u683c\u7684\u5224\u636e\u3002<\/p>\n<h3>3.\u4e3b\u8981\u7406\u8bba\u7ed3\u679c<\/h3>\n<h4>Theorem 1\uff1a\u901a\u7528\u63a8\u7406\uff08Universal Reasoning\uff09<\/h4>\n<p>\u8fd9\u662f\u5168\u6587\u7684\u57fa\u77f3\u6027\u7ed3\u8bba\u3002<\/p>\n<p>\u5b83\u65ad\u8a00\u4efb\u610f\u7531\u7279\u5b9a\u95e8\u96c6\u00a0GG\u00a0\u6784\u6210\u7684\u7535\u8def\uff0c\u90fd\u53ef\u4ee5\u901a\u8fc7\u5b8c\u5168\u65e0\u7f3a\u9677\u7684\u201c\u7535\u8def\u624b\u672f\u201d\u8f6c\u5316\u4e3a\u4e00\u4e2a\u00a0ReLU\u00a0\u524d\u9988\u7f51\u7edc\uff0c\u5e76\u4e14\u5728\u6570\u5b57\u8ba1\u7b97\u673a\u4e0a\u7cbe\u786e\u590d\u73b0\u539f\u7535\u8def\u7684\u529f\u80fd\u3002<\/p>\n<p>\u66f4\u91cd\u8981\u7684\u662f\uff0c\u8fd9\u4e2a\u7f51\u7edc\u7684\u7a7a\u95f4\u590d\u6742\u5ea6\uff08\u795e\u7ecf\u5143\u6570\u91cf\uff09\u4e0e\u539f\u7535\u8def\u7684\u65f6\u95f4\u590d\u6742\u5ea6\uff08\u95e8\u6570\u91cf\uff09\u540c\u9636\uff0c\u8ba1\u7b97\u56fe\u7684\u5f62\u72b6\u4e5f\u4e0e\u539f\u7535\u8def\u4e00\u81f4\u3002\u8fd9\u610f\u5473\u7740\uff0c\u795e\u7ecf\u7f51\u7edc\u4e0d\u4ec5\u80fd\u201c\u7b97\u5bf9\u201d\uff0c\u8fd8\u80fd\u201c\u6309\u539f\u7b97\u6cd5\u7684\u8282\u594f\u53bb\u7b97\u201d\uff0c\u771f\u6b63\u5b9e\u73b0\u4e86\u63a8\u7406\u8fc7\u7a0b\u7684\u7ed3\u6784\u5316\u4fdd\u771f\u3002<\/p>\n<h4>Theorem 2\uff1a\u6709\u9650\u7cbe\u5ea6\u4e0b\u7684\u901a\u7528\u7535\u8def\u8bbe\u8ba1<\/h4>\n<p>\u5982\u679c\u8bf4\u00a0Theorem 1\u00a0\u89e3\u51b3\u4e86\u201c\u80fd\u4e0d\u80fd\u6a21\u62df\u201d\u7684\u95ee\u9898\uff0cTheorem 2\u00a0\u5219\u8fdb\u4e00\u6b65\u56de\u7b54\u4e86\u201c\u6709\u6ca1\u6709\u9057\u6f0f\u201d\u7684\u7591\u95ee\u3002<\/p>\n<p>\u5b83\u8bc1\u660e\u5728\u6709\u9650\u7cbe\u5ea6\u7684\u6570\u503c\u7a7a\u95f4\u4e0a\uff0c\u4efb\u4f55\u51fd\u6570\u90fd\u53ef\u4ee5\u7531\u4e00\u4e2a\u00a0ReLU MLP\u00a0\u7cbe\u786e\u5b9e\u73b0\u3002<\/p>\n<p>\u8fd9\u662f\u4e00\u4e2a\u6570\u5b57\u8ba1\u7b97\u7248\u672c\u7684\u201c\u8d85\u4f4d\u5b9a\u7406\u201d\uff0c\u4e0eKolmogorov\u2013Arnold\u00a0\u8d85\u4f4d\u5b9a\u7406\u5728\u601d\u60f3\u4e0a\u76f8\u547c\u5e94\u2014\u2014\u540e\u8005\u8bf4\u4efb\u4f55\u591a\u5143\u8fde\u7eed\u51fd\u6570\u90fd\u53ef\u4ee5\u7531\u5355\u53d8\u91cf\u51fd\u6570\u7684\u53e0\u52a0\u8868\u793a\uff0c\u8fd9\u91cc\u5219\u8bf4\u4efb\u4f55\u6709\u9650\u7cbe\u5ea6\u51fd\u6570\u90fd\u53ef\u4ee5\u7531\u4e00\u4e2a\u901a\u7528\u7f16\u7801\u5668\u7f51\u7edc\u52a0\u4e0a\u7ebf\u6027\u89e3\u7801\u5b9e\u73b0\u3002<\/p>\n<p>\u4e0e\u7ecf\u5178\u7684\u901a\u7528\u903c\u8fd1\u5b9a\u7406\u76f8\u6bd4\uff0c\u8fd9\u4e24\u4e2a\u7ed3\u679c\u7684\u8986\u76d6\u9762\u66f4\u5e7f\u3002\u901a\u7528\u903c\u8fd1\u5b9a\u7406\u53ea\u80fd\u4fdd\u8bc1\u5728\u65e0\u9650\u7cbe\u5ea6\u3001\u8fde\u7eed\u57df\u4e0a\u7684\u8fd1\u4f3c\uff0c\u800c\u8fd9\u91cc\u7684\u6784\u9020\u4e0d\u4ec5\u6db5\u76d6\u4e86\u903c\u8fd1\uff0c\u8fd8\u6db5\u76d6\u4e86\u63a8\u7406\u4efb\u52a1\u7684\u7cbe\u786e\u6267\u884c\uff0c\u5305\u62ec\u903b\u8f91\u8fd0\u7b97\u3001\u52a8\u6001\u89c4\u5212\u3001\u751a\u81f3\u6709\u9650\u6b65\u7684\u56fe\u7075\u673a\u6a21\u62df\u3002<\/p>\n<p>\u6362\u53e5\u8bdd\u8bf4\uff0c\u5b83\u4e0d\u4ec5\u56de\u7b54\u4e86\u201c\u795e\u7ecf\u7f51\u7edc\u80fd\u5426\u5b66\u4f1a\u67d0\u4e2a\u51fd\u6570\u201d\uff0c\u8fd8\u56de\u7b54\u4e86\u201c\u795e\u7ecf\u7f51\u7edc\u80fd\u5426\u539f\u5c01\u4e0d\u52a8\u5730\u6267\u884c\u67d0\u4e2a\u7b97\u6cd5\u201d\u3002<\/p>\n<p><img data-dominant-color=\"ece7ef\" data-has-transparency=\"false\" style=\"--dominant-color: #ece7ef;\" loading=\"lazy\" decoding=\"async\" class=\"not-transparent alignnone size-full wp-image-26905\" src=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/09\/42f2cc8021ff93847c0955520f32c89976ea6c.png\" width=\"1080\" height=\"543\" alt=\"\u56fe\u7247\" title=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/09\/42f2cc8021ff93847c0955520f32c89976ea6c.png 1080w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/09\/42f2cc8021ff93847c0955520f32c89976ea6c-300x151.png 300w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/09\/42f2cc8021ff93847c0955520f32c89976ea6c-1024x515.png 1024w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/09\/42f2cc8021ff93847c0955520f32c89976ea6c-150x75.png 150w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/09\/42f2cc8021ff93847c0955520f32c89976ea6c-768x386.png 768w\" sizes=\"auto, (max-width: 1080px) 100vw, 1080px\" \/><span class=\"data-image-title\">\u56fe\u7247<\/span><\/p>\n<p>\u56fe3\uff1a\u5b9a\u74062\u4e2d\u6784\u9020\u7684\u6700\u574f\u60c5\u51b5\u8fd1\u4f3c\u503c\u7684\u8bf4\u660e\u3002<\/p>\n<p>\u8fd9\u79cd\u4ece\u7535\u8def\u5230\u7f51\u7edc\u7684\u7cfb\u7edf\u5316\u6620\u5c04\uff0c\u8ba9\u201cAI\u00a0\u63a8\u7406\u80fd\u529b\u201d\u7b2c\u4e00\u6b21\u6709\u4e86\u53ef\u8ba1\u7b97\u3001\u53ef\u9a8c\u8bc1\u7684\u6570\u5b66\u523b\u753b\uff0c\u4e5f\u4e3a\u672a\u6765\u5728\u590d\u6742\u63a8\u7406\u4efb\u52a1\u4e2d\u8bbe\u8ba1\u9ad8\u6548\u3001\u53ef\u89e3\u91ca\u7684\u795e\u7ecf\u7f51\u7edc\u67b6\u6784\u63d0\u4f9b\u4e86\u575a\u5b9e\u7684\u7406\u8bba\u652f\u6491\u3002<\/p>\n<h3>4.\u5e94\u7528\u6848\u4f8b\u5206\u6790<\/h3>\n<p>\u5728\u7406\u8bba\u6846\u67b6\u5960\u5b9a\u4e4b\u540e\uff0c\u7814\u7a76\u56e2\u961f\u7528\u4e00\u7cfb\u5217\u63a8\u8bba\uff08Corollary\uff09\u5c55\u793a\u4e86\u8fd9\u4e00\u65b9\u6cd5\u5728\u4e0d\u540c\u7c7b\u578b\u63a8\u7406\u4efb\u52a1\u4e2d\u7684\u5a01\u529b\u3002\u8fd9\u4e9b\u6848\u4f8b\u4e0d\u4ec5\u662f\u6570\u5b66\u4e0a\u7684\u201c\u5b58\u5728\u6027\u8bc1\u660e\u201d\uff0c\u66f4\u662f\u5bf9\u795e\u7ecf\u7f51\u7edc\u63a8\u7406\u8fb9\u754c\u7684\u4e00\u6b21\u6b21\u51b2\u51fb\u3002<\/p>\n<h4>\u5e03\u5c14\u51fd\u6570\u5b9e\u73b0\u590d\u6742\u5ea6\u4f18\u5316\uff08Corollary 1\uff09<\/h4>\n<p>\u4f20\u7edf\u4e0a\uff0c\u67d0\u4e9b\u5e03\u5c14\u51fd\u6570\u7684\u795e\u7ecf\u7f51\u7edc\u5b9e\u73b0\u590d\u6742\u5ea6\u4f1a\u5448\u73b0\u53cc\u6307\u6570\u7ea7\u589e\u957f\uff0c\u8fd9\u51e0\u4e4e\u8ba9\u76f4\u63a5\u6a21\u62df\u53d8\u5f97\u4e0d\u53ef\u884c\u3002<\/p>\n<p>\u7814\u7a76\u56e2\u961f\u901a\u8fc7\u7cfb\u7edf\u5316\u5143\u7b97\u6cd5\uff0c\u5c06\u8fd9\u79cd\u590d\u6742\u5ea6\u538b\u7f29\u5230\u5355\u6307\u6570\u7ea7\uff0c\u903c\u8fd1\u5df2\u77e5\u7684\u7406\u8bba\u4e0b\u754c\u3002\u8fd9\u610f\u5473\u7740\uff0c\u5728\u53ef\u8ba1\u7b97\u6027\u8fb9\u754c\u9644\u8fd1\uff0cReLU\u00a0\u7f51\u7edc\u7684\u8868\u8fbe\u6548\u7387\u88ab\u663e\u8457\u63d0\u5347\uff0c\u5c24\u5176\u662f\u5728\u9700\u8981\u7cbe\u786e\u903b\u8f91\u63a8\u7406\u7684\u4efb\u52a1\u4e2d\u3002<\/p>\n<h4>\u968f\u673a\u5316\u903b\u8f91\u7535\u8def\u53bb\u968f\u673a\u5316\uff08Corollary 2\uff09<\/h4>\n<p>\u5728\u7ecf\u5178\u8ba1\u7b97\u7406\u8bba\u4e2d\uff0c\u968f\u673a\u5316\u5e03\u5c14\u7535\u8def\u5e38\u88ab\u7528\u6765\u7b80\u5316\u67d0\u4e9b\u95ee\u9898\u7684\u5b9e\u73b0\u3002\u4f46\u7814\u7a76\u56e2\u961f\u8bc1\u660e\uff0c\u8fd9\u4e9b\u7535\u8def\u53ef\u4ee5\u88ab\u7b49\u4ef7\u7684\u786e\u5b9a\u6027\u00a0ReLU\u00a0\u7f51\u7edc\u66ff\u4ee3\uff0c\u4e14\u4e0d\u635f\u5931\u529f\u80fd\u3002<\/p>\n<p>\u8fd9\u4e0d\u4ec5\u662f\u4e00\u6b21\u201c\u53bb\u968f\u673a\u5316\u201d\u7684\u80dc\u5229\uff0c\u4e5f\u4e3a\u6784\u5efa\u53ef\u9a8c\u8bc1\u3001\u53ef\u5ba1\u8ba1\u7684\u63a8\u7406\u7f51\u7edc\u63d0\u4f9b\u4e86\u8def\u5f84\u2014\u2014\u6bd5\u7adf\uff0c\u786e\u5b9a\u6027\u610f\u5473\u7740\u53ef\u91cd\u590d\u6027\u548c\u53ef\u8ffd\u6eaf\u6027\u3002<\/p>\n<h4>\u6709\u9650\u65f6\u95f4\u56fe\u7075\u673a\u6a21\u62df\uff08Corollary 3\uff09<\/h4>\n<p>\u66f4\u5177\u51b2\u51fb\u529b\u7684\u662f\uff0c\u7814\u7a76\u56e2\u961f\u5c55\u793a\u4e86\u5982\u4f55\u7528\u00a0ReLU\u00a0\u7f51\u7edc\u7cbe\u786e\u6a21\u62df\u6709\u9650\u6b65\u8fd0\u884c\u7684\u56fe\u7075\u673a\uff0c\u5e76\u4fdd\u7559\u663e\u5f0f\u7684\u63a8\u7406\u94fe\u3002<\/p>\n<p>\u8fd9\u79cd\u6a21\u62df\u4e0d\u662f\u9ed1\u7bb1\u5f0f\u7684\uff0c\u800c\u662f\u7ed3\u6784\u4e0a\u5bf9\u5e94\u539f\u56fe\u7075\u673a\u7684\u72b6\u6001\u8f6c\u79fb\u4e0e\u7b26\u53f7\u64cd\u4f5c\uff0c\u8ba9\u7f51\u7edc\u7684\u6bcf\u4e00\u6b65\u8ba1\u7b97\u90fd\u80fd\u88ab\u89e3\u91ca\u4e3a\u5177\u4f53\u7684\u7b97\u6cd5\u6b65\u9aa4\u3002<\/p>\n<h4>\u52a8\u6001\u89c4\u5212\u4e0e\u56fe\u8ba1\u7b97\uff08Corollary 4\uff09<\/h4>\n<p>\u5728\u56fe\u8ba1\u7b97\u9886\u57df\uff0c\u7814\u7a76\u56e2\u961f\u4ee5\u5168\u70b9\u5bf9\u6700\u77ed\u8def\u5f84\uff08All-Pairs Shortest Path, ASP\uff09\u95ee\u9898\u4e3a\u4f8b\uff0c\u6784\u9020\u4e86\u4e00\u4e2a\u7acb\u65b9\u590d\u6742\u5ea6\u7684\u00a0ReLU\u00a0\u7f51\u7edc\u5b9e\u73b0\u3002<\/p>\n<p>\u8fd9\u79cd\u5b9e\u73b0\u4e0d\u4ec5\u4fdd\u7559\u4e86\u52a8\u6001\u89c4\u5212\u7684\u9012\u63a8\u7ed3\u6784\uff0c\u8fd8\u5728\u7f51\u7edc\u4e2d\u663e\u5f0f\u7f16\u7801\u4e86\u56fe\u7684\u62d3\u6251\u4fe1\u606f\uff0c\u5c55\u793a\u4e86\u795e\u7ecf\u7f51\u7edc\u5728\u7ed3\u6784\u5316\u63a8\u7406\u4efb\u52a1\u4e2d\u7684\u6f5c\u529b\u3002<\/p>\n<p><img data-dominant-color=\"c6c4ca\" data-has-transparency=\"false\" style=\"--dominant-color: #c6c4ca;\" loading=\"lazy\" decoding=\"async\" class=\"not-transparent alignnone size-full wp-image-26906\" src=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/09\/e588cd969f3a3b4419c603d19100cbee1c588a.png\" width=\"1080\" height=\"550\" alt=\"\u56fe4\uff1a\u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60\u4e2d\u56fe\u5f62\u7684\u6781\u503c\u793a\u4f8b\u3002\" title=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/09\/e588cd969f3a3b4419c603d19100cbee1c588a.png 1080w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/09\/e588cd969f3a3b4419c603d19100cbee1c588a-300x153.png 300w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/09\/e588cd969f3a3b4419c603d19100cbee1c588a-1024x521.png 1024w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/09\/e588cd969f3a3b4419c603d19100cbee1c588a-150x76.png 150w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2025\/09\/e588cd969f3a3b4419c603d19100cbee1c588a-768x391.png 768w\" sizes=\"auto, (max-width: 1080px) 100vw, 1080px\" \/><span class=\"data-image-title\">\u56fe4\uff1a\u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60\u4e2d\u56fe\u5f62\u7684\u6781\u503c\u793a\u4f8b\u3002<\/span><\/p>\n<h4>\u63a8\u7406\u80fd\u529b\u8574\u542b\u901a\u7528\u903c\u8fd1\uff08Corollary 5\uff09<\/h4>\n<p>\u6700\u540e\u7814\u7a76\u56e2\u961f\u6307\u51fa\uff0c\u5982\u679c\u4e00\u4e2a\u7f51\u7edc\u80fd\u591f\u6267\u884c\u4e0a\u8ff0\u63a8\u7406\u4efb\u52a1\uff0c\u90a3\u4e48\u5b83\u5728\u6709\u9650\u7cbe\u5ea6\u4e0b\u4e5f\u5fc5\u7136\u5177\u5907\u901a\u7528\u903c\u8fd1\u80fd\u529b\u3002<\/p>\n<p>\u6362\u53e5\u8bdd\u8bf4\uff0c\u63a8\u7406\u80fd\u529b\u672c\u8eab\u5c31\u6db5\u76d6\u4e86\u51fd\u6570\u903c\u8fd1\u7684\u80fd\u529b\u2014\u2014\u800c\u4e14\u662f\u7cbe\u786e\u7684\u3001\u975e\u8fd1\u4f3c\u7684\u3002\u8fd9\u4e3a\u201c\u63a8\u7406\u4f18\u4e8e\u903c\u8fd1\u201d\u7684\u89c2\u70b9\u63d0\u4f9b\u4e86\u575a\u5b9e\u7684\u7406\u8bba\u652f\u6491\u3002<\/p>\n<h3>5.\u7406\u8bba\u610f\u4e49\u4e0e\u521b\u65b0\u70b9<\/h3>\n<p>\u8fd9\u9879\u5de5\u4f5c\u7684\u610f\u4e49\uff0c\u4e0d\u4ec5\u5728\u4e8e\u63d0\u51fa\u4e86\u4e00\u4e2a\u65b0\u7684\u6784\u9020\u65b9\u6cd5\uff0c\u66f4\u5728\u4e8e\u5b83\u5efa\u7acb\u4e86\u4e00\u4e2a\u7edf\u4e00\u7684\u7406\u8bba\u6846\u67b6\uff0c\u5c06\u7535\u8def\u590d\u6742\u5ea6\u3001\u53ef\u8ba1\u7b97\u6027\u7406\u8bba\u4e0e\u795e\u7ecf\u7f51\u7edc\u7684\u8868\u8fbe\u80fd\u529b\u7d27\u5bc6\u8fde\u63a5\u8d77\u6765\u3002<\/p>\n<p>\u8fc7\u53bb\u6211\u4eec\u5e38\u7528\u201c\u901a\u7528\u903c\u8fd1\u5b9a\u7406\u201d\u6765\u63cf\u8ff0\u7f51\u7edc\u7684\u6f5c\u529b\uff0c\u4f46\u90a3\u53ea\u662f\u51fd\u6570\u6620\u5c04\u7684\u89c6\u89d2\uff1b\u73b0\u5728\uff0c\u6211\u4eec\u6709\u4e86\u4e00\u4e2a\u80fd\u76f4\u63a5\u523b\u753b\u7b97\u6cd5\u8fc7\u7a0b\u7684\u5de5\u5177\u3002<\/p>\n<p>\u8fd9\u79cd\u65b9\u6cd5\u7684\u53e6\u4e00\u4e2a\u4eae\u70b9\u662f\u63a8\u7406\u53ef\u89e3\u91ca\u6027\u3002\u7531\u4e8e\u7f51\u7edc\u7684\u8ba1\u7b97\u56fe\u4e0e\u539f\u7b97\u6cd5\u7684\u6b65\u9aa4\u4e00\u4e00\u5bf9\u5e94\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u5728\u7f51\u7edc\u7ed3\u6784\u4e2d\u201c\u770b\u5230\u201d\u63a8\u7406\u94fe\u6761\u3002\u8fd9\u5bf9\u4e8e\u9700\u8981\u5ba1\u8ba1\u3001\u9a8c\u8bc1\u6216\u8c03\u8bd5\u7684\u9ad8\u98ce\u9669\u5e94\u7528\uff08\u5982\u91d1\u878d\u5408\u89c4\u3001\u533b\u7597\u8bca\u65ad\uff09\u5c24\u4e3a\u91cd\u8981\u3002<\/p>\n<p>\u5728\u590d\u6742\u5ea6\u53ef\u91cf\u5316\u65b9\u9762\uff0c\u7814\u7a76\u56e2\u961f\u660e\u786e\u4e86\u7f51\u7edc\u89c4\u6a21\u4e0e\u7b97\u6cd5\u590d\u6742\u5ea6\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u4f7f\u5f97\u6211\u4eec\u53ef\u4ee5\u5728\u8bbe\u8ba1\u9636\u6bb5\u5c31\u9884\u6d4b\u6240\u9700\u7684\u8ba1\u7b97\u8d44\u6e90\u3002\u8fd9\u79cd\u53ef\u9884\u6d4b\u6027\u4e3a\u5de5\u7a0b\u5b9e\u73b0\u548c\u786c\u4ef6\u90e8\u7f72\u63d0\u4f9b\u4e86\u575a\u5b9e\u7684\u57fa\u7840\u3002<\/p>\n<p>\u6700\u91cd\u8981\u7684\u662f\uff0c\u8fd9\u9879\u7814\u7a76\u8d85\u8d8a\u4e86\u903c\u8fd1\u7406\u8bba\u7684\u5c40\u9650\u3002\u5b83\u4e0d\u518d\u505c\u7559\u5728\u201c\u7f51\u7edc\u80fd\u5426\u903c\u8fd1\u67d0\u4e2a\u51fd\u6570\u201d\u7684\u95ee\u9898\u4e0a\uff0c\u800c\u662f\u76f4\u63a5\u56de\u7b54\u201c\u7f51\u7edc\u80fd\u5426\u7cbe\u786e\u6267\u884c\u67d0\u4e2a\u7b97\u6cd5\u201d\u3002\u8fd9\u4e3a\u672a\u6765\u6784\u5efa\u5177\u5907\u53ef\u9a8c\u8bc1\u63a8\u7406\u80fd\u529b\u7684\u795e\u7ecf\u7f51\u7edc\u67b6\u6784\u6253\u5f00\u4e86\u65b0\u7684\u5927\u95e8\uff0c\u4e5f\u4e3a\u00a0AI\u00a0\u63a8\u7406\u7684\u53ef\u8ba1\u7b97\u6027\u7814\u7a76\u63d0\u4f9b\u4e86\u65b0\u7684\u5750\u6807\u7cfb\u3002<\/p>\n<h3>6.\u672a\u6765\u7814\u7a76\u65b9\u5411<\/h3>\n<p>\u8fd9\u9879\u7814\u7a76\u867d\u7136\u5df2\u7ecf\u4e3a\u201c\u795e\u7ecf\u7f51\u7edc\u80fd\u5426\u7cbe\u786e\u6267\u884c\u7b97\u6cd5\u201d\u7ed9\u51fa\u4e86\u575a\u5b9e\u7684\u7406\u8bba\u7b54\u6848\uff0c\u4f46\u7814\u7a76\u56e2\u961f\u4e5f\u6e05\u695a\uff0c\u8fd9\u53ea\u662f\u4e00\u4e2a\u8d77\u70b9\u3002\u672a\u6765\u7684\u63a2\u7d22\u7a7a\u95f4\uff0c\u65e2\u6709\u6570\u5b66\u4e0a\u7684\u6df1\u6c34\u533a\uff0c\u4e5f\u6709\u5de5\u7a0b\u843d\u5730\u7684\u5e7f\u9614\u5929\u5730\u3002<\/p>\n<p>\u9996\u5148\uff0c\u662f\u6269\u5c55\u5230\u975e\u6b27\u51e0\u91cc\u5f97\u4e0e\u65e0\u9650\u7ef4\u8f93\u5165\u8f93\u51fa\u7684\u6311\u6218\u3002\u5f53\u524d\u7684\u6784\u9020\u4e3b\u8981\u9488\u5bf9\u6b27\u51e0\u91cc\u5f97\u7a7a\u95f4\u4e2d\u7684\u6709\u9650\u7ef4\u5411\u91cf\u8f93\u5165\u8f93\u51fa\uff0c\u800c\u73b0\u5b9e\u4e2d\u7684\u8bb8\u591a\u63a8\u7406\u4efb\u52a1\u2014\u2014\u6bd4\u5982\u56fe\u7ed3\u6784\u5206\u6790\u3001\u6d41\u5f62\u4e0a\u7684\u4fe1\u53f7\u5904\u7406\u3001\u751a\u81f3\u51fd\u6570\u7a7a\u95f4\u4e0a\u7684\u7b97\u5b50\u6c42\u89e3\u2014\u2014\u90fd\u5929\u7136\u5904\u4e8e\u975e\u6b27\u51e0\u91cc\u5f97\u6216\u65e0\u9650\u7ef4\u73af\u5883\u4e2d\u3002<\/p>\n<p>\u5982\u4f55\u5728\u8fd9\u4e9b\u7a7a\u95f4\u4e2d\u5b9a\u4e49\u201c\u7535\u8def\u624b\u672f\u201d\uff0c\u5e76\u4fdd\u6301\u8ba1\u7b97\u56fe\u7684\u7ed3\u6784\u4fdd\u771f\uff0c\u5c06\u662f\u4e0b\u4e00\u6b65\u7684\u5173\u952e\u3002\u8fd9\u4e0d\u4ec5\u6d89\u53ca\u5230\u62d3\u6251\u4e0e\u51e0\u4f55\u7684\u5d4c\u5165\u95ee\u9898\uff0c\u8fd8\u53ef\u80fd\u5f15\u5165\u8c31\u56fe\u7406\u8bba\u3001\u6838\u65b9\u6cd5\u7b49\u5de5\u5177\uff0c\u4e3a\u795e\u7ecf\u7f51\u7edc\u7684\u63a8\u7406\u80fd\u529b\u5f00\u8f9f\u65b0\u7684\u7ef4\u5ea6\u3002<\/p>\n<p>\u5176\u6b21\uff0c\u662f\u5c06\u7ecf\u5178\u903c\u8fd1\u6784\u9020\uff08\u5982\u5c0f\u6ce2\u3001\u6837\u6761\uff09\u8f6c\u5316\u4e3a\u7535\u8def\u8868\u793a\u3002\u5c0f\u6ce2\u5206\u89e3\u3001B\u6837\u6761\u63d2\u503c\u7b49\u65b9\u6cd5\u5728\u4fe1\u53f7\u5904\u7406\u548c\u6570\u503c\u5206\u6790\u4e2d\u6709\u7740\u6210\u719f\u7684\u7406\u8bba\u4e0e\u9ad8\u6548\u7684\u5b9e\u73b0\uff0c\u5982\u679c\u80fd\u5c06\u5b83\u4eec\u7cfb\u7edf\u5316\u5730\u8f6c\u5316\u4e3a\u7535\u8def\uff0c\u518d\u6620\u5c04\u5230\u00a0ReLU\u00a0\u7f51\u7edc\uff0c\u5c31\u80fd\u628a\u8fd9\u4e9b\u201c\u4eba\u7c7b\u8bbe\u8ba1\u7684\u9ad8\u6548\u57fa\u201d\u76f4\u63a5\u6ce8\u5165\u5230\u795e\u7ecf\u7f51\u7edc\u7684\u7ed3\u6784\u4e2d\u3002<\/p>\n<p>\u8fd9\u4e0d\u4ec5\u53ef\u80fd\u5e26\u6765\u66f4\u7d27\u51d1\u7684\u7f51\u7edc\u89c4\u6a21\uff0c\u8fd8\u80fd\u5728\u7279\u5b9a\u4efb\u52a1\u4e0a\u83b7\u5f97\u66f4\u5f3a\u7684\u5f52\u7eb3\u504f\u7f6e\uff0c\u8ba9\u7f51\u7edc\u5728\u8bad\u7ec3\u6837\u672c\u6709\u9650\u7684\u60c5\u51b5\u4e0b\u4f9d\u7136\u4fdd\u6301\u9ad8\u7cbe\u5ea6\u63a8\u7406\u3002<\/p>\n<p>\u6700\u540e\u662f\u7ed3\u5408\u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60\u4e0e\u7b97\u5b50\u5b66\u4e60\u7684\u5e94\u7528\u573a\u666f\uff0c\u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60\uff08Geometric Deep Learning\uff09\u5f3a\u8c03\u5728\u56fe\u3001\u6d41\u5f62\u3001\u7fa4\u7b49\u7ed3\u6784\u5316\u7a7a\u95f4\u4e2d\u8fdb\u884c\u5b66\u4e60\uff0c\u800c\u7b97\u5b50\u5b66\u4e60\uff08Operator Learning\uff09\u5219\u5173\u6ce8\u4ece\u51fd\u6570\u5230\u51fd\u6570\u7684\u6620\u5c04\uff0c\u4f8b\u5982\u6c42\u89e3\u504f\u5fae\u5206\u65b9\u7a0b\u6216\u6a21\u62df\u7269\u7406\u7cfb\u7edf\u3002<\/p>\n<p>\u5c06\u672c\u7814\u7a76\u7684\u201c\u7b97\u6cd5\u5230\u7f51\u7edc\u201d\u6620\u5c04\u65b9\u6cd5\u4e0e\u8fd9\u4e24\u7c7b\u524d\u6cbf\u65b9\u5411\u7ed3\u5408\uff0c\u6709\u671b\u6784\u5efa\u51fa\u65e2\u80fd\u4fdd\u7559\u63a8\u7406\u94fe\u6761\u3001\u53c8\u80fd\u5904\u7406\u590d\u6742\u7ed3\u6784\u5316\u6570\u636e\u7684\u901a\u7528\u63a8\u7406\u7f51\u7edc\u3002\u4f8b\u5982\uff0c\u5728\u5206\u5b50\u6a21\u62df\u4e2d\uff0c\u7f51\u7edc\u53ef\u4ee5\u76f4\u63a5\u5d4c\u5165\u5316\u5b66\u53cd\u5e94\u7684\u7b97\u6cd5\u6d41\u7a0b\uff1b\u5728\u6c14\u5019\u5efa\u6a21\u4e2d\uff0c\u7f51\u7edc\u53ef\u4ee5\u7cbe\u786e\u6267\u884c\u6570\u503c\u79ef\u5206\u4e0e\u8fb9\u754c\u6761\u4ef6\u5904\u7406\u3002<\/p>\n<p>\u53ef\u4ee5\u9884\u89c1\uff0c\u8fd9\u4e9b\u65b9\u5411\u7684\u63a8\u8fdb\uff0c\u5c06\u8ba9\u795e\u7ecf\u7f51\u7edc\u7684\u63a8\u7406\u80fd\u529b\u4ece\u201c\u80fd\u505a\u201d\u8d70\u5411\u201c\u80fd\u89e3\u91ca\u3001\u80fd\u6cdb\u5316\u3001\u80fd\u8fc1\u79fb\u201d\uff0c\u5e76\u6700\u7ec8\u5728\u79d1\u5b66\u8ba1\u7b97\u3001\u5de5\u7a0b\u8bbe\u8ba1\u3001\u91d1\u878d\u5efa\u6a21\u7b49\u9ad8\u4ef7\u503c\u9886\u57df\u91ca\u653e\u51fa\u66f4\u5927\u7684\u6f5c\u529b\u3002\uff08END\uff09<\/p>\n<p>\u53c2\u8003\u8d44\u6599\uff1ahttps:\/\/arxiv.org\/pdf\/2508.18526<\/p>\n<p>\u6587\u7ae0\u6765\u81ea\uff1a51CTO<\/p>\n<\/div>\n<\/div>\n<div class=\"pvc_clear\"><\/div>\n<p id=\"pvc_stats_26900\" class=\"pvc_stats total_only  \" data-element-id=\"26900\" style=\"\"><i class=\"pvc-stats-icon medium\" aria-hidden=\"true\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" version=\"1.0\" viewBox=\"0 0 502 315\" preserveAspectRatio=\"xMidYMid meet\"><g transform=\"translate(0,332) scale(0.1,-0.1)\" fill=\"\" stroke=\"none\"><path d=\"M2394 3279 l-29 -30 -3 -207 c-2 -182 0 -211 15 -242 39 -76 157 -76 196 0 15 31 17 60 15 243 l-3 209 -33 29 c-26 23 -41 29 -80 29 -41 0 -53 -5 -78 -31z\"\/><path d=\"M3085 3251 c-45 -19 -58 -50 -96 -229 -47 -217 -49 -260 -13 -295 52 -53 146 -42 177 20 16 31 87 366 87 410 0 70 -86 122 -155 94z\"\/><path d=\"M1751 3234 c-13 -9 -29 -31 -37 -50 -12 -29 -10 -49 21 -204 19 -94 39 -189 45 -210 14 -50 54 -80 110 -80 34 0 48 6 76 34 21 21 34 44 34 59 0 14 -18 113 -40 219 -37 178 -43 195 -70 221 -36 32 -101 37 -139 11z\"\/><path d=\"M1163 3073 c-36 -7 -73 -59 -73 -102 0 -56 133 -378 171 -413 34 -32 83 -37 129 -13 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