{"id":296,"date":"2023-09-15T17:29:20","date_gmt":"2023-09-15T09:29:20","guid":{"rendered":"http:\/\/106.52.213.145:21080\/?p=296"},"modified":"2023-09-17T23:51:21","modified_gmt":"2023-09-17T15:51:21","slug":"wenxuefanyitujuanjijieshaofanyi","status":"publish","type":"post","link":"https:\/\/apifj.com\/index.php\/2023\/09\/15\/wenxuefanyitujuanjijieshaofanyi\/","title":{"rendered":"[\u6587\u732e\u7ffb\u8bd1]\u56fe\u5377\u79ef\u4ecb\u7ecd"},"content":{"rendered":"

\u539f\u6587\u732e\uff1ahttp:\/\/distill.pub\/2021\/gnn-intro\/<\/a><\/h1>\n

\u56fe\u5377\u79ef\u4ecb\u7ecd<\/h1>\n

\u795e\u7ecf\u7f51\u7edc\u5df2\u7ecf\u88ab\u8c03\u6574\u4ee5\u5229\u7528\u56fe\u7684\u7ed3\u6784\u548c\u5c5e\u6027\u3002\u6211\u4eec\u63a2\u8ba8\u4e86\u6784\u5efa\u56fe\u795e\u7ecf\u7f51\u7edc\u6240\u9700\u7684\u7ec4\u4ef6\uff0c\u5e76\u89e3\u91ca\u4e86\u5b83\u4eec\u80cc\u540e\u7684\u8bbe\u8ba1\u9009\u62e9\u52a8\u673a\u3002<\/p>\n

\"Screenshot<\/p>\n

\n

AUTHORS AFFILIATIONS<\/p>\n

Benjamin Sanchez-Lengeling Google Research<\/p>\n

Emily Reif Google Research<\/p>\n

Adam Pearce<\/a> Google Research<\/p>\n

Alexander B. Wiltschko Google Research<\/p>\n

PUBLISHED Sept. 2, 2021<\/p>\n

DOI 10.23915\/distill.00033<\/a><\/p>\n<\/blockquote>\n

\u8fd9\u7bc7\u6587\u7ae0\u662f\u300aDistill\u300b\u5173\u4e8e\u56fe\u795e\u7ecf\u7f51\u7edc\u7684\u4e24\u7bc7\u51fa\u7248\u7269\u4e4b\u4e00\u3002\u8bf7\u67e5\u770b\u300a\u7406\u89e3\u56fe\u4e0a\u7684\u5377\u79ef\u300b[1]\uff0c\u4ee5\u4e86\u89e3\u5982\u4f55\u5c06\u56fe\u4e0a\u7684\u5377\u79ef\u81ea\u7136\u5730\u63a8\u5e7f\u5230\u56fe\u4e0a\u7684\u5377\u79ef\u3002<\/p>\n

\u56fe\u5f62\u65e0\u5904\u4e0d\u5728\uff1b\u73b0\u5b9e\u4e16\u754c\u4e2d\u7684\u7269\u4f53\u901a\u5e38\u662f\u901a\u8fc7\u4e0e\u5176\u4ed6\u4e8b\u7269\u7684\u8fde\u63a5\u6765\u5b9a\u4e49\u7684\u3002\u4e00\u7ec4\u5bf9\u8c61\u53ca\u5176\u4e4b\u95f4\u7684\u8fde\u63a5\u53ef\u4ee5\u81ea\u7136\u5730\u8868\u793a\u4e3a\u4e00\u4e2a\u56fe\u3002\u7814\u7a76\u4eba\u5458\u5728\u8fc7\u53bb\u5341\u591a\u5e74\u4e2d\u5f00\u53d1\u4e86\u5728\u56fe\u6570\u636e\u4e0a\u8fd0\u884c\u7684\u795e\u7ecf\u7f51\u7edc\uff08\u79f0\u4e3a\u56fe\u795e\u7ecf\u7f51\u7edc\u6216GNNs\uff09[2]\u3002\u6700\u8fd1\u7684\u53d1\u5c55\u63d0\u5347\u4e86\u5b83\u4eec\u7684\u80fd\u529b\u548c\u8868\u8fbe\u80fd\u529b\u3002\u6211\u4eec\u5f00\u59cb\u5728\u6297\u83cc\u836f\u7269\u53d1\u73b0[3]\u3001\u7269\u7406\u6a21\u62df[4]\u3001\u5047\u65b0\u95fb\u68c0\u6d4b[5]\u3001\u4ea4\u901a\u9884\u6d4b[6]\u548c\u63a8\u8350\u7cfb\u7edf[7]\u7b49\u9886\u57df\u770b\u5230\u5b9e\u9645\u5e94\u7528\u3002<\/p>\n

\u672c\u6587\u63a2\u8ba8\u5e76\u89e3\u91ca\u4e86\u73b0\u4ee3\u56fe\u795e\u7ecf\u7f51\u7edc\u3002\u6211\u4eec\u5c06\u8fd9\u9879\u5de5\u4f5c\u5206\u4e3a\u56db\u4e2a\u90e8\u5206\u3002\u9996\u5148\uff0c\u6211\u4eec\u770b\u770b\u54ea\u79cd\u7c7b\u578b\u7684\u6570\u636e\u6700\u81ea\u7136\u5730\u8868\u8fbe\u4e3a\u4e00\u4e2a\u56fe\uff0c\u4ee5\u53ca\u4e00\u4e9b\u5e38\u89c1\u7684\u4f8b\u5b50\u3002\u5176\u6b21\uff0c\u6211\u4eec\u63a2\u8ba8\u4e86\u56fe\u4e0e\u5176\u4ed6\u7c7b\u578b\u7684\u6570\u636e\u7684\u533a\u522b\uff0c\u4ee5\u53ca\u5728\u4f7f\u7528\u56fe\u65f6\u9700\u8981\u505a\u51fa\u7684\u4e00\u4e9b\u4e13\u95e8\u9009\u62e9\u3002\u7b2c\u4e09\uff0c\u6211\u4eec\u6784\u5efa\u4e00\u4e2a\u73b0\u4ee3\u7684GNN\uff0c\u9010\u6b65\u4ecb\u7ecd\u6a21\u578b\u7684\u5404\u4e2a\u90e8\u5206\uff0c\u4ece\u8be5\u9886\u57df\u7684\u5386\u53f2\u5efa\u6a21\u521b\u65b0\u5f00\u59cb\u3002\u6211\u4eec\u4ece\u4e00\u4e2a\u6700\u57fa\u672c\u7684\u5b9e\u73b0\u9010\u6e10\u8fc7\u6e21\u5230\u4e00\u4e2a\u6700\u5148\u8fdb\u7684GNN\u6a21\u578b\u3002\u7b2c\u56db\uff0c\u6700\u540e\uff0c\u6211\u4eec\u63d0\u4f9b\u4e86\u4e00\u4e2aGNN\u6e38\u4e50\u573a\uff0c\u60a8\u53ef\u4ee5\u5728\u5176\u4e2d\u73a9\u800d\u4e00\u4e2a\u771f\u5b9e\u4e16\u754c\u7684\u4efb\u52a1\u548c\u6570\u636e\u96c6\uff0c\u4ee5\u66f4\u597d\u5730\u7406\u89e3GNN\u6a21\u578b\u7684\u6bcf\u4e2a\u7ec4\u4ef6\u5982\u4f55\u5f71\u54cd\u5176\u6240\u505a\u7684\u9884\u6d4b\u3002<\/p>\n

\u9996\u5148\uff0c\u8ba9\u6211\u4eec\u786e\u5b9a\u4ec0\u4e48\u662f\u4e00\u4e2a\u56fe\u3002\u4e00\u4e2a\u56fe\u8868\u793a\u4e86\u4e00\u7ec4\u5b9e\u4f53\uff08\u8282\u70b9\uff09\u4e4b\u95f4\u7684\u5173\u7cfb\uff08\u8fb9\uff09\u3002<\/p>\n

\"Screenshot<\/p>\n

\u4e3a\u4e86\u8fdb\u4e00\u6b65\u63cf\u8ff0\u6bcf\u4e2a\u8282\u70b9\u3001\u8fb9\u6216\u6574\u4e2a\u56fe\uff0c\u6211\u4eec\u53ef\u4ee5\u5728\u56fe\u7684\u6bcf\u4e2a\u90e8\u5206\u4e2d\u5b58\u50a8\u4fe1\u606f\u3002<\/p>\n

\"Screenshot<\/p>\n

\u6b64\u5916\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5c06\u65b9\u5411\u6027\u4e0e\u8fb9\u5173\u8054\uff08\u6709\u5411\u7684\u3001\u65e0\u5411\u7684\uff09\u6765\u8fdb\u4e00\u6b65\u7279\u6b8a\u5316\u56fe\u5f62\u3002<\/p>\n

\"Screenshot<\/p>\n

\u8fb9\u53ef\u4ee5\u662f\u6709\u5411\u7684\uff0c\u5176\u4e2d\u8fb9 \ud835\udc52 \u6709\u4e00\u4e2a\u6e90\u8282\u70b9 \ud835\udc63_{\ud835\udc60\ud835\udc5f\ud835\udc50}<\/code> \u548c\u4e00\u4e2a\u76ee\u6807\u8282\u70b9 \ud835\udc63_{\ud835\udc51\ud835\udc60\ud835\udc61}<\/code>\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u4fe1\u606f\u4ece \ud835\udc63_{\ud835\udc60\ud835\udc5f\ud835\udc50}<\/code> \u6d41\u5411 \ud835\udc63_{\ud835\udc51\ud835\udc60\ud835\udc61}<\/code>\u3002\u5b83\u4eec\u4e5f\u53ef\u4ee5\u662f\u65e0\u5411\u7684\uff0c\u5176\u4e2d\u6ca1\u6709\u6e90\u8282\u70b9\u6216\u76ee\u6807\u8282\u70b9\u7684\u6982\u5ff5\uff0c\u4fe1\u606f\u5728\u4e24\u4e2a\u65b9\u5411\u4e0a\u90fd\u6d41\u52a8\u3002\u8bf7\u6ce8\u610f\uff0c\u62e5\u6709\u4e00\u4e2a\u5355\u72ec\u7684\u65e0\u5411\u8fb9\u7b49\u6548\u4e8e\u5177\u6709\u4e00\u6761\u4ece \ud835\udc63_{\ud835\udc60\ud835\udc5f\ud835\udc50}<\/code> \u5230 \ud835\udc63_{\ud835\udc51\ud835\udc60\ud835\udc61}<\/code> \u7684\u6709\u5411\u8fb9\uff0c\u4ee5\u53ca\u53e6\u4e00\u6761\u4ece \ud835\udc63_{\ud835\udc51\ud835\udc60\ud835\udc61}<\/code>\u5230 \ud835\udc63_{\ud835\udc60\ud835\udc5f\ud835\udc50}<\/code> \u7684\u6709\u5411\u8fb9\u3002<\/em><\/p>\n

\u56fe\u662f\u975e\u5e38\u7075\u6d3b\u7684\u6570\u636e\u7ed3\u6784\uff0c\u5982\u679c\u73b0\u5728\u770b\u8d77\u6765\u62bd\u8c61\uff0c\u6211\u4eec\u5c06\u5728\u4e0b\u4e00\u8282\u901a\u8fc7\u4f8b\u5b50\u6765\u5177\u4f53\u8bf4\u660e\u3002<\/p>\n

\u56fe\u53ca\u5176\u5e94\u7528\u9886\u57df<\/h2>\n

\u4f60\u53ef\u80fd\u5df2\u7ecf\u719f\u6089\u4e86\u4e00\u4e9b\u7c7b\u578b\u7684\u56fe\u6570\u636e\uff0c\u6bd4\u5982\u793e\u4ea4\u7f51\u7edc\u3002\u7136\u800c\uff0c\u56fe\u662f\u4e00\u79cd\u975e\u5e38\u5f3a\u5927\u4e14\u901a\u7528\u7684\u6570\u636e\u8868\u793a\u65b9\u5f0f\uff0c\u6211\u4eec\u5c06\u5c55\u793a\u4e24\u79cd\u4f60\u53ef\u80fd\u6ca1\u6709\u60f3\u5230\u53ef\u4ee5\u5efa\u6a21\u4e3a\u56fe\u7684\u6570\u636e\u7c7b\u578b\uff1a\u56fe\u50cf\u548c\u6587\u672c\u3002\u867d\u7136\u6709\u4e9b\u4ee4\u4eba\u8d39\u89e3\uff0c\u4f46\u901a\u8fc7\u5c06\u5b83\u4eec\u89c6\u4e3a\u56fe\u5f62\u6765\u5b66\u4e60\u56fe\u50cf\u548c\u6587\u672c\u7684\u5bf9\u79f0\u6027\u548c\u7ed3\u6784\uff0c\u53ef\u4ee5\u5efa\u7acb\u76f4\u89c2\u7684\u7406\u89e3\uff0c\u4ece\u800c\u5e2e\u52a9\u7406\u89e3\u5176\u4ed6\u4e0d\u90a3\u4e48\u7f51\u683c\u72b6\u7684\u56fe\u6570\u636e\uff0c\u6211\u4eec\u5c06\u5728\u540e\u9762\u8ba8\u8bba\u3002<\/p>\n

\u56fe\u50cf\u4f5c\u4e3a\u56fe\u8868\u8fbe<\/h3>\n

\u901a\u5e38\u6211\u4eec\u4f1a\u5c06\u56fe\u50cf\u770b\u4f5c\u662f\u5177\u6709\u56fe\u50cf\u901a\u9053\u7684\u77e9\u5f62\u7f51\u683c\uff0c\u5c06\u5176\u8868\u793a\u4e3a\u6570\u7ec4\uff08\u4f8b\u5982\uff0c244x244x3 \u7684\u6d6e\u70b9\u6570\u6570\u7ec4\uff09\u3002\u53e6\u4e00\u79cd\u601d\u8003\u56fe\u50cf\u7684\u65b9\u5f0f\u662f\u5c06\u5176\u89c6\u4e3a\u5177\u6709\u89c4\u5219\u7ed3\u6784\u7684\u56fe\uff0c\u5176\u4e2d\u6bcf\u4e2a\u50cf\u7d20\u8868\u793a\u4e00\u4e2a\u8282\u70b9\uff0c\u5e76\u901a\u8fc7\u8fb9\u4e0e\u76f8\u90bb\u50cf\u7d20\u76f8\u8fde\u3002\u6bcf\u4e2a\u975e\u8fb9\u7f18\u50cf\u7d20\u6070\u597d\u67098\u4e2a\u90bb\u5c45\uff0c\u800c\u6bcf\u4e2a\u8282\u70b9\u5b58\u50a8\u7684\u4fe1\u606f\u662f\u4e00\u4e2a\u4e09\u7ef4\u5411\u91cf\uff0c\u8868\u793a\u50cf\u7d20\u7684RGB\u503c\u3002<\/p>\n

\u901a\u8fc7\u90bb\u63a5\u77e9\u9635\u662f\u4e00\u79cd\u53ef\u89c6\u5316\u56fe\u7684\u8fde\u63a5\u65b9\u5f0f\u3002\u6211\u4eec\u5bf9\u8282\u70b9\u8fdb\u884c\u6392\u5e8f\uff0c\u4f8b\u5982\u5728\u4e00\u4e2a\u7b80\u5355\u7684 5×5 \u5fae\u7b11\u8138\u56fe\u50cf\u4e2d\u6709 25 \u4e2a\u50cf\u7d20\u70b9\uff0c\u7136\u540e\u586b\u5145\u4e00\u4e2a\u5927\u5c0f\u4e3a \ud835\udc5b_{\ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52\ud835\udc60}<\/code>\u00d7 \ud835\udc5b_{\ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52\ud835\udc60}<\/code> \u7684\u77e9\u9635\uff0c\u5982\u679c\u4e24\u4e2a\u8282\u70b9\u5171\u4eab\u4e00\u6761\u8fb9\uff0c\u5219\u5728\u76f8\u5e94\u7684\u4f4d\u7f6e\u586b\u5165\u4e00\u4e2a\u6761\u76ee\u3002\u8bf7\u6ce8\u610f\uff0c\u4ee5\u4e0b\u8fd9\u4e09\u79cd\u8868\u8fbe\u65b9\u5f0f\u5b9e\u9645\u4e0a\u662f\u540c\u4e00\u7ec4\u6570\u636e\u7684\u4e0d\u540c\u89c6\u56fe\u3002<\/p>\n

\"Screenshot<\/p>\n

\u6587\u5b57\u4f5c\u4e3a\u56fe\u8868\u8fbe<\/h3>\n

\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4e3a\u6bcf\u4e2a\u5b57\u7b26\u3001\u5355\u8bcd\u6216\u6807\u8bb0\u5206\u914d\u7d22\u5f15\uff0c\u5e76\u5c06\u6587\u672c\u8868\u793a\u4e3a\u8fd9\u4e9b\u7d22\u5f15\u7684\u5e8f\u5217\u6765\u6570\u5b57\u5316\u6587\u672c\u3002\u8fd9\u6837\u521b\u5efa\u4e86\u4e00\u4e2a\u7b80\u5355\u7684\u6709\u5411\u56fe\uff0c\u5176\u4e2d\u6bcf\u4e2a\u5b57\u7b26\u6216\u7d22\u5f15\u662f\u4e00\u4e2a\u8282\u70b9\uff0c\u5e76\u901a\u8fc7\u4e00\u6761\u8fb9\u8fde\u63a5\u5230\u5176\u540e\u9762\u7684\u8282\u70b9\u3002<\/p>\n

\"Screenshot<\/p>\n

\u5f53\u7136\uff0c\u5728\u5b9e\u8df5\u4e2d\uff0c\u901a\u5e38\u4e0d\u4f1a\u4ee5\u8fd9\u79cd\u65b9\u5f0f\u5bf9\u6587\u672c\u548c\u56fe\u50cf\u8fdb\u884c\u7f16\u7801\uff1a\u8fd9\u4e9b\u56fe\u5f62\u8868\u793a\u662f\u5197\u4f59\u7684\uff0c\u56e0\u4e3a\u6240\u6709\u56fe\u50cf\u548c\u6240\u6709\u6587\u672c\u90fd\u5177\u6709\u975e\u5e38\u89c4\u5219\u7684\u7ed3\u6784\u3002\u4f8b\u5982\uff0c\u56fe\u50cf\u5728\u5176\u90bb\u63a5\u77e9\u9635\u4e2d\u5177\u6709\u5e26\u72b6\u7ed3\u6784\uff0c\u56e0\u4e3a\u6240\u6709\u8282\u70b9\uff08\u50cf\u7d20\uff09\u90fd\u5728\u7f51\u683c\u4e2d\u76f8\u4e92\u8fde\u63a5\u3002\u6587\u672c\u7684\u90bb\u63a5\u77e9\u9635\u53ea\u662f\u4e00\u6761\u5bf9\u89d2\u7ebf\uff0c\u56e0\u4e3a\u6bcf\u4e2a\u5355\u8bcd\u53ea\u4e0e\u524d\u4e00\u4e2a\u5355\u8bcd\u548c\u540e\u4e00\u4e2a\u5355\u8bcd\u76f8\u8fde\u3002<\/p>\n

\u8fd9\u79cd\u8868\u793a\u65b9\u5f0f\uff08\u5b57\u7b26\u6807\u8bb0\u7684\u5e8f\u5217\uff09\u6307\u7684\u662f\u6587\u672c\u5728\u5faa\u73af\u795e\u7ecf\u7f51\u7edc\uff08RNNs\uff09\u4e2d\u901a\u5e38\u7684\u8868\u793a\u65b9\u5f0f\uff1b\u5176\u4ed6\u6a21\u578b\uff0c\u6bd4\u5982\u53d8\u538b\u5668\uff08Transformers\uff09\uff0c\u53ef\u4ee5\u88ab\u770b\u4f5c\u662f\u5c06\u6587\u672c\u89c6\u4e3a\u4e00\u4e2a\u5b8c\u5168\u8fde\u63a5\u7684\u56fe\uff0c\u6211\u4eec\u5728\u5176\u4e2d\u5b66\u4e60\u6807\u8bb0\u4e4b\u95f4\u7684\u5173\u7cfb\u3002\u66f4\u591a\u4fe1\u606f\u8bf7\u53c2\u9605\u300a\u56fe\u6ce8\u610f\u529b\u7f51\u7edc\u300b\uff08Graph Attention Networks\uff09\u3002<\/em><\/p>\n

\u81ea\u7136\u754c\u4e2d\u7684\u56fe<\/h3>\n

\u56fe\u662f\u63cf\u8ff0\u4f60\u53ef\u80fd\u5df2\u7ecf\u719f\u6089\u7684\u6570\u636e\u7684\u6709\u7528\u5de5\u5177\u3002\u8ba9\u6211\u4eec\u7ee7\u7eed\u8ba8\u8bba\u7ed3\u6784\u66f4\u52a0\u5f02\u6784\u7684\u6570\u636e\u3002\u5728\u8fd9\u4e9b\u4f8b\u5b50\u4e2d\uff0c\u6bcf\u4e2a\u8282\u70b9\u7684\u90bb\u5c45\u6570\u91cf\u662f\u53ef\u53d8\u7684\uff08\u4e0e\u56fe\u50cf\u548c\u6587\u672c\u7684\u56fa\u5b9a\u90bb\u57df\u5927\u5c0f\u76f8\u5bf9\uff09\u3002\u9664\u4e86\u4ee5\u56fe\u7684\u65b9\u5f0f\u8868\u8fbe\u4e4b\u5916\uff0c\u5f88\u96be\u7528\u4efb\u4f55\u5176\u4ed6\u65b9\u5f0f\u8868\u8fbe\u8fd9\u79cd\u6570\u636e\u3002<\/p>\n

\u5206\u5b50\u4f5c\u4e3a\u56fe\u5f62\uff1a<\/h4>\n

\u5206\u5b50\u662f\u7269\u8d28\u7684\u57fa\u672c\u7ec4\u6210\u5355\u4f4d\uff0c\u7531\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u7684\u539f\u5b50\u548c\u7535\u5b50\u6784\u6210\u3002\u6240\u6709\u7c92\u5b50\u90fd\u5728\u76f8\u4e92\u4f5c\u7528\uff0c\u4f46\u5f53\u4e00\u5bf9\u539f\u5b50\u88ab\u56fa\u5b9a\u5728\u5f7c\u6b64\u7a33\u5b9a\u7684\u8ddd\u79bb\u65f6\uff0c\u6211\u4eec\u79f0\u5b83\u4eec\u5171\u7528\u4e00\u4e2a\u5171\u4ef7\u952e\u3002\u4e0d\u540c\u7684\u539f\u5b50\u5bf9\u548c\u952e\u5177\u6709\u4e0d\u540c\u7684\u8ddd\u79bb\uff08\u4f8b\u5982\u5355\u952e\u3001\u53cc\u952e\uff09\u3002\u5c06\u8fd9\u4e2a\u4e09\u7ef4\u5bf9\u8c61\u63cf\u8ff0\u4e3a\u4e00\u4e2a\u56fe\u5f62\u662f\u4e00\u4e2a\u975e\u5e38\u65b9\u4fbf\u548c\u5e38\u89c1\u7684\u62bd\u8c61\uff0c\u5176\u4e2d\u8282\u70b9\u662f\u539f\u5b50\uff0c\u8fb9\u662f\u5171\u4ef7\u952e\u3002[8]\u4ee5\u4e0b\u662f\u4e24\u79cd\u5e38\u89c1\u5206\u5b50\u53ca\u5176\u5173\u8054\u7684\u56fe\u5f62\u3002<\/p>\n

\"Screenshot<\/p>\n

\uff08\u5de6\uff09\u67e0\u6aac\u9999\u919b\u5206\u5b50\u7684\u4e09\u7ef4\u8868\u793a\uff08\u4e2d\uff09\u8be5\u5206\u5b50\u4e2d\u952e\u7684\u90bb\u63a5\u77e9\u9635\uff08\u53f3\uff09\u5206\u5b50\u7684\u56fe\u5f62\u8868\u793a\u3002<\/p>\n

\"Screenshot<\/p>\n

(\u5de6) \u5496\u5561\u56e0\u5206\u5b50\u7684\u4e09\u7ef4\u8868\u793a\uff08\u4e2d\uff09\u8be5\u5206\u5b50\u4e2d\u952e\u7684\u90bb\u63a5\u77e9\u9635\uff08\u53f3\uff09\u5206\u5b50\u7684\u56fe\u5f62\u8868\u793a\u3002<\/p>\n

\u793e\u4ea4\u7f51\u7edc\u4f5c\u4e3a\u56fe\uff1a<\/h4>\n

\u793e\u4ea4\u7f51\u7edc\u662f\u7814\u7a76\u4eba\u5458\u3001\u673a\u6784\u548c\u7ec4\u7ec7\u96c6\u4f53\u884c\u4e3a\u6a21\u5f0f\u7684\u5de5\u5177\u3002\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5c06\u4e2a\u4f53\u5efa\u6a21\u4e3a\u8282\u70b9\uff0c\u5c06\u5b83\u4eec\u4e4b\u95f4\u7684\u5173\u7cfb\u5efa\u6a21\u4e3a\u8fb9\uff0c\u6765\u6784\u5efa\u4ee3\u8868\u4eba\u7fa4\u7684\u56fe\u5f62\u3002<\/p>\n

\"Screenshot<\/p>\n

\uff08\u5de6\uff09\u6765\u81ea\u620f\u5267\u300a\u5965\u8d5b\u7f57\u300b\u7684\u573a\u666f\u56fe\u50cf\u3002\uff08\u4e2d\uff09\u8be5\u5267\u4e2d\u89d2\u8272\u4e4b\u95f4\u4e92\u52a8\u7684\u90bb\u63a5\u77e9\u9635\u3002\uff08\u53f3\uff09\u8fd9\u4e9b\u4e92\u52a8\u7684\u56fe\u5f62\u8868\u793a\u3002<\/em><\/p>\n

\u4e0e\u56fe\u50cf\u548c\u6587\u672c\u6570\u636e\u4e0d\u540c\uff0c\u793e\u4ea4\u7f51\u7edc\u7684\u90bb\u63a5\u77e9\u9635\u5e76\u4e0d\u76f8\u540c\u3002<\/p>\n

\"Screenshot<\/p>\n

(\u5de6) \u7a7a\u624b\u9053\u6bd4\u8d5b\u7684\u56fe\u50cf\u3002\uff08\u4e2d\uff09\u7a7a\u624b\u9053\u4ff1\u4e50\u90e8\u6210\u5458\u4e4b\u95f4\u4e92\u52a8\u7684\u90bb\u63a5\u77e9\u9635\u3002\uff08\u53f3\uff09\u8fd9\u4e9b\u4e92\u52a8\u7684\u56fe\u5f62\u8868\u793a\u3002<\/p>\n

\u5f15\u7528\u7f51\u7edc\u4f5c\u4e3a\u56fe \uff1a<\/h4>\n

\u79d1\u5b66\u5bb6\u5728\u53d1\u8868\u8bba\u6587\u65f6\u901a\u5e38\u4f1a\u5f15\u7528\u5176\u4ed6\u79d1\u5b66\u5bb6\u7684\u5de5\u4f5c\u3002\u6211\u4eec\u53ef\u4ee5\u5c06\u8fd9\u4e9b\u5f15\u7528\u7f51\u7edc\u53ef\u89c6\u5316\u4e3a\u4e00\u4e2a\u56fe\u5f62\uff0c\u5176\u4e2d\u6bcf\u7bc7\u8bba\u6587\u662f\u4e00\u4e2a\u8282\u70b9\uff0c\u6bcf\u6761\u6709\u5411\u8fb9\u8868\u793a\u4e00\u7bc7\u8bba\u6587\u5bf9\u53e6\u4e00\u7bc7\u8bba\u6587\u7684\u5f15\u7528\u3002\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u5c06\u6709\u5173\u6bcf\u7bc7\u8bba\u6587\u7684\u4fe1\u606f\u6dfb\u52a0\u5230\u6bcf\u4e2a\u8282\u70b9\u4e2d\uff0c\u4f8b\u5982\u6458\u8981\u7684\u8bcd\u5d4c\u5165\uff08\u53c2\u89c1[9]\uff0c[10]\uff0c[11]\uff09\u3002<\/p>\n

\u5176\u4ed6\u4f8b\u5b50:<\/h4>\n

\u5728\u8ba1\u7b97\u673a\u89c6\u89c9\u4e2d\uff0c\u6211\u4eec\u6709\u65f6\u60f3\u8981\u5728\u89c6\u89c9\u573a\u666f\u4e2d\u6807\u8bb0\u7269\u4f53\u3002\u6211\u4eec\u53ef\u4ee5\u5c06\u8fd9\u4e9b\u7269\u4f53\u89c6\u4e3a\u8282\u70b9\uff0c\u5c06\u5b83\u4eec\u4e4b\u95f4\u7684\u5173\u7cfb\u89c6\u4e3a\u8fb9\u6765\u6784\u5efa\u56fe\u5f62\u3002\u673a\u5668\u5b66\u4e60\u6a21\u578b\u3001\u7f16\u7a0b\u4ee3\u7801[12]\u548c\u6570\u5b66\u65b9\u7a0b[13]\u4e5f\u53ef\u4ee5\u88ab\u770b\u4f5c\u662f\u56fe\u5f62\uff0c\u5176\u4e2d\u53d8\u91cf\u662f\u8282\u70b9\uff0c\u800c\u8fb9\u662f\u5c06\u8fd9\u4e9b\u53d8\u91cf\u4f5c\u4e3a\u8f93\u5165\u548c\u8f93\u51fa\u7684\u64cd\u4f5c\u3002\u4f60\u53ef\u80fd\u4f1a\u5728\u67d0\u4e9b\u4e0a\u4e0b\u6587\u4e2d\u770b\u5230\u672f\u8bed\u201c\u6570\u636e\u6d41\u56fe\u201d\u7684\u4f7f\u7528\u3002<\/p>\n\n\n\n\n\n\n\n\n
\u6570\u636e\u96c6<\/strong><\/th>\n\u9886\u57df<\/strong><\/th>\n\u56fe\u91cf<\/strong><\/th>\n\u8282\u70b9\u6570<\/strong><\/th>\n\u8fb9\u6570<\/strong><\/th>\n\u6700\u5c0f\u5ea6<\/strong><\/th>\n\u5e73\u5747\u5ea6<\/th>\n\u6700\u5927\u5ea6<\/strong><\/th>\n<\/tr>\n<\/thead>\n
karate club<\/td>\nSocial network<\/td>\n1<\/td>\n34<\/td>\n78<\/td>\n<\/td>\n4.5<\/td>\n17<\/td>\n<\/tr>\n
qm9<\/td>\nSmall molecules<\/td>\n134k<\/td>\n<=9<\/td>\n<=26<\/td>\n1<\/td>\n2<\/td>\n5<\/td>\n<\/tr>\n
Cora<\/td>\nCitation network<\/td>\n1<\/td>\n23166<\/td>\n91500<\/td>\n1<\/td>\n7.8<\/td>\n379<\/td>\n<\/tr>\n
Wikipedia links, English<\/td>\nKnowledge graph<\/td>\n1<\/td>\n12M<\/td>\n378M<\/td>\n<\/td>\n62.24<\/td>\n1M<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u5b9e\u9645\u4e16\u754c\u4e2d\u53d1\u73b0\u7684\u56fe\u5f62\u7684\u6458\u8981\u7edf\u8ba1\u6570\u636e\u3002\u8fd9\u4e9b\u6570\u5b57\u53d6\u51b3\u4e8e\u7279\u5f81\u5316\u51b3\u7b56\u3002\u53ef\u4ee5\u5728KONECT\u4e2d\u627e\u5230\u66f4\u591a\u6709\u7528\u7684\u7edf\u8ba1\u6570\u636e\u548c\u56fe\u5f62\u3002<\/em><\/p>\n

\u54ea\u4e9b\u95ee\u9898\u6d89\u53ca\u5230\u56fe\u7ed3\u6784\u5316\u6570\u636e\uff1f<\/h2>\n

\u6211\u4eec\u5df2\u7ecf\u63cf\u8ff0\u4e86\u4e00\u4e9b\u73b0\u5b9e\u4e16\u754c\u4e2d\u7684\u56fe\u5f62\u793a\u4f8b\uff0c\u4f46\u6211\u4eec\u60f3\u8981\u5bf9\u8fd9\u4e9b\u6570\u636e\u6267\u884c\u54ea\u4e9b\u4efb\u52a1\u5462\uff1f\u5173\u4e8e\u56fe\u5f62\u7684\u9884\u6d4b\u4efb\u52a1\u901a\u5e38\u53ef\u4ee5\u5206\u4e3a\u4e09\u7c7b\uff1a\u56fe\u7ea7\u522b\u3001\u8282\u70b9\u7ea7\u522b\u548c\u8fb9\u7ea7\u522b\u3002<\/p>\n

\u5728\u56fe\u7ea7\u522b\u4efb\u52a1\u4e2d\uff0c\u6211\u4eec\u9884\u6d4b\u6574\u4e2a\u56fe\u7684\u5355\u4e00\u5c5e\u6027\u3002\u5728\u8282\u70b9\u7ea7\u522b\u4efb\u52a1\u4e2d\uff0c\u6211\u4eec\u9884\u6d4b\u56fe\u4e2d\u6bcf\u4e2a\u8282\u70b9\u7684\u67d0\u4e9b\u5c5e\u6027\u3002\u5728\u8fb9\u7ea7\u522b\u4efb\u52a1\u4e2d\uff0c\u6211\u4eec\u5e0c\u671b\u9884\u6d4b\u56fe\u4e2d\u8fb9\u7684\u5c5e\u6027\u6216\u5b58\u5728\u4e0e\u5426\u3002<\/p>\n

\u5bf9\u4e8e\u4e0a\u8ff0\u4e09\u4e2a\u7ea7\u522b\u7684\u9884\u6d4b\u95ee\u9898\uff08\u56fe\u7ea7\u522b\u3001\u8282\u70b9\u7ea7\u522b\u548c\u8fb9\u7ea7\u522b\uff09\uff0c\u6211\u4eec\u5c06\u5c55\u793a\u6240\u6709\u4ee5\u4e0b\u95ee\u9898\u90fd\u53ef\u4ee5\u4f7f\u7528\u5355\u4e00\u6a21\u578b\u7c7b\u522b\uff0c\u5373GNN\u6765\u89e3\u51b3\u3002\u4f46\u9996\u5148\uff0c\u8ba9\u6211\u4eec\u66f4\u8be6\u7ec6\u5730\u4e86\u89e3\u8fd9\u4e09\u7c7b\u56fe\u5f62\u9884\u6d4b\u95ee\u9898\uff0c\u5e76\u63d0\u4f9b\u6bcf\u4e2a\u95ee\u9898\u7684\u5177\u4f53\u793a\u4f8b\u3002<\/p>\n

\u8fd8\u6709\u5176\u4ed6\u76f8\u5173\u7684\u4efb\u52a1\u662f\u6d3b\u8dc3\u7814\u7a76\u9886\u57df\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u53ef\u80fd\u60f3\u8981\u751f\u6210\u56fe\u5f62\uff0c\u6216\u8005\u89e3\u91ca\u5bf9\u56fe\u5f62\u7684\u9884\u6d4b\u7ed3\u679c\u3002\u66f4\u591a\u7684\u4e3b\u9898\u53ef\u4ee5\u5728\u201c\u6df1\u5165\u7ec6\u8282\u201d\u90e8\u5206\u627e\u5230\u3002<\/em><\/p>\n

\u56fe\u7ea7\u522b\u4efb\u52a1<\/h3>\n

\u5728\u56fe\u7ea7\u522b\u4efb\u52a1\u4e2d\uff0c\u6211\u4eec\u7684\u76ee\u6807\u662f\u9884\u6d4b\u6574\u4e2a\u56fe\u7684\u67d0\u79cd\u5c5e\u6027\u3002\u4f8b\u5982\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u4ee5\u56fe\u5f62\u8868\u793a\u7684\u5206\u5b50\uff0c\u6211\u4eec\u53ef\u80fd\u60f3\u8981\u9884\u6d4b\u8fd9\u4e2a\u5206\u5b50\u7684\u6c14\u5473\uff0c\u6216\u8005\u5b83\u662f\u5426\u4f1a\u4e0e\u4e0e\u4e00\u79cd\u4e0e\u75be\u75c5\u76f8\u5173\u7684\u53d7\u4f53\u7ed3\u5408\u3002<\/p>\n

\"image-20230914225658269\"<\/p>\n

\u8fd9\u7c7b\u4f3c\u4e8eMNIST\u548cCIFAR\u7b49\u56fe\u50cf\u5206\u7c7b\u95ee\u9898\uff0c\u5176\u4e2d\u6211\u4eec\u60f3\u8981\u4e3a\u6574\u4e2a\u56fe\u50cf\u5173\u8054\u4e00\u4e2a\u6807\u7b7e\u3002\u5728\u6587\u672c\u65b9\u9762\uff0c\u7c7b\u4f3c\u7684\u95ee\u9898\u662f\u60c5\u611f\u5206\u6790\uff0c\u6211\u4eec\u5e0c\u671b\u4e00\u6b21\u6027\u8bc6\u522b\u4e00\u6574\u4e2a\u53e5\u5b50\u7684\u60c5\u611f\u6216\u60c5\u7eea\u3002<\/p>\n

\u8282\u70b9\u7ea7\u522b\u4efb\u52a1<\/h3>\n

\u8282\u70b9\u7ea7\u522b\u4efb\u52a1\u6d89\u53ca\u5728\u56fe\u4e2d\u9884\u6d4b\u6bcf\u4e2a\u8282\u70b9\u7684\u8eab\u4efd\u6216\u89d2\u8272\u3002<\/p>\n

\u4e00\u4e2a\u7ecf\u5178\u7684\u8282\u70b9\u7ea7\u522b\u9884\u6d4b\u95ee\u9898\u7684\u4f8b\u5b50\u662f\u624e\u514b\u7684\u7a7a\u624b\u9053\u4ff1\u4e50\u90e8[15]\u3002\u8be5\u6570\u636e\u96c6\u662f\u4e00\u4e2a\u5355\u4e00\u7684\u793e\u4ea4\u7f51\u7edc\u56fe\uff0c\u7531\u5728\u653f\u6cbb\u7eb7\u4e89\u540e\u5ba3\u8a93\u6548\u5fe0\u4e24\u4e2a\u7a7a\u624b\u9053\u4ff1\u4e50\u90e8\u4e4b\u4e00\u7684\u4e2a\u4eba\u7ec4\u6210\u3002\u6545\u4e8b\u5982\u4e0b\uff0cMr. Hi\uff08\u6559\u7ec3\uff09\u548cJohn H\uff08\u7ba1\u7406\u5458\uff09\u4e4b\u95f4\u7684\u7eb7\u4e89\u5728\u7a7a\u624b\u9053\u4ff1\u4e50\u90e8\u4e2d\u9020\u6210\u4e86\u5206\u88c2\u3002\u8282\u70b9\u4ee3\u8868\u4e2a\u4f53\u7a7a\u624b\u9053\u7ec3\u4e60\u8005\uff0c\u8fb9\u4ee3\u8868\u8fd9\u4e9b\u6210\u5458\u5728\u7a7a\u624b\u9053\u4ee5\u5916\u7684\u9886\u57df\u4e4b\u95f4\u7684\u4e92\u52a8\u3002\u9884\u6d4b\u95ee\u9898\u662f\u5728\u7eb7\u4e89\u540e\uff0c\u9884\u6d4b\u7ed9\u5b9a\u6210\u5458\u662f\u5426\u4f1a\u5fe0\u8bda\u4e8eMr. Hi\u6216John H\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u8282\u70b9\u5230\u6559\u7ec3\u6216\u7ba1\u7406\u5458\u7684\u8ddd\u79bb\u4e0e\u8be5\u6807\u7b7e\u9ad8\u5ea6\u76f8\u5173\u3002<\/p>\n

\"image-20230914225845389\"<\/p>\n

\u5728\u5de6\u4fa7\uff0c\u6211\u4eec\u6709\u95ee\u9898\u7684\u521d\u59cb\u6761\u4ef6\uff0c\u5728\u53f3\u4fa7\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u53ef\u80fd\u7684\u89e3\u51b3\u65b9\u6848\uff0c\u5176\u4e2d\u6bcf\u4e2a\u8282\u70b9\u6839\u636e\u5176\u6240\u5c5e\u8054\u76df\u8fdb\u884c\u4e86\u5206\u7c7b\u3002\u8be5\u6570\u636e\u96c6\u53ef\u4ee5\u5728\u5176\u4ed6\u56fe\u95ee\u9898\u4e2d\u4f7f\u7528\uff0c\u5982\u65e0\u76d1\u7763\u5b66\u4e60\u3002<\/em><\/p>\n

\u7c7b\u6bd4\u56fe\u50cf\uff0c\u8282\u70b9\u7ea7\u522b\u9884\u6d4b\u95ee\u9898\u7c7b\u4f3c\u4e8e\u56fe\u50cf\u5206\u5272\uff0c\u6211\u4eec\u8bd5\u56fe\u4e3a\u56fe\u50cf\u4e2d\u7684\u6bcf\u4e2a\u50cf\u7d20\u8d34\u4e0a\u6807\u7b7e\u3002\u5728\u6587\u672c\u65b9\u9762\uff0c\u7c7b\u4f3c\u7684\u4efb\u52a1\u662f\u9884\u6d4b\u53e5\u5b50\u4e2d\u6bcf\u4e2a\u5355\u8bcd\u7684\u8bcd\u6027\uff08\u5982\u540d\u8bcd\u3001\u52a8\u8bcd\u3001\u526f\u8bcd\u7b49\uff09\u3002<\/p>\n

\u8fb9\u7ea7\u522b\u4efb\u52a1<\/h3>\n

\u5728\u56fe\u5f62\u4e2d\u5269\u4e0b\u7684\u9884\u6d4b\u95ee\u9898\u662f\u8fb9\u7ea7\u522b\u7684\u9884\u6d4b\u3002<\/p>\n

\u8fb9\u7ea7\u522b\u63a8\u65ad\u7684\u4e00\u4e2a\u4f8b\u5b50\u662f\u56fe\u50cf\u573a\u666f\u7406\u89e3\u3002\u9664\u4e86\u5728\u56fe\u50cf\u4e2d\u8bc6\u522b\u5bf9\u8c61\u5916\uff0c\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\u53ef\u4ee5\u7528\u4e8e\u9884\u6d4b\u5b83\u4eec\u4e4b\u95f4\u7684\u5173\u7cfb\u3002\u6211\u4eec\u53ef\u4ee5\u5c06\u8fd9\u89c6\u4e3a\u8fb9\u7ea7\u522b\u7684\u5206\u7c7b\u95ee\u9898\uff1a\u5728\u7ed9\u5b9a\u4ee3\u8868\u56fe\u50cf\u4e2d\u7684\u5bf9\u8c61\u7684\u8282\u70b9\u7684\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5e0c\u671b\u9884\u6d4b\u8fd9\u4e9b\u8282\u70b9\u4e2d\u54ea\u4e9b\u5171\u4eab\u4e00\u6761\u8fb9\uff0c\u6216\u8005\u8fd9\u6761\u8fb9\u7684\u503c\u662f\u4ec0\u4e48\u3002\u5982\u679c\u6211\u4eec\u5e0c\u671b\u53d1\u73b0\u5b9e\u4f53\u4e4b\u95f4\u7684\u8fde\u63a5\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u56fe\u5f62\u89c6\u4e3a\u5b8c\u5168\u8fde\u63a5\u7684\uff0c\u5e76\u6839\u636e\u5b83\u4eec\u7684\u9884\u6d4b\u503c\u4fee\u526a\u8fb9\u7f18\u4ee5\u5f97\u5230\u7a00\u758f\u7684\u56fe\u5f62\u3002<\/p>\n

\"image-20230914230244731\"<\/p>\n

\u5728\u4e0a\u56fe\u7684(b)\u90e8\u5206\u4e2d\uff0c\u539f\u59cb\u56fe\u50cf(a)\u5df2\u7ecf\u88ab\u5206\u5272\u6210\u4e86\u4e94\u4e2a\u5b9e\u4f53\uff1a\u6bcf\u4e2a\u6597\u58eb\u3001\u88c1\u5224\u3001\u89c2\u4f17\u548c\u5730\u57ab\u3002\u800c(c)\u5c55\u793a\u4e86\u8fd9\u4e9b\u5b9e\u4f53\u4e4b\u95f4\u7684\u5173\u7cfb\u3002<\/em><\/p>\n

\"image-20230914230324643\"<\/p>\n

\u5728\u5de6\u4fa7\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u4ece\u4e4b\u524d\u7684\u89c6\u89c9\u573a\u666f\u6784\u5efa\u7684\u521d\u59cb\u56fe\u5f62\u3002\u5728\u53f3\u4fa7\u662f\u8be5\u56fe\u5f62\u7684\u4e00\u4e2a\u53ef\u80fd\u7684\u8fb9\u6807\u7b7e\uff0c\u5f53\u4e00\u4e9b\u8fde\u63a5\u57fa\u4e8e\u6a21\u578b\u7684\u8f93\u51fa\u88ab\u526a\u9664\u65f6\u3002<\/em><\/p>\n

\u5728\u673a\u5668\u5b66\u4e60\u4e2d\u4f7f\u7528\u56fe\u5f62\u6240\u9762\u4e34\u7684\u6311\u6218<\/h2>\n

\u90a3\u4e48\uff0c\u6211\u4eec\u5982\u4f55\u7528\u795e\u7ecf\u7f51\u7edc\u89e3\u51b3\u8fd9\u4e9b\u4e0d\u540c\u7684\u56fe\u4efb\u52a1\u5462\uff1f\u7b2c\u4e00\u6b65\u662f\u8003\u8651\u5982\u4f55\u8868\u793a\u56fe\uff0c\u4ee5\u4f7f\u5176\u4e0e\u795e\u7ecf\u7f51\u7edc\u517c\u5bb9\u3002<\/p>\n

\u673a\u5668\u5b66\u4e60\u6a21\u578b\u901a\u5e38\u5c06\u77e9\u5f62\u6216\u7c7b\u4f3c\u7f51\u683c\u7684\u6570\u7ec4\u4f5c\u4e3a\u8f93\u5165\u3002\u56e0\u6b64\uff0c\u5982\u4f55\u4ee5\u4e0e\u6df1\u5ea6\u5b66\u4e60\u517c\u5bb9\u7684\u683c\u5f0f\u8868\u793a\u5b83\u4eec\u5e76\u4e0d\u662f\u7acb\u5373\u76f4\u89c2\u7684\u3002\u56fe\u5f62\u5177\u6709\u591a\u8fbe\u56db\u79cd\u7c7b\u578b\u7684\u4fe1\u606f\uff0c\u6211\u4eec\u53ef\u80fd\u5e0c\u671b\u7528\u6765\u8fdb\u884c\u9884\u6d4b\uff1a\u8282\u70b9\u3001\u8fb9\u3001\u5168\u5c40\u4e0a\u4e0b\u6587\u548c\u8fde\u63a5\u6027\u3002\u524d\u4e09\u8005\u76f8\u5bf9\u7b80\u5355\uff1a\u4f8b\u5982\uff0c\u5bf9\u4e8e\u8282\u70b9\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4e3a\u6bcf\u4e2a\u8282\u70b9\u5206\u914d\u4e00\u4e2a\u7d22\u5f15 \ud835\udc56<\/code> \u5e76\u5c06 \ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52_\ud835\udc56<\/code> \u7684\u7279\u5f81\u5b58\u50a8\u5728 \ud835\udc41<\/code> \u4e2d\u6765\u5f62\u6210\u4e00\u4e2a\u8282\u70b9\u7279\u5f81\u77e9\u9635 \ud835\udc41<\/code>\u3002\u867d\u7136\u8fd9\u4e9b\u77e9\u9635\u5177\u6709\u53ef\u53d8\u6570\u91cf\u7684\u793a\u4f8b\uff0c\u4f46\u5b83\u4eec\u53ef\u4ee5\u5728\u4e0d\u9700\u8981\u4efb\u4f55\u7279\u6b8a\u6280\u5de7\u7684\u60c5\u51b5\u4e0b\u8fdb\u884c\u5904\u7406\u3002<\/p>\n

\u7136\u800c\uff0c\u8868\u793a\u56fe\u7684\u8fde\u63a5\u6027\u5c31\u6bd4\u8f83\u590d\u6742\u4e86\u3002\u4e5f\u8bb8\u6700\u660e\u663e\u7684\u9009\u62e9\u662f\u4f7f\u7528\u90bb\u63a5\u77e9\u9635\uff0c\u56e0\u4e3a\u8fd9\u5f88\u5bb9\u6613\u8f6c\u5316\u4e3a\u5f20\u91cf\u3002\u7136\u800c\uff0c\u8fd9\u79cd\u8868\u793a\u65b9\u6cd5\u6709\u4e00\u4e9b\u7f3a\u70b9\u3002\u4ece\u793a\u4f8b\u6570\u636e\u96c6\u8868\u683c\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u56fe\u4e2d\u7684\u8282\u70b9\u6570\u91cf\u53ef\u80fd\u8fbe\u5230\u767e\u4e07\u7ea7\uff0c\u6bcf\u4e2a\u8282\u70b9\u7684\u8fb9\u6570\u53ef\u80fd\u4f1a\u53d8\u5316\u5f88\u5927\u3002\u901a\u5e38\uff0c\u8fd9\u4f1a\u5bfc\u81f4\u975e\u5e38\u7a00\u758f\u7684\u90bb\u63a5\u77e9\u9635\uff0c\u8fd9\u5728\u7a7a\u95f4\u4e0a\u6548\u7387\u4f4e\u4e0b\u3002<\/p>\n

\u53e6\u4e00\u4e2a\u95ee\u9898\u662f\u6709\u8bb8\u591a\u90bb\u63a5\u77e9\u9635\u53ef\u4ee5\u7f16\u7801\u76f8\u540c\u7684\u8fde\u63a5\u6027\uff0c\u5e76\u4e14\u4e0d\u80fd\u4fdd\u8bc1\u8fd9\u4e9b\u4e0d\u540c\u7684\u77e9\u9635\u5728\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u4e2d\u4f1a\u4ea7\u751f\u76f8\u540c\u7684\u7ed3\u679c\uff08\u4e5f\u5c31\u662f\u8bf4\uff0c\u5b83\u4eec\u4e0d\u662f\u7f6e\u6362\u4e0d\u53d8\u7684\uff09\u3002<\/p>\n

\u4f8b\u5982\uff0c\u4e4b\u524d\u63d0\u5230\u7684\u300a\u5965\u8d5b\u7f57\u300b\u56fe\u53ef\u4ee5\u7528\u8fd9\u4e24\u4e2a\u90bb\u63a5\u77e9\u9635\u7b49\u6548\u5730\u63cf\u8ff0\u3002\u5b83\u8fd8\u53ef\u4ee5\u7528\u8282\u70b9\u7684\u6bcf\u4e00\u79cd\u53ef\u80fd\u7684\u7f6e\u6362\u6765\u63cf\u8ff0\u3002<\/p>\n

\"image-20230914231304026\"<\/p>\n

\u4e24\u4e2a\u8868\u793a\u540c\u4e00\u56fe\u7684\u90bb\u63a5\u77e9\u9635\u3002<\/em><\/p>\n

\u4e0b\u9762\u7684\u793a\u4f8b\u663e\u793a\u4e86\u53ef\u4ee5\u63cf\u8ff0\u8fd9\u4e2a\u5305\u542b4\u4e2a\u8282\u70b9\u7684\u5c0f\u56fe\u7684\u6bcf\u4e2a\u90bb\u63a5\u77e9\u9635\u3002\u8fd9\u5df2\u7ecf\u662f\u76f8\u5f53\u5927\u91cf\u7684\u90bb\u63a5\u77e9\u9635\u4e86\uff0c\u5bf9\u4e8e\u50cf\u300a\u5965\u8d5b\u7f57\u300b\u8fd9\u6837\u66f4\u5927\u7684\u793a\u4f8b\uff0c\u8fd9\u4e2a\u6570\u91cf\u662f\u96be\u4ee5\u5904\u7406\u7684\u3002<\/p>\n

\"image-20230914231430325\"<\/p>\n

\u6240\u6709\u8fd9\u4e9b\u90bb\u63a5\u77e9\u9635\u4ee3\u8868\u540c\u4e00\u4e2a\u56fe\u3002\u70b9\u51fb\u4e00\u6761\u8fb9\u4ee5\u79fb\u9664\u5b83\uff0c\u70b9\u51fb\u201c\u865a\u62df\u8fb9\u201d\u4ee5\u6dfb\u52a0\u5b83\uff0c\u77e9\u9635\u5c06\u76f8\u5e94\u5730\u66f4\u65b0\u3002<\/em><\/p>\n

\u4e00\u79cd\u4f18\u96c5\u4e14\u5185\u5b58\u9ad8\u6548\u7684\u7a00\u758f\u77e9\u9635\u8868\u793a\u65b9\u6cd5\u662f\u90bb\u63a5\u8868\u3002\u5b83\u4eec\u5c06\u8fb9 \ud835\udc52_\ud835\udc58<\/code> \u5728\u8282\u70b9 \ud835\udc5b_\ud835\udc56<\/code> \u548c \ud835\udc5b_\ud835\udc57<\/code> \u4e4b\u95f4\u7684\u8fde\u63a5\u6027\u63cf\u8ff0\u4e3a\u90bb\u63a5\u8868\u7684\u7b2c k<\/code> \u4e2a\u6761\u76ee\u4e2d\u7684\u5143\u7ec4 (i,j)<\/code>\u3002\u7531\u4e8e\u6211\u4eec\u9884\u671f\u8fb9\u7684\u6570\u91cf\u8fdc\u8fdc\u4f4e\u4e8e\u90bb\u63a5\u77e9\u9635\u7684\u6761\u76ee\u6570\uff08\ud835\udc5b^2_{\ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52\ud835\udc60}<\/code>\uff09\uff0c\u6211\u4eec\u907f\u514d\u4e86\u5728\u56fe\u7684\u672a\u8fde\u63a5\u90e8\u5206\u8fdb\u884c\u8ba1\u7b97\u548c\u5b58\u50a8\u3002<\/p>\n

\u53e6\u4e00\u79cd\u9648\u8ff0\u8fd9\u4e00\u70b9\u7684\u65b9\u5f0f\u662f\u4f7f\u7528\u5927O<\/code>\u7b26\u53f7\u8868\u793a\uff0c\u6700\u597d\u662f\u5177\u6709O(\ud835\udc5b_{\ud835\udc52\ud835\udc51\ud835\udc54\ud835\udc52\ud835\udc60}<\/code>)\u7684\u590d\u6742\u5ea6\uff0c\u800c\u4e0d\u662fO<\/code>(\ud835\udc5b^2_{\ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52\ud835\udc60}<\/code>)\u3002<\/p>\n

\u4e3a\u4e86\u4f7f\u8fd9\u4e2a\u6982\u5ff5\u5177\u4f53\u5316\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u770b\u5728\u8fd9\u79cd\u89c4\u8303\u4e0b\u5982\u4f55\u8868\u793a\u4e0d\u540c\u56fe\u7684\u4fe1\u606f\uff1a<\/p>\n

\"image-20230914231740666\"<\/p>\n

\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u8be5\u56fe\u4e2d\u4f7f\u7528\u4e86\u6bcf\u4e2a\u8282\u70b9\/\u8fb9\/\u5168\u5c40\u7684\u6807\u91cf\u503c\uff0c\u4f46\u5927\u591a\u6570\u5b9e\u9645\u7684\u5f20\u91cf\u8868\u793a\u4f1a\u6709\u6bcf\u4e2a\u56fe\u5c5e\u6027\u7684\u5411\u91cf\u3002\u6211\u4eec\u5c06\u5904\u7406\u5927\u5c0f\u4e3a [\ud835\udc5b_{\ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52\ud835\udc60}<\/code>,\ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52_{\ud835\udc51\ud835\udc56\ud835\udc5a}<\/code>] \u7684\u8282\u70b9\u5f20\u91cf\uff0c\u800c\u4e0d\u662f\u5927\u5c0f\u4e3a [\ud835\udc5b_{\ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52\ud835\udc60}<\/code>] \u7684\u8282\u70b9\u5f20\u91cf\u3002\u5176\u4ed6\u56fe\u5c5e\u6027\u4e5f\u662f\u5982\u6b64\u3002<\/p>\n

\u56fe\u795e\u7ecf\u7f51\u7edc<\/h2>\n

\u73b0\u5728\u56fe\u7684\u63cf\u8ff0\u4ee5\u4e00\u4e2a\u7f6e\u6362\u4e0d\u53d8\u7684\u77e9\u9635\u683c\u5f0f\u5448\u73b0\u51fa\u6765\uff0c\u6211\u4eec\u5c06\u63cf\u8ff0\u5982\u4f55\u4f7f\u7528\u56fe\u795e\u7ecf\u7f51\u7edc\uff08GNN\uff09\u6765\u89e3\u51b3\u56fe\u9884\u6d4b\u4efb\u52a1\u3002GNN\u662f\u5bf9\u56fe\u7684\u6240\u6709\u5c5e\u6027\uff08\u8282\u70b9\u3001\u8fb9\u3001\u5168\u5c40\u4e0a\u4e0b\u6587\uff09\u8fdb\u884c\u4f18\u5316\u7684\u53d8\u6362\uff0c\u5b83\u4fdd\u7559\u4e86\u56fe\u7684\u5bf9\u79f0\u6027\uff08\u7f6e\u6362\u4e0d\u53d8\u6027\uff09\u3002\u6211\u4eec\u5c06\u4f7f\u7528Gilmer\u7b49\u4eba\u63d0\u51fa\u7684\u201c\u6d88\u606f\u4f20\u9012\u795e\u7ecf\u7f51\u7edc\u201d\u6846\u67b6[18]\uff0c\u5e76\u501f\u52a9Battaglia\u7b49\u4eba\u5f15\u5165\u7684Graph Nets\u67b6\u6784\u793a\u610f[19]\u6765\u6784\u5efaGNN\u3002GNN\u91c7\u7528\u4e86\u201c\u56fe\u8f93\u5165\uff0c\u56fe\u8f93\u51fa\u201d\u7684\u67b6\u6784\uff0c\u8fd9\u610f\u5473\u7740\u8fd9\u4e9b\u6a21\u578b\u7c7b\u578b\u63a5\u53d7\u4e00\u4e2a\u56fe\u4f5c\u4e3a\u8f93\u5165\uff0c\u5c06\u4fe1\u606f\u52a0\u8f7d\u5230\u5176\u8282\u70b9\u3001\u8fb9\u548c\u5168\u5c40\u4e0a\u4e0b\u6587\u4e2d\uff0c\u5e76\u9010\u6e10\u8f6c\u6362\u8fd9\u4e9b\u5d4c\u5165\uff0c\u800c\u4e0d\u6539\u53d8\u8f93\u5165\u56fe\u7684\u8fde\u63a5\u6027\u3002<\/p>\n

\u6700\u7b80\u5355\u7684\u56fe\u795e\u7ecf\u7f51\u7edc<\/h3>\n

\u6709\u4e86\u6211\u4eec\u4e0a\u9762\u6784\u5efa\u7684\u56fe\u7684\u6570\u503c\u8868\u793a\uff08\u4f7f\u7528\u5411\u91cf\u800c\u4e0d\u662f\u6807\u91cf\uff09\uff0c\u6211\u4eec\u73b0\u5728\u53ef\u4ee5\u5f00\u59cb\u6784\u5efa\u4e00\u4e2aGNN\u3002\u6211\u4eec\u5c06\u4ece\u6700\u7b80\u5355\u7684GNN\u67b6\u6784\u5f00\u59cb\uff0c\u5176\u4e2d\u6211\u4eec\u4e3a\u6240\u6709\u56fe\u5c5e\u6027\uff08\u8282\u70b9\u3001\u8fb9\u3001\u5168\u5c40\uff09\u5b66\u4e60\u65b0\u7684\u5d4c\u5165\uff0c\u4f46\u6211\u4eec\u8fd8\u4e0d\u4f7f\u7528\u56fe\u7684\u8fde\u63a5\u6027\u3002<\/p>\n

\u4e3a\u4e86\u7b80\u5355\u8d77\u89c1\uff0c\u524d\u9762\u7684\u56fe\u793a\u4e2d\u4f7f\u7528\u6807\u91cf\u6765\u8868\u793a\u56fe\u7684\u5c5e\u6027\uff1b\u5b9e\u9645\u4e0a\uff0c\u7279\u5f81\u5411\u91cf\u6216\u5d4c\u5165\u66f4\u52a0\u5b9e\u7528\u3002\u4f60\u4e5f\u53ef\u4ee5\u79f0\u5176\u4e3aGNN\u5757\uff0c\u56e0\u4e3a\u5b83\u5305\u542b\u591a\u4e2a\u64cd\u4f5c\/\u5c42\uff08\u7c7b\u4f3c\u4e8eResNet\u5757\uff09\u3002<\/em><\/p>\n

\u8fd9\u4e2aGNN\u5728\u56fe\u7684\u6bcf\u4e2a\u7ec4\u4ef6\u4e0a\u4f7f\u7528\u4e00\u4e2a\u5355\u72ec\u7684\u591a\u5c42\u611f\u77e5\u5668\uff08MLP\uff09\uff08\u6216\u8005\u4f60\u559c\u6b22\u7684\u53ef\u5fae\u5206\u6a21\u578b\uff09\uff1b\u6211\u4eec\u5c06\u5176\u79f0\u4e3a\u4e00\u4e2aGNN\u5c42\u3002\u5bf9\u4e8e\u6bcf\u4e2a\u8282\u70b9\u5411\u91cf\uff0c\u6211\u4eec\u5e94\u7528MLP\u5e76\u5f97\u5230\u4e00\u4e2a\u7ecf\u8fc7\u5b66\u4e60\u7684\u8282\u70b9\u5411\u91cf\u3002\u5bf9\u4e8e\u6bcf\u6761\u8fb9\uff0c\u6211\u4eec\u4e5f\u662f\u5982\u6b64\uff0c\u5b66\u4e60\u6bcf\u6761\u8fb9\u7684\u5d4c\u5165\uff0c\u5bf9\u4e8e\u5168\u5c40\u4e0a\u4e0b\u6587\u5411\u91cf\u4e5f\u662f\u5982\u6b64\uff0c\u5b66\u4e60\u6574\u4e2a\u56fe\u7684\u5355\u4e00\u5d4c\u5165\u3002<\/p>\n

\"image-20230914233111042\"<\/p>\n

\u7b80\u5355GNN\u7684\u5355\u4e2a\u5c42\u3002\u4e00\u4e2a\u56fe\u5f62\u662f\u8f93\u5165\uff0c\u6bcf\u4e2a\u7ec4\u4ef6(V\u3001E\u3001U)<\/code>\u90fd\u901a\u8fc7MLP\u8fdb\u884c\u66f4\u65b0\u4ee5\u4ea7\u751f\u4e00\u4e2a\u65b0\u7684\u56fe\u5f62\u3002\u6bcf\u4e2a\u51fd\u6570\u7684\u4e0b\u6807\u8868\u793aGNN\u6a21\u578b\u7684\u7b2cn\u5c42\u4e2d\u4e0d\u540c\u56fe\u5c5e\u6027\u7684\u5355\u72ec\u51fd\u6570\u3002<\/em><\/p>\n

\u4e0e\u795e\u7ecf\u7f51\u7edc\u6a21\u5757\u6216\u5c42\u4e00\u6837\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u8fd9\u4e9bGNN\u5c42\u5806\u53e0\u5728\u4e00\u8d77\u3002<\/p>\n

\u7531\u4e8eGNN\u4e0d\u4f1a\u66f4\u65b0\u8f93\u5165\u56fe\u7684\u8fde\u63a5\u6027\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u76f8\u540c\u7684\u90bb\u63a5\u8868\u548c\u4e0e\u8f93\u5165\u56fe\u76f8\u540c\u6570\u91cf\u7684\u7279\u5f81\u5411\u91cf\u6765\u63cf\u8ff0GNN\u7684\u8f93\u51fa\u56fe\u3002\u4f46\u662f\uff0c\u8f93\u51fa\u56fe\u5177\u6709\u66f4\u65b0\u7684\u5d4c\u5165\uff0c\u56e0\u4e3aGNN\u5df2\u7ecf\u66f4\u65b0\u4e86\u8282\u70b9\u3001\u8fb9\u548c\u5168\u5c40\u4e0a\u4e0b\u6587\u7684\u8868\u793a\u3002<\/p>\n

\u901a\u8fc7\u6c47\u96c6\u4fe1\u606f\u8fdb\u884cGNN\u9884\u6d4b<\/h3>\n

\u6211\u4eec\u5df2\u7ecf\u6784\u5efa\u4e86\u4e00\u4e2a\u7b80\u5355\u7684GNN\uff0c\u4f46\u662f\u5982\u4f55\u5728\u6211\u4eec\u4e0a\u9762\u63cf\u8ff0\u7684\u4efb\u4f55\u4efb\u52a1\u4e2d\u8fdb\u884c\u9884\u6d4b\u5462\uff1f<\/p>\n

\u6211\u4eec\u5c06\u8003\u8651\u4e8c\u5143\u5206\u7c7b\u7684\u60c5\u51b5\uff0c\u4f46\u662f\u8fd9\u4e2a\u6846\u67b6\u53ef\u4ee5\u5f88\u5bb9\u6613\u5730\u6269\u5c55\u5230\u591a\u7c7b\u522b\u6216\u56de\u5f52\u7684\u60c5\u51b5\u3002\u5982\u679c\u4efb\u52a1\u662f\u5728\u8282\u70b9\u4e0a\u8fdb\u884c\u4e8c\u5143\u9884\u6d4b\uff0c\u5e76\u4e14\u56fe\u5df2\u7ecf\u5305\u542b\u8282\u70b9\u4fe1\u606f\uff0c\u90a3\u4e48\u65b9\u6cd5\u5f88\u7b80\u5355\u2014\u2014\u5bf9\u4e8e\u6bcf\u4e2a\u8282\u70b9\u5d4c\u5165\uff0c\u5e94\u7528\u4e00\u4e2a\u7ebf\u6027\u5206\u7c7b\u5668\u3002<\/p>\n

\"image-20230914233540252\"<\/p>\n

\u6211\u4eec\u53ef\u4ee5\u60f3\u8c61\u4e00\u4e2a\u793e\u4ea4\u7f51\u7edc\uff0c\u6211\u4eec\u5e0c\u671b\u901a\u8fc7\u4e0d\u4f7f\u7528\u7528\u6237\u6570\u636e\uff08\u8282\u70b9\uff09\uff0c\u800c\u53ea\u4f7f\u7528\u5173\u7cfb\u6570\u636e\uff08\u8fb9\uff09\u6765\u5b9e\u73b0\u533f\u540d\u5316\u3002\u8fd9\u6837\u7684\u60c5\u51b5\u4e4b\u4e00\u662f\u6211\u4eec\u5728\u201c\u8282\u70b9\u7ea7\u4efb\u52a1\u201d\u5c0f\u8282\u4e2d\u6307\u5b9a\u7684\u8282\u70b9\u4efb\u52a1\u3002\u5728\u7a7a\u624b\u9053\u4ff1\u4e50\u90e8\u7684\u4f8b\u5b50\u4e2d\uff0c\u8fd9\u53ea\u662f\u4f7f\u7528\u4eba\u4eec\u4e4b\u95f4\u7684\u4f1a\u8bae\u6b21\u6570\u6765\u786e\u5b9a\u5bf9Mr. Hi\u6216John H\u7684\u5fe0\u8bda\u5ea6\u3002<\/em><\/p>\n

\u7136\u800c\uff0c\u5e76\u4e0d\u603b\u662f\u8fd9\u4e48\u7b80\u5355\u7684\u3002\u4f8b\u5982\uff0c\u4f60\u53ef\u80fd\u5728\u56fe\u4e2d\u7684\u8fb9\u7f18\u5b58\u50a8\u4e86\u4fe1\u606f\uff0c\u4f46\u5728\u8282\u70b9\u4e2d\u6ca1\u6709\u4fe1\u606f\uff0c\u4f46\u4ecd\u7136\u9700\u8981\u5bf9\u8282\u70b9\u8fdb\u884c\u9884\u6d4b\u3002\u6211\u4eec\u9700\u8981\u4e00\u79cd\u65b9\u6cd5\u6765\u4ece\u8fb9\u7f18\u6536\u96c6\u4fe1\u606f\u5e76\u5c06\u5176\u4f20\u9012\u7ed9\u8282\u70b9\u8fdb\u884c\u9884\u6d4b\u3002\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u6c47\u96c6\u6765\u5b9e\u73b0\u8fd9\u4e00\u70b9\u3002\u6c47\u96c6\u5206\u4e3a\u4e24\u4e2a\u6b65\u9aa4\uff1a<\/p>\n

    \n
  1. \n

    \u5bf9\u4e8e\u6bcf\u4e2a\u8981\u6c47\u805a\u7684\u9879\u76ee\uff0c\u6536\u96c6\u5b83\u4eec\u7684\u6bcf\u4e2a\u5d4c\u5165\u5e76\u5c06\u5b83\u4eec\u8fde\u63a5\u6210\u4e00\u4e2a\u77e9\u9635\u3002<\/p>\n<\/li>\n

  2. \n

    \u7136\u540e\u901a\u8fc7\u4e00\u4e2a\u6c47\u603b\u64cd\u4f5c\u6765\u5bf9\u6536\u96c6\u5230\u7684\u5d4c\u5165\u8fdb\u884c\u805a\u5408\uff0c\u901a\u5e38\u662f\u6c42\u548c\u64cd\u4f5c\u3002<\/p>\n

    \u5982\u679c\u60f3\u66f4\u6df1\u5165\u5730\u8ba8\u8bba\u805a\u5408\u64cd\u4f5c\uff0c\u8bf7\u8f6c\u5230\u201c\u6bd4\u8f83\u805a\u5408\u64cd\u4f5c\u201d\u90e8\u5206\u3002<\/em><\/p>\n<\/li>\n<\/ol>\n

    \u6211\u4eec\u7528\u7b26\u53f7 \ud835\udc5d<\/code> \u6765\u8868\u793a\u6c47\u805a\u64cd\u4f5c\uff0c\u5e76\u8868\u793a\u6211\u4eec\u4ece\u8fb9\u5230\u8282\u70b9\u7684\u4fe1\u606f\u6536\u96c6\u4e3a \ud835\udc5d_{\ud835\udc38\ud835\udc5b\u2192\ud835\udc49\ud835\udc5b}<\/code>\u3002<\/p>\n

    \"image-20230914234015323\"<\/p>\n

    \u56e0\u6b64\uff0c\u5982\u679c\u6211\u4eec\u53ea\u6709\u8fb9\u7ea7\u7279\u5f81\uff0c\u5e76\u8bd5\u56fe\u9884\u6d4b\u4e8c\u5143\u8282\u70b9\u4fe1\u606f\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u6c47\u805a\u6765\u5c06\u4fe1\u606f\u4f20\u9012\u5230\u9700\u8981\u7684\u4f4d\u7f6e\u3002\u6a21\u578b\u770b\u8d77\u6765\u50cf\u8fd9\u6837\u3002<\/p>\n

    \"image-20230914234204792\"<\/p>\n

    \u5982\u679c\u6211\u4eec\u53ea\u6709\u8282\u70b9\u7ea7\u7279\u5f81\uff0c\u5e76\u8bd5\u56fe\u9884\u6d4b\u4e8c\u5143\u8fb9\u7ea7\u4fe1\u606f\uff0c\u6a21\u578b\u770b\u8d77\u6765\u50cf\u8fd9\u6837\u3002<\/p>\n

    \"image-20230914234250036\"<\/p>\n

    \u8fd9\u6837\u4e00\u4e2a\u60c5\u666f\u7684\u4e00\u4e2a\u4f8b\u5b50\u662f\u6211\u4eec\u5728\u8fb9\u7ea7\u4efb\u52a1\u5c0f\u8282\u4e2d\u6307\u5b9a\u7684\u8fb9\u4efb\u52a1\u3002\u8282\u70b9\u53ef\u4ee5\u88ab\u8bc6\u522b\u4e3a\u56fe\u50cf\u5b9e\u4f53\uff0c\u6211\u4eec\u8bd5\u56fe\u9884\u6d4b\u5b9e\u4f53\u662f\u5426\u5171\u4eab\u4e00\u4e2a\u5173\u7cfb\uff08\u4e8c\u5143\u8fb9\uff09\u3002<\/em><\/p>\n

    \u5982\u679c\u6211\u4eec\u53ea\u6709\u8282\u70b9\u7ea7\u7279\u5f81\uff0c\u9700\u8981\u9884\u6d4b\u4e00\u4e2a\u4e8c\u5143\u7684\u5168\u5c40\u5c5e\u6027\uff0c\u6211\u4eec\u9700\u8981\u5c06\u6240\u6709\u53ef\u7528\u7684\u8282\u70b9\u4fe1\u606f\u6536\u96c6\u5728\u4e00\u8d77\u5e76\u8fdb\u884c\u805a\u5408\u3002\u8fd9\u7c7b\u4f3c\u4e8e\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\u4e2d\u7684\u5168\u5c40\u5e73\u5747\u6c60\u5316\u5c42\u3002\u5bf9\u4e8e\u8fb9\u4e5f\u53ef\u4ee5\u505a\u540c\u6837\u7684\u64cd\u4f5c\u3002<\/p>\n

    \"image-20230914234454844\"<\/p>\n

    \u5728\u6211\u4eec\u7684\u793a\u4f8b\u4e2d\uff0c\u5206\u7c7b\u6a21\u578b \ud835\udc50 \u53ef\u4ee5\u8f7b\u677e\u5730\u88ab\u4efb\u4f55\u53ef\u5fae\u5206\u6a21\u578b\u53d6\u4ee3\uff0c\u6216\u8005\u53ef\u4ee5\u901a\u8fc7\u4f7f\u7528\u5e7f\u4e49\u7ebf\u6027\u6a21\u578b\u6765\u8fdb\u884c\u591a\u7c7b\u5206\u7c7b\u7684\u9002\u5e94\u3002<\/p>\n

    \"image-20230914234523426\"<\/p>\n

    \u4e00\u4e2a\u7aef\u5230\u7aef\u7684GNN\u9884\u6d4b<\/em><\/p>\n

    \u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u6f14\u793a\u4e86\u5982\u4f55\u6784\u5efa\u4e00\u4e2a\u7b80\u5355\u7684GNN\u6a21\u578b\uff0c\u5e76\u901a\u8fc7\u5728\u56fe\u7684\u4e0d\u540c\u90e8\u5206\u4e4b\u95f4\u4f20\u9012\u4fe1\u606f\u6765\u8fdb\u884c\u4e8c\u5143\u9884\u6d4b\u3002\u8fd9\u79cd\u6c47\u805a\u6280\u672f\u5c06\u4f5c\u4e3a\u6784\u5efa\u66f4\u590d\u6742\u7684GNN\u6a21\u578b\u7684\u57fa\u77f3\u3002\u5982\u679c\u6211\u4eec\u6709\u65b0\u7684\u56fe\u5c5e\u6027\uff0c\u6211\u4eec\u53ea\u9700\u5b9a\u4e49\u5982\u4f55\u5c06\u4fe1\u606f\u4ece\u4e00\u4e2a\u5c5e\u6027\u4f20\u9012\u5230\u53e6\u4e00\u4e2a\u5c5e\u6027\u3002<\/p>\n

    \u8bf7\u6ce8\u610f\uff0c\u5728\u8fd9\u4e2a\u6700\u7b80\u5355\u7684GNN\u516c\u5f0f\u4e2d\uff0c\u5728GNN\u5c42\u5185\u90e8\u6211\u4eec\u6839\u672c\u4e0d\u4f7f\u7528\u56fe\u7684\u8fde\u63a5\u6027\u3002\u6bcf\u4e2a\u8282\u70b9\u90fd\u662f\u72ec\u7acb\u5904\u7406\u7684\uff0c\u6bcf\u6761\u8fb9\u4e5f\u662f\u5982\u6b64\uff0c\u5168\u5c40\u4e0a\u4e0b\u6587\u4e5f\u662f\u5982\u6b64\u3002\u53ea\u6709\u5728\u6c47\u805a\u4fe1\u606f\u8fdb\u884c\u9884\u6d4b\u65f6\u624d\u4f7f\u7528\u8fde\u63a5\u6027\u3002<\/p>\n

    \u5728\u56fe\u7684\u5404\u90e8\u5206\u4e4b\u95f4\u4f20\u9012\u6d88\u606f<\/h3>\n

    \u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5728GNN\u5c42\u5185\u90e8\u4f7f\u7528\u6c47\u805a\u6765\u8fdb\u884c\u66f4\u590d\u6742\u7684\u9884\u6d4b\uff0c\u4ee5\u4f7f\u6211\u4eec\u5b66\u5230\u7684\u5d4c\u5165\u80fd\u591f\u611f\u77e5\u56fe\u7684\u8fde\u63a5\u6027\u3002\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u6d88\u606f\u4f20\u9012\u6765\u5b9e\u73b0\u8fd9\u4e00\u70b9\uff0c\u5373\u76f8\u90bb\u8282\u70b9\u6216\u8fb9\u4ea4\u6362\u4fe1\u606f\u5e76\u5f71\u54cd\u5f7c\u6b64\u66f4\u65b0\u540e\u7684\u5d4c\u5165\u3002<\/p>\n

    \u6d88\u606f\u4f20\u9012\u5206\u4e3a\u4e09\u4e2a\u6b65\u9aa4\uff1a<\/p>\n

      \n
    1. \n

      \u5bf9\u4e8e\u56fe\u4e2d\u7684\u6bcf\u4e2a\u8282\u70b9\uff0c\u6536\u96c6\u6240\u6709\u76f8\u90bb\u8282\u70b9\u7684\u5d4c\u5165\uff08\u6216\u6d88\u606f\uff09\uff0c\u8fd9\u662f\u4e0a\u9762\u63cf\u8ff0\u7684 \ud835\udc54 \u51fd\u6570\u3002<\/p>\n<\/li>\n

    2. \n

      \u901a\u8fc7\u805a\u5408\u51fd\u6570\uff08\u5982\u6c42\u548c\uff09\u5bf9\u6240\u6709\u6d88\u606f\u8fdb\u884c\u805a\u5408\u3002<\/p>\n<\/li>\n

    3. \n

      \u6240\u6709\u6c47\u805a\u7684\u6d88\u606f\u90fd\u901a\u8fc7\u4e00\u4e2a\u66f4\u65b0\u51fd\u6570\u4f20\u9012\uff0c\u901a\u5e38\u662f\u4e00\u4e2a\u5b66\u4e60\u7684\u795e\u7ecf\u7f51\u7edc\u3002<\/p>\n<\/li>\n<\/ol>\n

      \u4f60\u4e5f\u53ef\u4ee5\u5148\u6536\u96c6\u6d88\u606f\uff0c\u7136\u540e\u66f4\u65b0\u5b83\u4eec\uff0c\u6700\u540e\u805a\u5408\u5b83\u4eec\uff0c\u4ecd\u7136\u53ef\u4ee5\u5f97\u5230\u4e00\u4e2a\u7f6e\u6362\u4e0d\u53d8\u7684\u64cd\u4f5c\u3002<\/em><\/p>\n

      \u5c31\u50cf\u6c47\u805a\u53ef\u4ee5\u5e94\u7528\u4e8e\u8282\u70b9\u6216\u8fb9\u4e00\u6837\uff0c\u6d88\u606f\u4f20\u9012\u53ef\u4ee5\u53d1\u751f\u5728\u8282\u70b9\u6216\u8fb9\u4e4b\u95f4\u3002<\/p>\n

      \u8fd9\u4e9b\u6b65\u9aa4\u5bf9\u4e8e\u5229\u7528\u56fe\u7684\u8fde\u63a5\u6027\u81f3\u5173\u91cd\u8981\u3002\u6211\u4eec\u5c06\u6784\u5efa\u66f4\u590d\u6742\u7684\u6d88\u606f\u4f20\u9012\u53d8\u4f53\uff0c\u4ee5\u4ea7\u751f\u8868\u8fbe\u529b\u548c\u80fd\u529b\u4e0d\u65ad\u589e\u5f3a\u7684GNN\u6a21\u578b\u3002<\/p>\n

      \"image-20230914234952946\"<\/p>\n

      \u5c06\u9f20\u6807\u60ac\u505c\u5728\u4e00\u4e2a\u8282\u70b9\u4e0a\uff0c\u4ee5\u7a81\u51fa\u663e\u793a\u76f8\u90bb\u8282\u70b9\uff0c\u5e76\u53ef\u89c6\u5316\u5c06\u8fdb\u884c\u6c47\u603b\u3001\u66f4\u65b0\u548c\u5b58\u50a8\u7684\u76f8\u90bb\u5d4c\u5165\u3002<\/em><\/p>\n

      \u8fd9\u4e00\u7cfb\u5217\u7684\u64cd\u4f5c\uff0c\u5f53\u5e94\u7528\u4e00\u6b21\u65f6\uff0c\u5c31\u6784\u6210\u4e86\u6700\u7b80\u5355\u7684\u6d88\u606f\u4f20\u9012GNN\u5c42\u3002<\/p>\n

      \u8fd9\u8ba9\u4eba\u60f3\u8d77\u4e86\u6807\u51c6\u7684\u5377\u79ef\u64cd\u4f5c\uff1a\u5b9e\u8d28\u4e0a\uff0c\u6d88\u606f\u4f20\u9012\u548c\u5377\u79ef\u90fd\u662f\u4e3a\u4e86\u805a\u5408\u548c\u5904\u7406\u4e00\u4e2a\u5143\u7d20\u7684\u76f8\u90bb\u5143\u7d20\u7684\u4fe1\u606f\uff0c\u4ee5\u66f4\u65b0\u8be5\u5143\u7d20\u7684\u503c\u3002\u5728\u56fe\u4e2d\uff0c\u8be5\u5143\u7d20\u662f\u4e00\u4e2a\u8282\u70b9\uff0c\u5728\u56fe\u50cf\u4e2d\uff0c\u8be5\u5143\u7d20\u662f\u4e00\u4e2a\u50cf\u7d20\u3002\u7136\u800c\uff0c\u4e0e\u56fe\u50cf\u4e2d\u6bcf\u4e2a\u50cf\u7d20\u90fd\u6709\u4e00\u7ec4\u56fa\u5b9a\u6570\u91cf\u7684\u76f8\u90bb\u5143\u7d20\u4e0d\u540c\uff0c\u5728\u56fe\u4e2d\uff0c\u76f8\u90bb\u8282\u70b9\u7684\u6570\u91cf\u53ef\u4ee5\u662f\u53ef\u53d8\u7684\u3002<\/p>\n

      \u901a\u8fc7\u5806\u53e0\u6d88\u606f\u4f20\u9012GNN\u5c42\uff0c\u4e00\u4e2a\u8282\u70b9\u6700\u7ec8\u53ef\u4ee5\u6574\u5408\u6765\u81ea\u6574\u4e2a\u56fe\u7684\u4fe1\u606f\uff1a\u7ecf\u8fc7\u4e09\u5c42\u540e\uff0c\u4e00\u4e2a\u8282\u70b9\u5bf9\u8ddd\u79bb\u5b83\u4e09\u6b65\u7684\u8282\u70b9\u5177\u6709\u4fe1\u606f\u3002<\/p>\n

      \u6211\u4eec\u53ef\u4ee5\u66f4\u65b0\u6211\u4eec\u7684\u67b6\u6784\u56fe\uff0c\u4ee5\u5305\u62ec\u8282\u70b9\u7684\u8fd9\u4e2a\u65b0\u4fe1\u606f\u6765\u6e90\uff1a<\/p>\n

      \"image-20230914235112361\"<\/p>\n

      GCN\u67b6\u6784\u7684\u793a\u610f\u56fe\uff0c\u5b83\u901a\u8fc7\u5728\u4e00\u4e2a\u5ea6\u7684\u8ddd\u79bb\u4e0a\u805a\u5408\u76f8\u90bb\u8282\u70b9\u6765\u66f4\u65b0\u56fe\u7684\u8282\u70b9\u8868\u793a\u3002<\/em><\/p>\n

      \u5b66\u4e60\u8fb9\u7684\u8868\u793a<\/h3>\n

      \u6211\u4eec\u7684\u6570\u636e\u96c6\u5e76\u4e0d\u603b\u662f\u5305\u542b\u6240\u6709\u7c7b\u578b\u7684\u4fe1\u606f\uff08\u8282\u70b9\u3001\u8fb9\u548c\u5168\u5c40\u4e0a\u4e0b\u6587\uff09\u3002\u5f53\u6211\u4eec\u60f3\u8981\u5bf9\u8282\u70b9\u8fdb\u884c\u9884\u6d4b\uff0c\u4f46\u6211\u4eec\u7684\u6570\u636e\u96c6\u53ea\u5305\u542b\u8fb9\u4fe1\u606f\u65f6\uff0c\u6211\u4eec\u5728\u4e0a\u9762\u5c55\u793a\u4e86\u5982\u4f55\u5728\u6a21\u578b\u7684\u6700\u7ec8\u9884\u6d4b\u6b65\u9aa4\u4e2d\u4f7f\u7528\u6c47\u805a\u5c06\u4fe1\u606f\u4ece\u8fb9\u8def\u7531\u5230\u8282\u70b9\u3002\u6211\u4eec\u53ef\u4ee5\u5728GNN\u5c42\u5185\u90e8\u4f7f\u7528\u6d88\u606f\u4f20\u9012\u5728\u8282\u70b9\u548c\u8fb9\u4e4b\u95f4\u5171\u4eab\u4fe1\u606f\u3002<\/p>\n

      \u6211\u4eec\u53ef\u4ee5\u4ee5\u4e0e\u4e4b\u524d\u4f7f\u7528\u76f8\u90bb\u8282\u70b9\u4fe1\u606f\u76f8\u540c\u7684\u65b9\u5f0f\u5408\u5e76\u76f8\u90bb\u8fb9\u7684\u4fe1\u606f\uff0c\u9996\u5148\u5bf9\u8fb9\u4fe1\u606f\u8fdb\u884c\u6c47\u805a\uff0c\u7136\u540e\u7528\u4e00\u4e2a\u66f4\u65b0\u51fd\u6570\u8fdb\u884c\u8f6c\u6362\u5e76\u5b58\u50a8\u5b83\u3002<\/p>\n

      \u7136\u800c\uff0c\u5728\u56fe\u4e2d\u5b58\u50a8\u7684\u8282\u70b9\u548c\u8fb9\u7684\u4fe1\u606f\u53ef\u80fd\u5e76\u4e0d\u4e00\u5b9a\u5177\u6709\u76f8\u540c\u7684\u5927\u5c0f\u6216\u5f62\u72b6\uff0c\u56e0\u6b64\u5982\u4f55\u5c06\u5b83\u4eec\u7ec4\u5408\u8d77\u6765\u5e76\u4e0d\u662f\u7acb\u5373\u660e\u786e\u7684\u3002\u4e00\u79cd\u65b9\u6cd5\u662f\u5b66\u4e60\u4ece\u8fb9\u7684\u7a7a\u95f4\u5230\u8282\u70b9\u7684\u7a7a\u95f4\u7684\u7ebf\u6027\u6620\u5c04\uff0c\u53cd\u4e4b\u4ea6\u7136\u3002\u53e6\u4e00\u79cd\u65b9\u6cd5\u662f\u5728\u66f4\u65b0\u51fd\u6570\u4e4b\u524d\u5c06\u5b83\u4eec\u8fde\u63a5\u5728\u4e00\u8d77\u3002<\/p>\n

      \"image-20230914235330417\"<\/p>\n

      \u6d88\u606f\u4f20\u9012\u5c42\u7684\u67b6\u6784\u793a\u610f\u56fe\u3002\u7b2c\u4e00\u6b65\u201c\u51c6\u5907\u201d\u4e86\u4e00\u4e2a\u6d88\u606f\uff0c\u5176\u4e2d\u5305\u542b\u4e86\u6765\u81ea\u8fb9\u53ca\u5176\u8fde\u63a5\u7684\u8282\u70b9\u7684\u4fe1\u606f\uff0c\u7136\u540e\u5c06\u6d88\u606f\u201c\u4f20\u9012\u201d\u7ed9\u8282\u70b9\u3002<\/em><\/p>\n

      \u5728\u6784\u5efaGNN\u65f6\uff0c\u6211\u4eec\u66f4\u65b0\u54ea\u4e9b\u56fe\u5c5e\u6027\u4ee5\u53ca\u4ee5\u4f55\u79cd\u987a\u5e8f\u66f4\u65b0\u5b83\u4eec\u662f\u4e00\u4e2a\u8bbe\u8ba1\u51b3\u7b56\u3002\u6211\u4eec\u53ef\u4ee5\u9009\u62e9\u662f\u5728\u66f4\u65b0\u8282\u70b9\u5d4c\u5165\u4e4b\u524d\u66f4\u65b0\u8fb9\u5d4c\u5165\uff0c\u8fd8\u662f\u53cd\u8fc7\u6765\u3002\u8fd9\u662f\u4e00\u4e2a\u7814\u7a76\u9886\u57df\uff0c\u6709\u8bb8\u591a\u89e3\u51b3\u65b9\u6848 – \u4f8b\u5982\uff0c\u6211\u4eec\u53ef\u4ee5\u4ee5\u201c\u7f16\u7ec7\u201d\u65b9\u5f0f\u8fdb\u884c\u66f4\u65b0\uff0c\u5176\u4e2d\u6709\u56db\u4e2a\u66f4\u65b0\u7684\u8868\u793a\u88ab\u5408\u5e76\u6210\u65b0\u7684\u8282\u70b9\u548c\u8fb9\u7684\u8868\u793a\uff1a\u8282\u70b9\u5230\u8282\u70b9\uff08\u7ebf\u6027\uff09\uff0c\u8fb9\u5230\u8fb9\uff08\u7ebf\u6027\uff09\uff0c\u8282\u70b9\u5230\u8fb9\uff08\u8fb9\u5c42\uff09\uff0c\u8fb9\u5230\u8282\u70b9\uff08\u8282\u70b9\u5c42\uff09\u3002<\/p>\n

      \"image-20230914235519545\"<\/p>\n

      \u5728GNN\u5c42\u4e2d\uff0c\u6211\u4eec\u53ef\u80fd\u7ed3\u5408\u8fb9\u548c\u8282\u70b9\u8868\u793a\u7684\u4e00\u4e9b\u4e0d\u540c\u65b9\u5f0f\u3002<\/em><\/p>\n

      \u6dfb\u52a0\u5168\u5c40\u8868\u793a<\/h3>\n

      \u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u6211\u4eec\u63cf\u8ff0\u7684\u7f51\u7edc\u5b58\u5728\u4e00\u4e2a\u7f3a\u9677\uff1a\u5728\u56fe\u4e2d\u76f8\u8ddd\u8f83\u8fdc\u7684\u8282\u70b9\u53ef\u80fd\u6c38\u8fdc\u65e0\u6cd5\u6709\u6548\u5730\u76f8\u4e92\u4f20\u9012\u4fe1\u606f\uff0c\u5373\u4f7f\u6211\u4eec\u591a\u6b21\u5e94\u7528\u6d88\u606f\u4f20\u9012\u4e5f\u662f\u5982\u6b64\u3002\u5bf9\u4e8e\u4e00\u4e2a\u8282\u70b9\uff0c\u5982\u679c\u6211\u4eec\u6709k\u5c42\uff0c\u4fe1\u606f\u6700\u591a\u4f1a\u4f20\u64adk\u6b65\u3002\u8fd9\u53ef\u80fd\u5bf9\u4f9d\u8d56\u4e8e\u76f8\u8ddd\u8f83\u8fdc\u7684\u8282\u70b9\u6216\u8282\u70b9\u7ec4\u7684\u9884\u6d4b\u4efb\u52a1\u9020\u6210\u95ee\u9898\u3002\u4e00\u4e2a\u89e3\u51b3\u65b9\u6848\u662f\u4f7f\u6240\u6709\u8282\u70b9\u80fd\u591f\u76f8\u4e92\u4f20\u9012\u4fe1\u606f\u3002\u7136\u800c\uff0c\u5bf9\u4e8e\u5927\u578b\u56fe\u5f62\uff0c\u8fd9\u5f88\u5feb\u53d8\u5f97\u8ba1\u7b97\u6210\u672c\u9ad8\u6602\uff08\u5c3d\u7ba1\u5bf9\u4e8e\u5c0f\u578b\u5206\u5b50\u7b49\u5c0f\u56fe\uff0c\u5df2\u7ecf\u4f7f\u7528\u4e86\u79f0\u4e3a\u201c\u865a\u62df\u8fb9\u201d\u7684\u65b9\u6cd5\uff09\u3002<\/p>\n

      \u89e3\u51b3\u6b64\u95ee\u9898\u7684\u4e00\u79cd\u65b9\u6cd5\u662f\u4f7f\u7528\u56fe\u7684\u5168\u5c40\u8868\u793a\uff08U\uff09\uff0c\u6709\u65f6\u79f0\u4e3a\u4e3b\u8282\u70b9\u6216\u4e0a\u4e0b\u6587\u5411\u91cf\u3002\u8fd9\u4e2a\u5168\u5c40\u4e0a\u4e0b\u6587\u5411\u91cf\u4e0e\u7f51\u7edc\u4e2d\u7684\u6240\u6709\u5176\u4ed6\u8282\u70b9\u548c\u8fb9\u76f8\u8fde\u63a5\uff0c\u5e76\u4e14\u53ef\u4ee5\u4f5c\u4e3a\u5b83\u4eec\u4e4b\u95f4\u4f20\u9012\u4fe1\u606f\u7684\u6865\u6881\uff0c\u4ece\u800c\u6784\u5efa\u4e86\u5bf9\u6574\u4e2a\u56fe\u7684\u8868\u793a\u3002\u8fd9\u6bd4\u4ee5\u5176\u4ed6\u65b9\u5f0f\u5b66\u5230\u7684\u56fe\u7684\u8868\u793a\u66f4\u4e30\u5bcc\u3001\u66f4\u590d\u6742\u3002<\/p>\n

      \"image-20230914235734086\"<\/p>\n

      \u5229\u7528\u5168\u5c40\u8868\u793a\u7684\u56fe\u5f62\u7f51\u7edc\u67b6\u6784\u793a\u610f\u56fe\u3002<\/em><\/p>\n

      \u5728\u8fd9\u79cd\u89c6\u56fe\u4e2d\uff0c\u6240\u6709\u7684\u56fe\u5c5e\u6027\u90fd\u6709\u4e86\u5b66\u4e60\u5230\u7684\u8868\u793a\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u5728\u6c47\u805a\u8fc7\u7a0b\u4e2d\u5229\u7528\u5b83\u4eec\uff0c\u901a\u8fc7\u5c06\u6211\u4eec\u611f\u5174\u8da3\u7684\u5c5e\u6027\u7684\u4fe1\u606f\u4e0e\u5176\u4f59\u5c5e\u6027\u76f8\u5bf9\u5e94\u3002\u4f8b\u5982\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u8282\u70b9\uff0c\u6211\u4eec\u53ef\u4ee5\u8003\u8651\u6765\u81ea\u76f8\u90bb\u8282\u70b9\u3001\u8fde\u63a5\u7684\u8fb9\u548c\u5168\u5c40\u4fe1\u606f\u7684\u4fe1\u606f\u3002\u4e3a\u4e86\u5c06\u65b0\u7684\u8282\u70b9\u5d4c\u5165\u4e0e\u6240\u6709\u8fd9\u4e9b\u53ef\u80fd\u7684\u4fe1\u606f\u6e90\u76f8\u5bf9\u5e94\uff0c\u6211\u4eec\u53ef\u4ee5\u7b80\u5355\u5730\u5c06\u5b83\u4eec\u8fde\u63a5\u8d77\u6765\u3002\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u901a\u8fc7\u7ebf\u6027\u6620\u5c04\u5c06\u5b83\u4eec\u6620\u5c04\u5230\u76f8\u540c\u7684\u7a7a\u95f4\u5e76\u76f8\u52a0\uff0c\u6216\u8005\u5e94\u7528\u4e00\u4e2a\u7279\u5f81\u8c03\u5236\u5c42\uff0c\u8fd9\u53ef\u4ee5\u88ab\u770b\u4f5c\u662f\u4e00\u79cd\u7279\u5f81-wise \u7684\u6ce8\u610f\u673a\u5236\u3002<\/p>\n

      \"image-20230915001432874\"<\/p>\n

      \u57fa\u4e8e\u4e09\u4e2a\u5176\u4ed6\u5d4c\u5165\uff08\u76f8\u90bb\u8282\u70b9\u3001\u76f8\u90bb\u8fb9\u3001\u5168\u5c40\uff09\u6765\u8c03\u6574\u4e00\u4e2a\u8282\u70b9\u4fe1\u606f\u7684\u793a\u610f\u56fe\u3002\u8fd9\u4e00\u6b65\u5bf9\u5e94\u4e8e\u56fe\u5f62\u7f51\u7edc\u5c42\u4e2d\u7684\u8282\u70b9\u64cd\u4f5c\u3002<\/em><\/p>\n

      GNN\u6e38\u4e50\u573a<\/h2>\n

      \u6211\u4eec\u5728\u8fd9\u91cc\u63cf\u8ff0\u4e86\u5404\u79cd\u4e0d\u540c\u7684GNN\u7ec4\u4ef6\uff0c\u4f46\u5728\u5b9e\u8df5\u4e2d\u5b83\u4eec\u7a76\u7adf\u6709\u4f55\u533a\u522b\u5462\uff1f\u8fd9\u4e2aGNN\u6e38\u4e50\u573a\u5141\u8bb8\u4f60\u770b\u5230\u8fd9\u4e9b\u4e0d\u540c\u7ec4\u4ef6\u548c\u67b6\u6784\u5982\u4f55\u5f71\u54cdGNN\u5b66\u4e60\u4e00\u4e2a\u771f\u5b9e\u4efb\u52a1\u7684\u80fd\u529b\u3002<\/p>\n

      \u6211\u4eec\u7684\u6e38\u4e50\u573a\u5c55\u793a\u4e86\u4e00\u4e2a\u5c0f\u5206\u5b50\u56fe\u7684\u56fe\u7ea7\u522b\u9884\u6d4b\u4efb\u52a1\u3002\u6211\u4eec\u4f7f\u7528\u4e86Leffingwell Odor\u6570\u636e\u96c6\uff0c\u8be5\u6570\u636e\u96c6\u7531\u5e26\u6709\u76f8\u5173\u6c14\u5473\u611f\u77e5\uff08\u6807\u7b7e\uff09\u7684\u5206\u5b50\u7ec4\u6210\u3002\u9884\u6d4b\u5206\u5b50\u7ed3\u6784\uff08\u56fe\uff09\u4e0e\u5176\u6c14\u5473\u4e4b\u95f4\u7684\u5173\u7cfb\u662f\u4e00\u4e2a\u6db5\u76d6\u4e86\u5316\u5b66\u3001\u7269\u7406\u3001\u795e\u7ecf\u79d1\u5b66\u548c\u673a\u5668\u5b66\u4e60\u7684\u767e\u5e74\u96be\u9898\u3002<\/p>\n

      \u4e3a\u4e86\u7b80\u5316\u95ee\u9898\uff0c\u6211\u4eec\u53ea\u8003\u8651\u6bcf\u4e2a\u5206\u5b50\u7684\u4e00\u4e2a\u4e8c\u5143\u6807\u7b7e\uff0c\u5373\u5bf9\u5206\u5b50\u56fe\u8fdb\u884c\u5206\u7c7b\uff0c\u5224\u65ad\u5176\u6c14\u5473\u662f\u5426\u201c\u8f9b\u8fa3\u201d\uff0c\u7531\u4e13\u4e1a\u8c03\u9999\u5e08\u6807\u8bb0\u3002\u6211\u4eec\u8bf4\u4e00\u4e2a\u5206\u5b50\u5177\u6709\u201c\u8f9b\u8fa3\u201d\u7684\u6c14\u5473\uff0c\u5982\u679c\u5b83\u5177\u6709\u5f3a\u70c8\u3001\u7a81\u51fa\u7684\u6c14\u5473\u3002\u4f8b\u5982\uff0c\u5927\u849c\u548c\u82a5\u672b\u53ef\u80fd\u542b\u6709\u70ef\u4e19\u9187\u5206\u5b50\uff0c\u5177\u6709\u8fd9\u79cd\u7279\u6027\u3002\u800c\u5e38\u7528\u4e8e\u8584\u8377\u5473\u7cd6\u679c\u7684\u8584\u8377\u916e\u5206\u5b50\uff0c\u4e5f\u88ab\u63cf\u8ff0\u4e3a\u5177\u6709\u8f9b\u8fa3\u6c14\u5473\u3002<\/p>\n

      \u6211\u4eec\u5c06\u6bcf\u4e2a\u5206\u5b50\u8868\u793a\u4e3a\u4e00\u4e2a\u56fe\uff0c\u5176\u4e2d\u539f\u5b50\u662f\u8282\u70b9\uff0c\u5305\u542b\u5176\u539f\u5b50\u79cd\u7c7b\u7684\u72ec\u70ed\u7f16\u7801\uff08\u78b3\u3001\u6c2e\u3001\u6c27\u3001\u6c1f\uff09\uff0c\u5316\u5b66\u952e\u662f\u8fb9\uff0c\u5305\u542b\u5176\u952e\u7c7b\u578b\u7684\u72ec\u70ed\u7f16\u7801\uff08\u5355\u952e\u3001\u53cc\u952e\u3001\u4e09\u952e\u6216\u82b3\u9999\u952e\uff09\u3002<\/p>\n

      \u6211\u4eec\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u7684\u901a\u7528\u5efa\u6a21\u6a21\u677f\u5c06\u901a\u8fc7\u9010\u5c42\u5806\u53e0\u7684GNN\u5c42\u6784\u5efa\uff0c\u7136\u540e\u4f7f\u7528\u5177\u6709sigmoid\u6fc0\u6d3b\u51fd\u6570\u7684\u7ebf\u6027\u6a21\u578b\u8fdb\u884c\u5206\u7c7b\u3002\u6211\u4eec\u7684GNN\u6a21\u578b\u7684\u8bbe\u8ba1\u7a7a\u95f4\u5305\u62ec\u8bb8\u591a\u53ef\u4ee5\u5b9a\u5236\u6a21\u578b\u7684\u6760\u6746\uff1a<\/p>\n

        \n
      1. GNN\u5c42\u7684\u6570\u91cf\uff0c\u4e5f\u79f0\u4e3a\u6df1\u5ea6\u3002<\/li>\n
      2. \u66f4\u65b0\u65f6\u6bcf\u4e2a\u5c5e\u6027\u7684\u7ef4\u5ea6\u3002\u66f4\u65b0\u51fd\u6570\u662f\u4e00\u4e2a\u5177\u6709relu\u6fc0\u6d3b\u51fd\u6570\u548c\u7528\u4e8e\u6fc0\u6d3b\u5f52\u4e00\u5316\u7684\u5c42\u89c4\u8303\u7684\u5355\u5c42MLP\u3002<\/li>\n
      3. \u7528\u4e8e\u6c47\u805a\u7684\u805a\u5408\u51fd\u6570\uff1a\u6700\u5927\u3001\u5747\u503c\u6216\u6c42\u548c\u3002<\/li>\n
      4. \u88ab\u66f4\u65b0\u7684\u56fe\u5c5e\u6027\uff0c\u6216\u6d88\u606f\u4f20\u9012\u7684\u6837\u5f0f\uff1a\u8282\u70b9\u3001\u8fb9\u548c\u5168\u5c40\u8868\u793a\u3002\u6211\u4eec\u901a\u8fc7\u5e03\u5c14\u5f00\u5173\uff08\u5f00\u542f\u6216\u5173\u95ed\uff09\u6765\u63a7\u5236\u8fd9\u4e9b\u9009\u9879\u3002\u4e00\u4e2a\u57fa\u7ebf\u6a21\u578b\u5c06\u662f\u4e00\u4e2a\u56fe\u72ec\u7acb\u7684GNN\uff08\u6240\u6709\u6d88\u606f\u4f20\u9012\u5173\u95ed\uff09\uff0c\u5b83\u5728\u6700\u540e\u5c06\u6240\u6709\u6570\u636e\u6c47\u805a\u5230\u4e00\u4e2a\u5355\u4e00\u7684\u5168\u5c40\u5c5e\u6027\u4e2d\u3002\u6253\u5f00\u6240\u6709\u6d88\u606f\u4f20\u9012\u529f\u80fd\u5c06\u4ea7\u751f\u4e00\u4e2aGraphNets\u67b6\u6784\u3002<\/li>\n<\/ol>\n

        \u4e3a\u4e86\u66f4\u597d\u5730\u7406\u89e3GNN\u5982\u4f55\u5b66\u4e60\u4e00\u4e2a\u4efb\u52a1\u4f18\u5316\u7684\u56fe\u5f62\u8868\u793a\uff0c\u6211\u4eec\u8fd8\u4f1a\u67e5\u770bGNN\u7684\u5012\u6570\u7b2c\u4e8c\u5c42\u6fc0\u6d3b\u3002\u8fd9\u4e9b\u201c\u56fe\u5d4c\u5165\u201d\u662f\u5728\u9884\u6d4b\u4e4b\u524dGNN\u6a21\u578b\u7684\u8f93\u51fa\u3002\u7531\u4e8e\u6211\u4eec\u5728\u9884\u6d4b\u4e2d\u4f7f\u7528\u4e86\u5e7f\u4e49\u7ebf\u6027\u6a21\u578b\uff0c\u56e0\u6b64\u7ebf\u6027\u6620\u5c04\u8db3\u4ee5\u8ba9\u6211\u4eec\u770b\u5230\u5982\u4f55\u56f4\u7ed5\u51b3\u7b56\u8fb9\u754c\u5b66\u4e60\u8868\u793a\u3002<\/p>\n

        \u7531\u4e8e\u8fd9\u4e9b\u662f\u9ad8\u7ef4\u5411\u91cf\uff0c\u6211\u4eec\u901a\u8fc7\u4e3b\u6210\u5206\u5206\u6790\uff08PCA\uff09\u5c06\u5b83\u4eec\u964d\u7ef4\u52302D\u3002\u4e00\u4e2a\u5b8c\u7f8e\u7684\u6a21\u578b\u4f1a\u6e05\u6670\u5730\u5c06\u6807\u8bb0\u7684\u6570\u636e\u5206\u5f00\uff0c\u4f46\u7531\u4e8e\u6211\u4eec\u5728\u964d\u7ef4\u540c\u65f6\u4e5f\u6709\u4e0d\u5b8c\u7f8e\u7684\u6a21\u578b\uff0c\u8fd9\u4e2a\u8fb9\u754c\u53ef\u80fd\u4f1a\u53d8\u5f97\u96be\u4ee5\u8bc6\u522b\u3002<\/p>\n

        \u5c1d\u8bd5\u4f7f\u7528\u4e0d\u540c\u7684\u6a21\u578b\u67b6\u6784\u6765\u5efa\u7acb\u4f60\u7684\u76f4\u89c9\u3002\u4f8b\u5982\uff0c\u770b\u770b\u4f60\u662f\u5426\u53ef\u4ee5\u7f16\u8f91\u5de6\u4fa7\u7684\u5206\u5b50\u4ee5\u589e\u52a0\u6a21\u578b\u7684\u9884\u6d4b\u3002\u76f8\u540c\u7684\u7f16\u8f91\u5bf9\u4e0d\u540c\u7684\u6a21\u578b\u67b6\u6784\u662f\u5426\u4ea7\u751f\u76f8\u540c\u7684\u6548\u679c\uff1f<\/p>\n

        \"image-20230915155525766\"<\/p>\n

        \u4e00\u4e9b\u7ecf\u9a8c\u6027\u7684GNN\u8bbe\u8ba1\u6559\u8bad<\/h3>\n

        \u5728\u4e0a\u8ff0\u63a2\u7d22\u67b6\u6784\u9009\u62e9\u65f6\uff0c\u60a8\u53ef\u80fd\u4f1a\u53d1\u73b0\u67d0\u4e9b\u6a21\u578b\u7684\u6027\u80fd\u4f18\u4e8e\u5176\u4ed6\u6a21\u578b\u3002\u662f\u5426\u6709\u4e00\u4e9b\u660e\u786e\u7684GNN\u8bbe\u8ba1\u9009\u62e9\u53ef\u4ee5\u63d0\u4f9b\u66f4\u597d\u7684\u6027\u80fd\uff1f\u4f8b\u5982\uff0c\u6df1\u5c42GNN\u6a21\u578b\u662f\u5426\u6bd4\u8f83\u6d45\u5c42\u7684\u6a21\u578b\u8868\u73b0\u66f4\u597d\uff1f\u6216\u8005\u5728\u805a\u5408\u529f\u80fd\u4e4b\u95f4\u662f\u5426\u6709\u660e\u786e\u7684\u9009\u62e9\uff1f\u7b54\u6848\u5c06\u53d6\u51b3\u4e8e\u6570\u636e\u3001[25] [26]\uff0c\u751a\u81f3\u4e0d\u540c\u7684\u7279\u5f81\u5316\u548c\u6784\u5efa\u56fe\u7684\u65b9\u6cd5\u53ef\u80fd\u4f1a\u5f97\u5230\u4e0d\u540c\u7684\u7b54\u6848\u3002<\/p>\n

        \u901a\u8fc7\u4ee5\u4e0b\u4ea4\u4e92\u5f0f\u56fe\uff0c\u6211\u4eec\u5c06\u63a2\u8ba8GNN\u67b6\u6784\u7684\u7a7a\u95f4\u4ee5\u53ca\u5728\u51e0\u4e2a\u4e3b\u8981\u8bbe\u8ba1\u9009\u62e9\u65b9\u9762\u7684\u4efb\u52a1\u6027\u80fd\uff1a\u6d88\u606f\u4f20\u9012\u7684\u65b9\u5f0f\u3001\u5d4c\u5165\u7684\u7ef4\u5ea6\u3001\u5c42\u6570\u4ee5\u53ca\u805a\u5408\u64cd\u4f5c\u7c7b\u578b\u3002<\/p>\n

        \u6563\u70b9\u56fe\u4e2d\u7684\u6bcf\u4e2a\u70b9\u4ee3\u8868\u4e00\u4e2a\u6a21\u578b\uff1ax\u8f74\u662f\u53ef\u8bad\u7ec3\u53d8\u91cf\u7684\u6570\u91cf\uff0cy\u8f74\u662f\u6027\u80fd\u3002\u5c06\u9f20\u6807\u60ac\u505c\u5728\u4e00\u4e2a\u70b9\u4e0a\uff0c\u53ef\u4ee5\u770b\u5230GNN\u67b6\u6784\u53c2\u6570\u3002<\/p>\n

        \"image-20230915155905484\"<\/p>\n

        \u4ee5\u4e0a\u662f\u6bcf\u4e2a\u6a21\u578b\u6027\u80fd\u4e0e\u5176\u53ef\u8bad\u7ec3\u53d8\u91cf\u6570\u91cf\u7684\u6563\u70b9\u56fe\u3002\u5c06\u9f20\u6807\u60ac\u505c\u5728\u4e00\u4e2a\u70b9\u4e0a\uff0c\u53ef\u4ee5\u770b\u5230 GNN \u67b6\u6784\u53c2\u6570\u3002<\/em><\/p>\n

        \u9996\u5148\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u4ee4\u4eba\u60ca\u8bb6\u7684\u662f\uff0c\u53c2\u6570\u6570\u91cf\u8f83\u9ad8\u4e0e\u6027\u80fd\u8f83\u9ad8\u5448\u6b63\u76f8\u5173\u5173\u7cfb\u3002 GNN \u662f\u4e00\u79cd\u975e\u5e38\u9ad8\u6548\u7684\u53c2\u6570\u6a21\u578b\u7c7b\u578b\uff1a\u5373\u4f7f\u5bf9\u4e8e\u5f88\u5c0f\u7684\u53c2\u6570\u6570\u91cf\uff083k\uff09\uff0c\u6211\u4eec\u5df2\u7ecf\u53ef\u4ee5\u627e\u5230\u6027\u80fd\u5f88\u9ad8\u7684\u6a21\u578b\u3002<\/p>\n

        \u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u53ef\u4ee5\u67e5\u770b\u6839\u636e\u4e0d\u540c\u56fe\u5c5e\u6027\u7684\u5b66\u4e60\u8868\u793a\u7684\u7ef4\u5ea6\u6765\u6c47\u603b\u6027\u80fd\u5206\u5e03\u3002<\/p>\n

        \"image-20230915160035371\"<\/p>\n

        \u5728\u4e0d\u540c\u8282\u70b9\u3001\u8fb9\u548c\u5168\u5c40\u7ef4\u5ea6\u4e0b\uff0c\u6a21\u578b\u7684\u603b\u4f53\u6027\u80fd\u3002<\/em><\/p>\n

        \u6211\u4eec\u53ef\u4ee5\u6ce8\u610f\u5230\uff0c\u5177\u6709\u66f4\u9ad8\u7ef4\u5ea6\u7684\u6a21\u578b\u5f80\u5f80\u5177\u6709\u66f4\u597d\u7684\u5e73\u5747\u6027\u80fd\u548c\u8f83\u4f4e\u7684\u4e0b\u9650\u6027\u80fd\uff0c\u4f46\u6700\u5927\u6027\u80fd\u5e76\u672a\u51fa\u73b0\u76f8\u540c\u7684\u8d8b\u52bf\u3002\u4e00\u4e9b\u6027\u80fd\u6392\u540d\u9760\u524d\u7684\u6a21\u578b\u53ef\u4ee5\u5728\u8f83\u5c0f\u7684\u7ef4\u5ea6\u4e0b\u627e\u5230\u3002\u7531\u4e8e\u8f83\u9ad8\u7684\u7ef4\u5ea6\u4e5f\u4f1a\u6d89\u53ca\u8f83\u9ad8\u6570\u91cf\u7684\u53c2\u6570\uff0c\u56e0\u6b64\u8fd9\u4e9b\u89c2\u5bdf\u7ed3\u679c\u4e0e\u524d\u56fe\u76f8\u4e00\u81f4\u3002<\/p>\n

        \u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u57fa\u4e8e GNN \u5c42\u6570\u7684\u6027\u80fd\u5206\u5e03\u60c5\u51b5\u3002<\/p>\n

        \"image-20230915160209921\"<\/p>\n

        \u5728\u56fe\u8868\u4e2d\uff0c\u663e\u793a\u4e86\u5c42\u6570\u4e0e\u6a21\u578b\u6027\u80fd\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u4ee5\u53ca\u6a21\u578b\u6027\u80fd\u4e0e\u53c2\u6570\u6570\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\u3002\u6bcf\u4e2a\u70b9\u7684\u989c\u8272\u4ee3\u8868\u4e86\u5c42\u6570\u3002\u5c06\u9f20\u6807\u60ac\u505c\u5728\u4e00\u4e2a\u70b9\u4e0a\u4ee5\u67e5\u770bGNN\u67b6\u6784\u53c2\u6570\u3002<\/em><\/p>\n

        \u7bb1\u7ebf\u56fe\u663e\u793a\u4e86\u7c7b\u4f3c\u7684\u8d8b\u52bf\uff0c\u968f\u7740\u5c42\u6570\u7684\u589e\u52a0\uff0c\u5e73\u5747\u6027\u80fd\u5f80\u5f80\u4f1a\u63d0\u9ad8\uff0c\u4f46\u8868\u73b0\u6700\u597d\u7684\u6a21\u578b\u5e76\u4e0d\u5177\u6709\u4e09\u5c42\u6216\u56db\u5c42\uff0c\u800c\u662f\u4e24\u5c42\u3002\u6b64\u5916\uff0c\u6027\u80fd\u7684\u4e0b\u754c\u968f\u7740\u56db\u5c42\u800c\u964d\u4f4e\u3002\u8fd9\u79cd\u6548\u5e94\u4e4b\u524d\u5df2\u7ecf\u88ab\u89c2\u5bdf\u5230\u8fc7\uff0c\u5177\u6709\u66f4\u591a\u5c42\u6b21\u7684GNN\u5c06\u5728\u66f4\u8fdc\u7684\u8ddd\u79bb\u4e0a\u5e7f\u64ad\u4fe1\u606f\uff0c\u5e76\u4e14\u53ef\u80fd\u4f1a\u5192\u7740\u8282\u70b9\u8868\u793a\u5728\u8bb8\u591a\u8fde\u7eed\u8fed\u4ee3\u4e2d\u88ab\u201c\u7a00\u91ca\u201d\u7684\u98ce\u9669\u3002<\/p>\n

        \u6211\u4eec\u7684\u6570\u636e\u96c6\u662f\u5426\u6709\u9996\u9009\u7684\u805a\u5408\u64cd\u4f5c\uff1f\u4e0b\u56fe\u5c06\u6027\u80fd\u6309\u805a\u5408\u7c7b\u578b\u8fdb\u884c\u4e86\u5206\u89e3\u3002<\/p>\n

        \"image-20230915160345404\"<\/p>\n

        \u5728\u8fd9\u5e45\u56fe\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u5728\u8fd9\u4e2a\u4efb\u52a1\u4e2d\uff0cmax\u6c60\u5316\u4f3c\u4e4e\u7a0d\u5fae\u4f18\u4e8e\u5176\u4ed6\u4e24\u79cd\u6c60\u5316\u65b9\u5f0f\u3002\u7136\u800c\uff0c\u8fd9\u4e5f\u53d6\u51b3\u4e8e\u5177\u4f53\u7684\u6570\u636e\u96c6\u548c\u4efb\u52a1\uff0c\u4e0d\u540c\u7684\u60c5\u51b5\u4e0b\u53ef\u80fd\u4f1a\u6709\u4e0d\u540c\u7684\u7ed3\u679c\u3002\u53e6\u5916\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u770b\u4e00\u4e0b\u5173\u4e8e\u6d88\u606f\u4f20\u9012\u7684\u4e0d\u540c\u98ce\u683c\u5bf9\u6a21\u578b\u6027\u80fd\u7684\u5f71\u54cd\u3002<\/em><\/p>\n

        \u5728\u8fd9\u4e2a\u56fe\u8868\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u5728\u8fd9\u4e2a\u4efb\u52a1\u4e2d\uff0c\u6ca1\u6709\u6d88\u606f\u4f20\u9012\u7684\u6a21\u578b\uff08\u201cnone\u201d\uff09\u6027\u80fd\u76f8\u5bf9\u8f83\u5dee\uff0c\u800c\u540c\u65f6\u4f20\u9012\u4fe1\u606f\u7ed9\u8282\u70b9\u3001\u8fb9\u548c\u5168\u5c40\u5c5e\u6027\u7684\u6a21\u578b\u5728\u5e73\u5747\u6027\u80fd\u4e0a\u66f4\u4e3a\u4f18\u8d8a\u3002<\/p>\n

        \u603b\u7684\u6765\u8bf4\uff0c\u901a\u8fc7\u8fd9\u4e9b\u63a2\u7d22\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u4e86\u4e00\u4e9b\u6a21\u578b\u8bbe\u8ba1\u7684\u4e00\u822c\u8d8b\u52bf\uff0c\u4f46\u4e5f\u53d1\u73b0\u4e86\u4e00\u4e9b\u76f8\u53cd\u7684\u4f8b\u5b50\u3002\u8fd9\u518d\u6b21\u5f3a\u8c03\u4e86\u6a21\u578b\u8bbe\u8ba1\u7684\u590d\u6742\u6027\uff0c\u4e0d\u540c\u7684\u56e0\u7d20\u53ef\u80fd\u4f1a\u5728\u4e0d\u540c\u7684\u60c5\u51b5\u4e0b\u4ea7\u751f\u4e0d\u540c\u7684\u5f71\u54cd\u3002<\/p>\n

        \"image-20230915160452209\"<\/p>\n

        \u8fd9\u5f20\u56fe\u8868\u5c55\u793a\u4e86\u57fa\u4e8e\u6d88\u606f\u4f20\u9012\u98ce\u683c\u7684\u6027\u80fd\u5bf9\u6bd4\uff0c\u540c\u65f6\u4e5f\u5305\u62ec\u4e86\u6a21\u578b\u6027\u80fd\u4e0e\u53ef\u8bad\u7ec3\u53c2\u6570\u6570\u91cf\u7684\u6563\u70b9\u56fe\u3002\u6bcf\u4e2a\u70b9\u7684\u989c\u8272\u8868\u793a\u4e86\u6d88\u606f\u4f20\u9012\u7684\u65b9\u5f0f\u3002\u5c06\u9f20\u6807\u60ac\u505c\u5728\u70b9\u4e0a\u53ef\u4ee5\u67e5\u770bGNN\u67b6\u6784\u7684\u53c2\u6570\u3002<\/em><\/p>\n

        \u603b\u4f53\u800c\u8a00\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\uff0c\u4e0e\u56fe\u5c5e\u6027\u95f4\u7684\u4ea4\u6d41\u8d8a\u591a\uff0c\u5e73\u5747\u6a21\u578b\u7684\u6027\u80fd\u8d8a\u597d\u3002\u6211\u4eec\u7684\u4efb\u52a1\u96c6\u4e2d\u5728\u5168\u5c40\u8868\u793a\u4e0a\uff0c\u56e0\u6b64\u660e\u786e\u5730\u5b66\u4e60\u8fd9\u4e2a\u5c5e\u6027\u4e5f\u5f80\u5f80\u4f1a\u63d0\u9ad8\u6027\u80fd\u3002\u6211\u4eec\u8fd8\u53d1\u73b0\u8282\u70b9\u8868\u793a\u6bd4\u8fb9\u8868\u793a\u66f4\u6709\u7528\uff0c\u8fd9\u4e5f\u5f88\u5408\u7406\uff0c\u56e0\u4e3a\u8282\u70b9\u5c5e\u6027\u4e2d\u52a0\u8f7d\u4e86\u66f4\u591a\u4fe1\u606f\u3002<\/p>\n

        \u4ece\u8fd9\u91cc\u53ef\u4ee5\u671d\u7740\u4e24\u4e2a\u4e00\u822c\u65b9\u5411\u53bb\u8ffd\u6c42\u66f4\u597d\u7684\u6027\u80fd\u3002\u4e00\u4e2a\u4e0e\u66f4\u590d\u6742\u7684\u56fe\u7b97\u6cd5\u76f8\u5173\uff0c\u53e6\u4e00\u4e2a\u4e0e\u56fe\u672c\u8eab\u76f8\u5173\u3002<\/p>\n

        \u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u6211\u4eec\u7684GNN\u57fa\u4e8e\u4e00\u4e2a\u57fa\u4e8e\u90bb\u57df\u7684\u6c47\u805a\u64cd\u4f5c\u3002\u6709\u4e00\u4e9b\u56fe\u7684\u6982\u5ff5\u5728\u8fd9\u79cd\u65b9\u5f0f\u4e0b\u66f4\u96be\u4ee5\u8868\u8fbe\uff0c\u4f8b\u5982\u7ebf\u6027\u56fe\u8def\u5f84\uff08\u7531\u8282\u70b9\u6784\u6210\u7684\u8fde\u901a\u94fe\uff09\u3002\u8bbe\u8ba1\u4e00\u79cd\u65b0\u7684\u673a\u5236\uff0c\u53ef\u4ee5\u5728GNN\u4e2d\u63d0\u53d6\u3001\u6267\u884c\u548c\u4f20\u64ad\u56fe\u4fe1\u606f\uff0c\u662f\u5f53\u524d\u7684\u7814\u7a76\u65b9\u5411\u4e4b\u4e00\u3002<\/p>\n

        GNN\u7814\u7a76\u7684\u524d\u6cbf\u4e4b\u4e00\u4e0d\u662f\u521b\u5efa\u65b0\u7684\u6a21\u578b\u548c\u67b6\u6784\uff0c\u800c\u662f\u201c\u5982\u4f55\u6784\u5efa\u56fe\u201d\uff0c\u66f4\u786e\u5207\u5730\u8bf4\uff0c\u662f\u8d4b\u4e88\u56fe\u9644\u52a0\u7684\u7ed3\u6784\u6216\u5173\u7cfb\uff0c\u4ee5\u4fbf\u5229\u7528\u3002\u6b63\u5982\u6211\u4eec\u6240\u770b\u5230\u7684\uff0c\u4e0e\u56fe\u5c5e\u6027\u95f4\u7684\u4ea4\u6d41\u8d8a\u591a\uff0c\u6211\u4eec\u5f80\u5f80\u4f1a\u6709\u66f4\u597d\u7684\u6a21\u578b\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u53ef\u4ee5\u8003\u8651\u4f7f\u5206\u5b50\u56fe\u66f4\u52a0\u4e30\u5bcc\uff0c\u65b9\u6cd5\u662f\u5728\u8282\u70b9\u4e4b\u95f4\u6dfb\u52a0\u989d\u5916\u7684\u7a7a\u95f4\u5173\u7cfb\uff0c\u6dfb\u52a0\u975e\u952e\u7684\u8fb9\uff0c\u6216\u5728\u5b50\u56fe\u4e4b\u95f4\u6dfb\u52a0\u663e\u5f0f\u53ef\u5b66\u4e60\u7684\u5173\u7cfb\u3002<\/p>\n

        \u8fdb\u4e00\u6b65\u6df1\u5165<\/h2>\n

        \u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u6709\u4e00\u4e9b\u5173\u4e8e\u4e0eGNN\u76f8\u5173\u7684\u5404\u79cd\u56fe\u5f62\u76f8\u5173\u4e3b\u9898\u7684\u7ae0\u8282\u3002<\/p>\n

        \u5176\u4ed6\u7c7b\u578b\u7684\u56fe\uff08\u591a\u91cd\u56fe\uff0c\u8d85\u56fe\uff0c\u8d85\u8282\u70b9\uff0c\u5206\u5c42\u56fe\uff09<\/h3>\n

        \u867d\u7136\u6211\u4eec\u53ea\u63cf\u8ff0\u4e86\u6bcf\u4e2a\u5c5e\u6027\u5177\u6709\u77e2\u91cf\u5316\u4fe1\u606f\u7684\u56fe\uff0c\u4f46\u56fe\u7ed3\u6784\u66f4\u52a0\u7075\u6d3b\uff0c\u53ef\u4ee5\u5bb9\u7eb3\u5176\u4ed6\u7c7b\u578b\u7684\u4fe1\u606f\u3002\u5e78\u8fd0\u7684\u662f\uff0c\u6d88\u606f\u4f20\u9012\u6846\u67b6\u8db3\u591f\u7075\u6d3b\uff0c\u901a\u5e38\u5c06GNNs\u9002\u5e94\u66f4\u590d\u6742\u7684\u56fe\u7ed3\u6784\u662f\u901a\u8fc7\u5b9a\u4e49\u5982\u4f55\u4f20\u9012\u548c\u66f4\u65b0\u65b0\u7684\u56fe\u5c5e\u6027\u6765\u5b9e\u73b0\u7684\u3002<\/p>\n

        \u4f8b\u5982\uff0c\u6211\u4eec\u53ef\u4ee5\u8003\u8651\u591a\u8fb9\u56fe\u6216\u591a\u91cd\u56fe\uff0c\u5176\u4e2d\u4e00\u5bf9\u8282\u70b9\u53ef\u4ee5\u5171\u4eab\u591a\u79cd\u7c7b\u578b\u7684\u8fb9\uff0c\u5f53\u6211\u4eec\u5e0c\u671b\u57fa\u4e8e\u5176\u7c7b\u578b\u6765\u5efa\u6a21\u8282\u70b9\u4e4b\u95f4\u7684\u4ea4\u4e92\u65f6\uff0c\u5c31\u4f1a\u53d1\u751f\u8fd9\u79cd\u60c5\u51b5\u3002\u4f8b\u5982\uff0c\u5728\u793e\u4ea4\u7f51\u7edc\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u5173\u7cfb\u7c7b\u578b\uff08\u719f\u4eba\uff0c\u670b\u53cb\uff0c\u5bb6\u4eba\uff09\u6307\u5b9a\u8fb9\u7f18\u7c7b\u578b\u3002\u53ef\u4ee5\u901a\u8fc7\u4e3a\u6bcf\u79cd\u8fb9\u7f18\u7c7b\u578b\u8bbe\u7f6e\u4e0d\u540c\u7c7b\u578b\u7684\u6d88\u606f\u4f20\u9012\u6b65\u9aa4\u6765\u8c03\u6574GNN\u3002\u6211\u4eec\u8fd8\u53ef\u4ee5\u8003\u8651\u5d4c\u5957\u56fe\uff0c\u4f8b\u5982\u4e00\u4e2a\u8282\u70b9\u4ee3\u8868\u4e00\u4e2a\u56fe\uff0c\u4e5f\u79f0\u4e3a\u8d85\u8282\u70b9\u56fe\u3002\u5d4c\u5957\u56fe\u5bf9\u4e8e\u8868\u793a\u5206\u5c42\u4fe1\u606f\u975e\u5e38\u6709\u7528\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u53ef\u4ee5\u8003\u8651\u4e00\u4e2a\u5206\u5b50\u7f51\u7edc\uff0c\u5176\u4e2d\u4e00\u4e2a\u8282\u70b9\u8868\u793a\u4e00\u4e2a\u5206\u5b50\uff0c\u5982\u679c\u6211\u4eec\u6709\u4e00\u79cd\u65b9\u6cd5\uff08\u53cd\u5e94\uff09\u5c06\u4e00\u4e2a\u5206\u5b50\u8f6c\u5316\u4e3a\u53e6\u4e00\u4e2a\u5206\u5b50\uff0c\u90a3\u4e48\u5b83\u4eec\u4e4b\u95f4\u5c31\u5171\u4eab\u4e00\u4e2a\u8fb9\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u8bad\u7ec3\u671f\u95f4\u5728\u5206\u5b50\u7ea7\u522b\u548c\u53cd\u5e94\u7f51\u7edc\u7ea7\u522b\u4e4b\u95f4\u5b66\u4e60\u8868\u793a\u7684GNN\u6765\u5728\u5d4c\u5957\u56fe\u4e0a\u5b66\u4e60\u3002<\/p>\n

        \u53e6\u4e00\u79cd\u7c7b\u578b\u7684\u56fe\u662f\u8d85\u56fe\uff0c\u5176\u4e2d\u4e00\u4e2a\u8fb9\u53ef\u4ee5\u8fde\u63a5\u5230\u591a\u4e2a\u8282\u70b9\uff0c\u800c\u4e0d\u4ec5\u4ec5\u662f\u4e24\u4e2a\u3002\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u56fe\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u8bc6\u522b\u8282\u70b9\u7684\u793e\u533a\u5e76\u5206\u914d\u4e0e\u793e\u533a\u4e2d\u6240\u6709\u8282\u70b9\u8fde\u63a5\u7684\u8d85\u8fb9\u6765\u6784\u5efa\u8d85\u56fe\u3002<\/p>\n

        \"image-20230915160802859\"<\/p>\n

        \u66f4\u590d\u6742\u56fe\u5f62\u7684\u793a\u610f\u56fe\u3002\u5de6\u4fa7\u662f\u4e00\u4e2a\u5177\u6709\u4e09\u79cd\u8fb9\u7c7b\u578b\u7684\u591a\u91cd\u56fe\u793a\u4f8b\uff0c\u5305\u62ec\u4e00\u4e2a\u6709\u5411\u8fb9\u3002\u53f3\u4fa7\u662f\u4e00\u4e2a\u4e09\u5c42\u6b21\u7684\u5206\u5c42\u56fe\uff0c\u4e2d\u95f4\u5c42\u8282\u70b9\u662f\u8d85\u8282\u70b9\u3002<\/em><\/p>\n

        \u5982\u4f55\u8bad\u7ec3\u548c\u8bbe\u8ba1\u5177\u6709\u591a\u79cd\u56fe\u5c5e\u6027\u7684GNN\u662f\u5f53\u524d\u7684\u7814\u7a76\u65b9\u5411\u3002<\/p>\n

        \u5728GNNs\u4e2d\u62bd\u6837\u56fe\u5f62\u548c\u6279\u5904\u7406<\/h3>\n

        \u8bad\u7ec3\u795e\u7ecf\u7f51\u7edc\u7684\u4e00\u79cd\u5e38\u89c1\u65b9\u6cd5\u662f\u4f7f\u7528\u5728\u8bad\u7ec3\u6570\u636e\u7684\u968f\u673a\u5e38\u91cf\u5927\u5c0f\u5b50\u96c6\uff08\u5c0f\u6279\u91cf\uff09\u4e0a\u8ba1\u7b97\u7684\u68af\u5ea6\u6765\u66f4\u65b0\u7f51\u7edc\u53c2\u6570\u3002\u7531\u4e8e\u56fe\u4e2d\u8282\u70b9\u548c\u8fb9\u7684\u6570\u91cf\u76f8\u90bb\u7684\u8282\u70b9\u548c\u8fb9\u4e4b\u95f4\u7684\u53d8\u5316\u5f88\u5927\uff0c\u56e0\u6b64\u8fd9\u79cd\u505a\u6cd5\u5bf9\u4e8e\u56fe\u5f62\u6784\u6210\u4e86\u6311\u6218\uff0c\u65e0\u6cd5\u4f7f\u7528\u5e38\u91cf\u6279\u91cf\u5927\u5c0f\u3002\u5173\u4e8e\u56fe\u5f62\u6279\u5904\u7406\u7684\u4e3b\u8981\u601d\u60f3\u662f\u521b\u5efa\u4fdd\u7559\u8f83\u5927\u56fe\u5f62\u7684\u57fa\u672c\u5c5e\u6027\u7684\u5b50\u56fe\u3002\u8fd9\u79cd\u56fe\u5f62\u62bd\u6837\u64cd\u4f5c\u9ad8\u5ea6\u4f9d\u8d56\u4e8e\u4e0a\u4e0b\u6587\uff0c\u5e76\u6d89\u53ca\u4ece\u56fe\u5f62\u4e2d\u9009\u62e9\u8282\u70b9\u548c\u8fb9\u3002\u8fd9\u4e9b\u64cd\u4f5c\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\u53ef\u80fd\u662f\u6709\u610f\u4e49\u7684\uff08\u5f15\u7528\u7f51\u7edc\uff09\uff0c\u800c\u5728\u5176\u4ed6\u60c5\u51b5\u4e0b\uff0c\u8fd9\u4e9b\u64cd\u4f5c\u53ef\u80fd\u4f1a\u8fc7\u4e8e\u5f3a\u5927\uff08\u5206\u5b50\uff0c\u5176\u4e2d\u4e00\u4e2a\u5b50\u56fe\u4ec5\u8868\u793a\u4e00\u4e2a\u65b0\u7684\u3001\u8f83\u5c0f\u7684\u5206\u5b50\uff09\u3002\u5982\u4f55\u5bf9\u56fe\u8fdb\u884c\u62bd\u6837\u662f\u4e00\u4e2a\u5c1a\u672a\u89e3\u51b3\u7684\u7814\u7a76\u95ee\u9898\u3002\u5982\u679c\u6211\u4eec\u5173\u5fc3\u4fdd\u7559\u90bb\u57df\u7ea7\u522b\u7684\u7ed3\u6784\uff0c\u4e00\u79cd\u65b9\u6cd5\u662f\u968f\u673a\u62bd\u6837\u4e00\u4e2a\u5747\u5300\u6570\u91cf\u7684\u8282\u70b9\uff0c\u6784\u6210\u8282\u70b9\u96c6\u5408\u3002\u7136\u540e\u6dfb\u52a0\u8ddd\u79bbk\u7684\u90bb\u63a5\u8282\u70b9\uff0c\u5305\u62ec\u5b83\u4eec\u7684\u8fb9\u3002\u6bcf\u4e2a\u90bb\u57df\u53ef\u4ee5\u89c6\u4e3a\u4e00\u4e2a\u5355\u72ec\u7684\u56fe\uff0c\u5e76\u4e14\u53ef\u4ee5\u5728\u8fd9\u4e9b\u5b50\u56fe\u7684\u6279\u6b21\u4e0a\u5bf9GNN\u8fdb\u884c\u8bad\u7ec3\u3002\u635f\u5931\u53ef\u4ee5\u88ab\u906e\u853d\uff0c\u53ea\u8003\u8651\u8282\u70b9\u96c6\u5408\uff0c\u56e0\u4e3a\u6240\u6709\u76f8\u90bb\u8282\u70b9\u90fd\u5177\u6709\u4e0d\u5b8c\u6574\u7684\u90bb\u57df\u3002\u66f4\u9ad8\u6548\u7684\u7b56\u7565\u53ef\u80fd\u662f\u9996\u5148\u968f\u673a\u62bd\u6837\u4e00\u4e2a\u5355\u4e00\u8282\u70b9\uff0c\u6269\u5c55\u5176\u90bb\u57df\u5230\u8ddd\u79bbk\uff0c\u7136\u540e\u4ece\u6269\u5c55\u96c6\u4e2d\u9009\u62e9\u53e6\u4e00\u4e2a\u8282\u70b9\u3002\u8fd9\u4e9b\u64cd\u4f5c\u53ef\u4ee5\u5728\u6784\u5efa\u4e00\u5b9a\u6570\u91cf\u7684\u8282\u70b9\u3001\u8fb9\u6216\u5b50\u56fe\u540e\u7ec8\u6b62\u3002\u5982\u679c\u4e0a\u4e0b\u6587\u5141\u8bb8\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u9009\u62e9\u521d\u59cb\u8282\u70b9\u96c6\uff0c\u7136\u540e\u901a\u8fc7\u968f\u673a\u3001\u968f\u673a\u6e38\u8d70\u6216Metropolis\u7b97\u6cd5\u7b49\u65b9\u5f0f\u5bf9\u4e00\u5b9a\u6570\u91cf\u7684\u8282\u70b9\u8fdb\u884c\u5b50\u62bd\u6837\u6765\u6784\u5efa\u5177\u6709\u6052\u5b9a\u5927\u5c0f\u90bb\u57df\u7684\u5b50\u56fe\u3002<\/p>\n

        \"image-20230915161048234\"<\/p>\n

        \u8fd9\u91cc\u5c55\u793a\u4e86\u5bf9\u540c\u4e00\u56fe\u8fdb\u884c\u62bd\u6837\u7684\u56db\u79cd\u4e0d\u540c\u65b9\u5f0f\u3002\u62bd\u6837\u7b56\u7565\u7684\u9009\u62e9\u9ad8\u5ea6\u4f9d\u8d56\u4e8e\u4e0a\u4e0b\u6587\uff0c\u56e0\u4e3a\u5b83\u4eec\u4f1a\u751f\u6210\u4e0d\u540c\u7684\u56fe\u7edf\u8ba1\u6570\u636e\u5206\u5e03\uff08\u8282\u70b9\u6570\u91cf\u3001\u8fb9\u6570\u91cf\u7b49\uff09\u3002\u5bf9\u4e8e\u9ad8\u5ea6\u8fde\u63a5\u7684\u56fe\uff0c\u4e5f\u53ef\u4ee5\u5bf9\u8fb9\u8fdb\u884c\u5b50\u62bd\u6837\u3002<\/em><\/p>\n

        \u5bf9\u4e8e\u65e0\u6cd5\u5b8c\u5168\u52a0\u8f7d\u5230\u5185\u5b58\u7684\u5927\u578b\u56fe\uff0c\u8fdb\u884c\u56fe\u62bd\u6837\u5c24\u5176\u91cd\u8981\u3002\u8fd9\u79cd\u60c5\u51b5\u5df2\u7ecf\u542f\u53d1\u4e86\u65b0\u7684\u67b6\u6784\u548c\u8bad\u7ec3\u7b56\u7565\uff0c\u6bd4\u5982Cluster-GCN\u548cGraphSaint\u3002\u6211\u4eec\u9884\u8ba1\u672a\u6765\u56fe\u6570\u636e\u96c6\u7684\u89c4\u6a21\u5c06\u7ee7\u7eed\u589e\u957f\u3002<\/p>\n

        \u5f52\u7eb3\u504f\u5dee<\/h3>\n

        \u5728\u6784\u5efa\u7528\u4e8e\u89e3\u51b3\u7279\u5b9a\u7c7b\u578b\u6570\u636e\u95ee\u9898\u7684\u6a21\u578b\u65f6\uff0c\u6211\u4eec\u5e0c\u671b\u4e13\u95e8\u9488\u5bf9\u8be5\u6570\u636e\u7684\u7279\u6027\u8fdb\u884c\u6a21\u578b\u5b9a\u5236\u3002\u6210\u529f\u5b9e\u73b0\u8fd9\u4e00\u70b9\u65f6\uff0c\u901a\u5e38\u4f1a\u770b\u5230\u66f4\u597d\u7684\u9884\u6d4b\u6027\u80fd\u3001\u66f4\u77ed\u7684\u8bad\u7ec3\u65f6\u95f4\u3001\u66f4\u5c11\u7684\u53c2\u6570\u4ee5\u53ca\u66f4\u597d\u7684\u6cdb\u5316\u6027\u80fd\u3002<\/p>\n

        \u4e3e\u4e2a\u4f8b\u5b50\uff0c\u5f53\u5728\u56fe\u50cf\u4e0a\u6807\u8bb0\u65f6\uff0c\u6211\u4eec\u5e0c\u671b\u5229\u7528\u8fd9\u6837\u4e00\u4e2a\u4e8b\u5b9e\uff0c\u5373\u65e0\u8bba\u4e00\u53ea\u72d7\u51fa\u73b0\u5728\u56fe\u50cf\u7684\u5de6\u4e0a\u89d2\u8fd8\u662f\u53f3\u4e0b\u89d2\uff0c\u5b83\u4ecd\u7136\u662f\u4e00\u53ea\u72d7\u3002\u56e0\u6b64\uff0c\u5927\u591a\u6570\u56fe\u50cf\u6a21\u578b\u4f7f\u7528\u5377\u79ef\uff0c\u5b83\u4eec\u5177\u6709\u5e73\u79fb\u4e0d\u53d8\u6027\u3002\u5bf9\u4e8e\u6587\u672c\u6765\u8bf4\uff0c\u6807\u8bb0\u7684\u987a\u5e8f\u975e\u5e38\u91cd\u8981\uff0c\u56e0\u6b64\u5faa\u73af\u795e\u7ecf\u7f51\u7edc\u4f1a\u6309\u987a\u5e8f\u5904\u7406\u6570\u636e\u3002\u6b64\u5916\uff0c\u4e00\u4e2a\u6807\u8bb0\u7684\u5b58\u5728\uff08\u4f8b\u5982\u5355\u8bcd\u201cnot\u201d\uff09\u53ef\u4ee5\u5f71\u54cd\u53e5\u5b50\u5176\u4f59\u90e8\u5206\u7684\u542b\u4e49\uff0c\u56e0\u6b64\u6211\u4eec\u9700\u8981\u7ec4\u4ef6\u80fd\u591f\u201c\u5173\u6ce8\u201d\u6587\u672c\u7684\u5176\u4ed6\u90e8\u5206\uff0c\u800c\u50cfBERT\u548cGPT-3\u8fd9\u6837\u7684\u53d8\u6362\u5668\u6a21\u578b\u53ef\u4ee5\u505a\u5230\u8fd9\u4e00\u70b9\u3002\u8fd9\u4e9b\u90fd\u662f\u5f52\u7eb3\u504f\u5dee\u7684\u4e00\u4e9b\u4f8b\u5b50\uff0c\u6211\u4eec\u5728\u6570\u636e\u4e2d\u8bc6\u522b\u5bf9\u79f0\u6027\u6216\u89c4\u5f8b\uff0c\u5e76\u6dfb\u52a0\u5229\u7528\u8fd9\u4e9b\u7279\u6027\u7684\u5efa\u6a21\u7ec4\u4ef6\u3002<\/p>\n

        \u5728\u5904\u7406\u56fe\u65f6\uff0c\u6211\u4eec\u5173\u5fc3\u6bcf\u4e2a\u56fe\u7ec4\u4ef6\uff08\u8fb9\u3001\u8282\u70b9\u3001\u5168\u5c40\uff09\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u56e0\u6b64\u6211\u4eec\u5bfb\u6c42\u5177\u6709\u5173\u7cfb\u5f52\u7eb3\u504f\u5dee\u7684\u6a21\u578b\u3002\u6a21\u578b\u5e94\u8be5\u4fdd\u7559\u5b9e\u4f53\u4e4b\u95f4\u7684\u663e\u5f0f\u5173\u7cfb\uff08\u90bb\u63a5\u77e9\u9635\uff09\uff0c\u5e76\u4fdd\u7559\u56fe\u7684\u5bf9\u79f0\u6027\uff08\u7f6e\u6362\u4e0d\u53d8\u6027\uff09\u3002\u6211\u4eec\u671f\u671b\u90a3\u4e9b\u5b9e\u4f53\u4e4b\u95f4\u7684\u4ea4\u4e92\u5f88\u91cd\u8981\u7684\u95ee\u9898\u5c06\u4ece\u56fe\u7ed3\u6784\u4e2d\u53d7\u76ca\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u8fd9\u610f\u5473\u7740\u8bbe\u8ba1\u5bf9\u96c6\u5408\u7684\u8f6c\u6362\uff1a\u5bf9\u8282\u70b9\u6216\u8fb9\u7684\u64cd\u4f5c\u987a\u5e8f\u4e0d\u5e94\u8be5\u91cd\u8981\uff0c\u800c\u4e14\u64cd\u4f5c\u5e94\u8be5\u9002\u7528\u4e8e\u53ef\u53d8\u6570\u91cf\u7684\u8f93\u5165\u3002<\/p>\n

        \u6bd4\u8f83\u805a\u5408\u64cd\u4f5c<\/h3>\n

        \u4ece\u76f8\u90bb\u8282\u70b9\u548c\u8fb9\u4e2d\u6c47\u603b\u4fe1\u606f\u662f\u4efb\u4f55\u5408\u7406\u5f3a\u5927\u7684GNN\u67b6\u6784\u4e2d\u7684\u5173\u952e\u6b65\u9aa4\u3002\u7531\u4e8e\u6bcf\u4e2a\u8282\u70b9\u5177\u6709\u53ef\u53d8\u6570\u91cf\u7684\u90bb\u5c45\uff0c\u5e76\u4e14\u56e0\u4e3a\u6211\u4eec\u5e0c\u671b\u4f7f\u7528\u4e00\u4e2a\u53ef\u5fae\u5206\u7684\u65b9\u6cd5\u6765\u805a\u5408\u8fd9\u4e9b\u4fe1\u606f\uff0c\u6211\u4eec\u5e0c\u671b\u4f7f\u7528\u4e00\u79cd\u5e73\u6ed1\u7684\u805a\u5408\u64cd\u4f5c\uff0c\u5b83\u5bf9\u8282\u70b9\u987a\u5e8f\u548c\u63d0\u4f9b\u7684\u8282\u70b9\u6570\u91cf\u4e0d\u53d8\u3002<\/p>\n

        \u9009\u62e9\u548c\u8bbe\u8ba1\u6700\u4f18\u805a\u5408\u64cd\u4f5c\u662f\u4e00\u4e2a\u5f00\u653e\u7684\u7814\u7a76\u8bfe\u9898\u3002\u805a\u5408\u64cd\u4f5c\u7684\u4e00\u4e2a\u7406\u60f3\u5c5e\u6027\u662f\u76f8\u4f3c\u7684\u8f93\u5165\u4f1a\u4ea7\u751f\u76f8\u4f3c\u7684\u805a\u5408\u8f93\u51fa\uff0c\u53cd\u4e4b\u4ea6\u7136\u3002\u4e00\u4e9b\u975e\u5e38\u7b80\u5355\u7684\u5019\u9009\u6392\u5217\u4e0d\u53d8\u64cd\u4f5c\u5305\u62ec\u6c42\u548c\u3001\u5747\u503c\u548c\u6700\u5927\u503c\u3002\u7c7b\u4f3c\u65b9\u5dee\u7684\u603b\u7ed3\u7edf\u8ba1\u4fe1\u606f\u4e5f\u53ef\u4ee5\u5de5\u4f5c\u3002\u6240\u6709\u8fd9\u4e9b\u64cd\u4f5c\u90fd\u63a5\u53d7\u53ef\u53d8\u6570\u91cf\u7684\u8f93\u5165\uff0c\u5e76\u63d0\u4f9b\u76f8\u540c\u7684\u8f93\u51fa\uff0c\u65e0\u8bba\u8f93\u5165\u7684\u987a\u5e8f\u5982\u4f55\u3002\u8ba9\u6211\u4eec\u63a2\u8ba8\u4e00\u4e0b\u8fd9\u4e9b\u64cd\u4f5c\u4e4b\u95f4\u7684\u533a\u522b\u3002<\/p>\n

        \"image-20230915161338024\"<\/p>\n

        \u6ca1\u6709\u4e00\u79cd\u6c47\u805a\u7c7b\u578b\u603b\u662f\u80fd\u591f\u533a\u5206\u5de6\u4fa7\u7684\u6700\u5927\u503c\u6c47\u805a\u548c\u53f3\u4fa7\u7684\u6c42\u548c\/\u5747\u503c\u6c47\u805a\u7b49\u56fe\u5bf9\u3002<\/em><\/p>\n

        \u6ca1\u6709\u4e00\u79cd\u64cd\u4f5c\u5728\u6240\u6709\u60c5\u51b5\u4e0b\u90fd\u662f\u6700\u4f73\u9009\u62e9\u3002\u5747\u503c\u64cd\u4f5c\u5728\u8282\u70b9\u90bb\u5c45\u6570\u91cf\u53d8\u5316\u5f88\u5927\u6216\u8005\u9700\u8981\u5bf9\u672c\u5730\u90bb\u57df\u7684\u7279\u5f81\u8fdb\u884c\u5f52\u4e00\u5316\u89c6\u56fe\u65f6\u53ef\u80fd\u5f88\u6709\u7528\u3002\u6700\u5927\u64cd\u4f5c\u5728\u60a8\u60f3\u8981\u7a81\u51fa\u663e\u793a\u672c\u5730\u90bb\u57df\u4e2d\u5355\u4e00\u663e\u8457\u7279\u5f81\u65f6\u53ef\u80fd\u5f88\u6709\u7528\u3002\u6c42\u548c\u5728\u8fd9\u4e24\u8005\u4e4b\u95f4\u63d0\u4f9b\u4e86\u5e73\u8861\uff0c\u5b83\u63d0\u4f9b\u4e86\u672c\u5730\u7279\u5f81\u5206\u5e03\u7684\u5feb\u7167\uff0c\u4f46\u7531\u4e8e\u5b83\u6ca1\u6709\u8fdb\u884c\u5f52\u4e00\u5316\uff0c\u4e5f\u53ef\u80fd\u7a81\u51fa\u663e\u793a\u79bb\u7fa4\u503c\u3002\u5728\u5b9e\u8df5\u4e2d\uff0c\u901a\u5e38\u4f7f\u7528\u6c42\u548c\u3002<\/p>\n

        \u8bbe\u8ba1\u805a\u5408\u64cd\u4f5c\u662f\u4e00\u4e2a\u5f00\u653e\u7684\u7814\u7a76\u95ee\u9898\uff0c\u5b83\u4e0e\u96c6\u5408\u4e0a\u7684\u673a\u5668\u5b66\u4e60\u4ea4\u53c9\u3002\u65b0\u65b9\u6cd5\uff0c\u6bd4\u5982\u4e3b\u8981\u90bb\u57df\u805a\u5408\uff0c\u901a\u8fc7\u5c06\u5b83\u4eec\u4e32\u8054\u8d77\u6765\u5e76\u6dfb\u52a0\u4e00\u4e2a\u4f9d\u8d56\u4e8e\u5f85\u805a\u5408\u5b9e\u4f53\u7684\u8fde\u63a5\u5ea6\u7684\u7f29\u653e\u51fd\u6570\uff0c\u540c\u65f6\u8003\u8651\u4e86\u51e0\u79cd\u805a\u5408\u64cd\u4f5c\u3002\u540c\u65f6\uff0c\u4e5f\u53ef\u4ee5\u8bbe\u8ba1\u7279\u5b9a\u4e8e\u9886\u57df\u7684\u805a\u5408\u64cd\u4f5c\u3002\u4e00\u4e2a\u4f8b\u5b50\u662f\u201c\u56db\u9762\u4f53\u624b\u6027\u201d\u805a\u5408\u8fd0\u7b97\u7b26\u3002<\/p>\n

        \u5c06GCN\u89c6\u4e3a\u5b50\u56fe\u51fd\u6570\u903c\u8fd1\u5668<\/h3>\n

        GCN\uff08\u4ee5\u53caMPNN\uff09\u5728\u5177\u67091\u5ea6\u90bb\u5c45\u67e5\u627e\u7684\u60c5\u51b5\u4e0b\uff0c\u53ef\u4ee5\u770b\u4f5c\u662f\u4e00\u4e2a\u64cd\u4f5c\u5728\u5927\u5c0f\u4e3ak\u7684\u5b50\u56fe\u4e0a\u7684\u5b66\u4e60\u5d4c\u5165\u7684\u795e\u7ecf\u7f51\u7edc\u3002<\/p>\n

        \u5f53\u5173\u6ce8\u4e00\u4e2a\u8282\u70b9\u65f6\uff0c\u5728k\u5c42\u4e4b\u540e\uff0c\u66f4\u65b0\u540e\u7684\u8282\u70b9\u8868\u793a\u5bf9\u6240\u6709\u8ddd\u79bb\u4e3ak\u7684\u90bb\u5c45\u5177\u6709\u6709\u9650\u7684\u89c6\u89d2\uff0c\u672c\u8d28\u4e0a\u662f\u5b50\u56fe\u8868\u793a\u3002\u5bf9\u4e8e\u8fb9\u8868\u793a\u4e5f\u662f\u5982\u6b64\u3002<\/p>\n

        \u56e0\u6b64\uff0cGCN\u6b63\u5728\u6536\u96c6\u6240\u6709\u53ef\u80fd\u7684\u5927\u5c0f\u4e3ak\u7684\u5b50\u56fe\uff0c\u5e76\u4ece\u4e00\u4e2a\u8282\u70b9\u6216\u8fb9\u7684\u89d2\u5ea6\u5b66\u4e60\u5411\u91cf\u8868\u793a\u3002\u53ef\u80fd\u7684\u5b50\u56fe\u6570\u91cf\u53ef\u4ee5\u7ec4\u5408\u5730\u589e\u957f\uff0c\u56e0\u6b64\u4ece\u4e00\u5f00\u59cb\u679a\u4e3e\u8fd9\u4e9b\u5b50\u56fe\u4e0e\u5728GCN\u4e2d\u52a8\u6001\u6784\u5efa\u5b83\u4eec\u53ef\u80fd\u4f1a\u4e0d\u5207\u5b9e\u9645\u3002<\/p>\n

        \"image-20230915161633208\"<\/p>\n

        \u8fb9\u548c\u56fe\u7684\u5bf9\u5076\u5173\u7cfb<\/h3>\n

        \u4e00\u4e2a\u9700\u8981\u6ce8\u610f\u7684\u4e8b\u60c5\u662f\uff0c\u5c3d\u7ba1\u8fb9\u7684\u9884\u6d4b\u548c\u8282\u70b9\u7684\u9884\u6d4b\u770b\u4f3c\u4e0d\u540c\uff0c\u4f46\u901a\u5e38\u53ef\u4ee5\u5f52\u7ed3\u4e3a\u76f8\u540c\u7684\u95ee\u9898\uff1a\u5728\u56fe\ud835\udc3a\u4e0a\u7684\u8fb9\u9884\u6d4b\u4efb\u52a1\u53ef\u4ee5\u8868\u8ff0\u4e3a\u5728\ud835\udc3a\u7684\u5bf9\u5076\u4e0a\u8fdb\u884c\u7684\u8282\u70b9\u7ea7\u522b\u9884\u6d4b\u3002<\/p>\n

        \u8981\u83b7\u5f97\ud835\udc3a\u7684\u5bf9\u5076\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u8282\u70b9\u8f6c\u6362\u4e3a\u8fb9\uff08\u5c06\u8fb9\u8f6c\u6362\u4e3a\u8282\u70b9\uff09\u3002\u4e00\u4e2a\u56fe\u53ca\u5176\u5bf9\u5076\u5305\u542b\u76f8\u540c\u7684\u4fe1\u606f\uff0c\u53ea\u662f\u4ee5\u4e0d\u540c\u7684\u65b9\u5f0f\u8868\u8fbe\u51fa\u6765\u3002\u6709\u65f6\uff0c\u8fd9\u79cd\u6027\u8d28\u4f7f\u5f97\u5728\u4e00\u4e2a\u8868\u793a\u4e2d\u89e3\u51b3\u95ee\u9898\u6bd4\u5728\u53e6\u4e00\u4e2a\u8868\u793a\u4e2d\u66f4\u5bb9\u6613\uff0c\u5c31\u50cf\u5728\u5085\u91cc\u53f6\u7a7a\u95f4\u4e2d\u7684\u9891\u7387\u4e00\u6837\u3002\u7b80\u800c\u8a00\u4e4b\uff0c\u8981\u5728\ud835\udc3a\u4e0a\u89e3\u51b3\u8fb9\u5206\u7c7b\u95ee\u9898\uff0c\u6211\u4eec\u53ef\u4ee5\u8003\u8651\u5728\ud835\udc3a\u7684\u5bf9\u5076\u4e0a\u8fdb\u884c\u56fe\u5377\u79ef\uff08\u8fd9\u4e0e\u5728\ud835\udc3a\u4e0a\u5b66\u4e60\u8fb9\u8868\u793a\u662f\u76f8\u540c\u7684\uff09\uff0c\u8fd9\u4e2a\u60f3\u6cd5\u662f\u7531Dual-Primal\u56fe\u5377\u79ef\u7f51\u7edc\u53d1\u5c55\u800c\u6765\u7684\u3002<\/p>\n

        \u56fe\u5377\u79ef\u4f5c\u4e3a\u77e9\u9635\u4e58\u6cd5\uff0c\u4ee5\u53ca\u77e9\u9635\u4e58\u6cd5\u4f5c\u4e3a\u56fe\u4e0a\u7684\u904d\u5386<\/h3>\n

        \u6211\u4eec\u5df2\u7ecf\u8ba8\u8bba\u4e86\u8bb8\u591a\u5173\u4e8e\u56fe\u5377\u79ef\u548c\u6d88\u606f\u4f20\u9012\u7684\u5185\u5bb9\uff0c\u5f53\u7136\uff0c\u8fd9\u5f15\u53d1\u4e86\u4e00\u4e2a\u5b9e\u9645\u4e0a\u5982\u4f55\u5b9e\u73b0\u8fd9\u4e9b\u64cd\u4f5c\u7684\u95ee\u9898\u3002\u5728\u672c\u8282\u4e2d\uff0c\u6211\u4eec\u5c06\u63a2\u8ba8\u77e9\u9635\u4e58\u6cd5\u3001\u6d88\u606f\u4f20\u9012\u4ee5\u53ca\u5b83\u4eec\u4e0e\u56fe\u904d\u5386\u7684\u8054\u7cfb\u7684\u4e00\u4e9b\u7279\u6027\u3002<\/p>\n

        \u6211\u4eec\u9996\u5148\u8981\u8bf4\u660e\u7684\u4e00\u70b9\u662f\uff0c\u90bb\u63a5\u77e9\u9635 \ud835\udc34<\/code> \uff08\u5927\u5c0f\u4e3a \ud835\udc5b_{\ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52\ud835\udc60}\u00d7\ud835\udc5b_{\ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52\ud835\udc60}<\/code> \uff09\u4e0e\u8282\u70b9\u7279\u5f81\u77e9\u9635 \ud835\udc4b<\/code>\uff08\u5927\u5c0f\u4e3a \ud835\udc5b_{\ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52\ud835\udc60}\u00d7\ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52\ud835\udc60_{dim}<\/code> \uff09\u7684\u77e9\u9635\u4e58\u6cd5\u5b9e\u73b0\u4e86\u4e00\u79cd\u7b80\u5355\u7684\u6d88\u606f\u4f20\u9012\uff0c\u5176\u4e2d\u5305\u62ec\u4e86\u6c42\u548c\u805a\u5408\u3002\u8bbe\u77e9\u9635\u4e3a \ud835\udc35=\ud835\udc34\ud835\udc4b<\/code> \uff0c\u6211\u4eec\u53ef\u4ee5\u89c2\u5bdf\u5230\u4efb\u4f55\u6761\u76ee \ud835\udc35_{\ud835\udc56\ud835\udc57}<\/code> \u90fd\u53ef\u4ee5\u8868\u793a\u4e3a <\ud835\udc34_{\ud835\udc5f\ud835\udc5c\ud835\udc64_\ud835\udc56}\ud835\udc4b_{\ud835\udc50\ud835\udc5c\ud835\udc59\ud835\udc62\ud835\udc5a\ud835\udc5b_\ud835\udc57}>=\ud835\udc34_{\ud835\udc56,1}\ud835\udc4b_{1,\ud835\udc57}+\ud835\udc34_{\ud835\udc56,2}\ud835\udc4b_{2,\ud835\udc57}+\u2026+\ud835\udc34_{\ud835\udc56,\ud835\udc5b}\ud835\udc4b_{\ud835\udc5b,\ud835\udc57}=\\sum_{\ud835\udc34_{\ud835\udc56,\ud835\udc58}>0}\ud835\udc4b_{\ud835\udc58,\ud835\udc57}<\/code> \u3002\u56e0\u4e3a \ud835\udc34_{\ud835\udc56,\ud835\udc58}<\/code> \u53ea\u6709\u5728\u8282\u70b9 \ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52_\ud835\udc56<\/code> \u4e0e\u8282\u70b9 \ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52_\ud835\udc58<\/code> \u4e4b\u95f4\u5b58\u5728\u8fb9\u7684\u60c5\u51b5\u4e0b\u624d\u4e3a\u4e8c\u8fdb\u5236\u6761\u76ee\uff0c\u6240\u4ee5\u5185\u79ef\u5b9e\u9645\u4e0a\u662f\u5728\u201c\u6536\u96c6\u201d\u6240\u6709\u4e0e\u8282\u70b9 \ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52_\ud835\udc56<\/code> \u5171\u4eab\u8fb9\u7684\u7ef4\u5ea6\u4e3a \ud835\udc57<\/code>\u7684\u8282\u70b9\u7279\u5f81\u503c\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u8fd9\u79cd\u6d88\u606f\u4f20\u9012\u5e76\u4e0d\u4f1a\u66f4\u65b0\u8282\u70b9\u7279\u5f81\u7684\u8868\u793a\uff0c\u53ea\u662f\u6c47\u805a\u76f8\u90bb\u8282\u70b9\u7684\u7279\u5f81\u3002\u4f46\u662f\u901a\u8fc7\u5728\u77e9\u9635\u76f8\u4e58\u4e4b\u524d\u6216\u4e4b\u540e\u5c06\ud835\udc4b<\/code> \u901a\u8fc7\u60a8\u559c\u7231\u7684\u53ef\u5fae\u53d8\u6362\uff08\u4f8b\u5982 MLP\uff09\u4f20\u9012\uff0c\u53ef\u4ee5\u8f7b\u677e\u5730\u8fdb\u884c\u9002\u5e94\u3002<\/p>\n

        \u4ece\u8fd9\u4e2a\u89c6\u89d2\u6765\u770b\uff0c\u6211\u4eec\u53ef\u4ee5\u6b23\u8d4f\u5230\u4f7f\u7528\u90bb\u63a5\u8868\u7684\u597d\u5904\u3002\u7531\u4e8e \ud835\udc34<\/code> \u7684\u9884\u671f\u7a00\u758f\u6027\uff0c\u6211\u4eec\u4e0d\u5fc5\u5bf9\u6240\u6709 \ud835\udc34_{\ud835\udc56,\ud835\udc57}<\/code> \u4e3a\u96f6\u7684\u503c\u8fdb\u884c\u6c42\u548c\u3002\u53ea\u8981\u6211\u4eec\u6709\u4e00\u79cd\u57fa\u4e8e\u7d22\u5f15\u6765\u6536\u96c6\u503c\u7684\u64cd\u4f5c\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u53ea\u68c0\u7d22\u6b63\u6761\u76ee\u3002\u6b64\u5916\uff0c\u8fd9\u79cd\u65e0\u9700\u77e9\u9635\u4e58\u6cd5\u7684\u65b9\u6cd5\u4f7f\u6211\u4eec\u6446\u8131\u4e86\u5c06\u6c42\u548c\u4f5c\u4e3a\u805a\u5408\u64cd\u4f5c\u7684\u5fc5\u8981\u6027\u3002<\/p>\n

        \u6211\u4eec\u53ef\u4ee5\u60f3\u8c61\u591a\u6b21\u5e94\u7528\u8fd9\u4e2a\u64cd\u4f5c\u53ef\u4ee5\u8ba9\u6211\u4eec\u5728\u66f4\u5927\u7684\u8ddd\u79bb\u4e0a\u4f20\u64ad\u4fe1\u606f\u3002\u4ece\u8fd9\u4e2a\u610f\u4e49\u4e0a\u8bf4\uff0c\u77e9\u9635\u4e58\u6cd5\u662f\u4e00\u79cd\u5728\u56fe\u4e0a\u904d\u5386\u7684\u5f62\u5f0f\u3002\u5f53\u6211\u4eec\u89c2\u5bdf\u90bb\u63a5\u77e9\u9635\u7684\u5e42 \ud835\udc34^\ud835\udc3e<\/code>\u65f6\uff0c\u8fd9\u79cd\u5173\u7cfb\u4e5f\u662f\u663e\u800c\u6613\u89c1\u7684\u3002\u5982\u679c\u6211\u4eec\u8003\u8651\u77e9\u9635 \ud835\udc34^2<\/code>\uff0c\u90a3\u4e48 \ud835\udc34^2_{\ud835\udc56\ud835\udc57}<\/code> \u5c31\u7edf\u8ba1\u4e86\u4ece\u8282\u70b9 \ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52_\ud835\udc56<\/code> \u5230 \ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52_\ud835\udc57<\/code> \u7684\u957f\u5ea6\u4e3a2\u7684\u6240\u6709\u8def\u5f84\uff0c\u5e76\u4e14\u53ef\u4ee5\u8868\u793a\u4e3a\u5185\u79ef <\ud835\udc34_{\ud835\udc5f\ud835\udc5c\ud835\udc64_\ud835\udc56}\ud835\udc4b_{\ud835\udc50\ud835\udc5c\ud835\udc59\ud835\udc62\ud835\udc5a\ud835\udc5b_\ud835\udc57}>=\ud835\udc34_{\ud835\udc56,1}\ud835\udc4b_{1,\ud835\udc57}+\ud835\udc34_{\ud835\udc56,2}\ud835\udc4b_{2,\ud835\udc57}+\u2026+\ud835\udc34_{\ud835\udc56,\ud835\udc5b}\ud835\udc4b_{\ud835\udc5b,\ud835\udc57}=\\sum_{\ud835\udc34_{\ud835\udc56,\ud835\udc58}>0}\ud835\udc4b_{\ud835\udc58,\ud835\udc57}<\/code>\u3002\u76f4\u89c2\u4e0a\uff0c\u7b2c\u4e00\u4e2a \ud835\udc4e_{\ud835\udc56,1}\ud835\udc4e_{1,\ud835\udc57}<\/code> \u4ec5\u5728\u4e24\u79cd\u60c5\u51b5\u4e0b\u4e3a\u6b63\u503c\uff1a\u5b58\u5728\u8fde\u63a5 \ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52_\ud835\udc56<\/code> \u4e0e \ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52_1<\/code> \u7684\u8fb9\uff0c\u4ee5\u53ca\u5b58\u5728\u8fde\u63a5 \ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52_\ud835\udc56<\/code> \u4e0e \ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52_j<\/code> \u7684\u8fb9\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u8fd9\u4e24\u6761\u8fb9\u5f62\u6210\u4e86\u4e00\u6761\u957f\u5ea6\u4e3a2\u7684\u8def\u5f84\uff0c\u4ece \ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52_\ud835\udc56<\/code> \u5230\ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52_j<\/code>\u7ecf\u8fc7\u4e86 \ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52_1<\/code> \u3002\u7531\u4e8e\u6c42\u548c\uff0c\u6211\u4eec\u5bf9\u6240\u6709\u53ef\u80fd\u7684\u4e2d\u95f4\u8282\u70b9\u8fdb\u884c\u8ba1\u6570\u3002\u5f53\u8003\u8651 \ud835\udc34^3=\ud835\udc34\ud835\udc34^2<\/code>.. \u7b49\u7b49\u76f4\u81f3 \ud835\udc34\ud835\udc58 \u65f6\uff0c\u8fd9\u4e00\u76f4\u89c2\u4e5f\u4f1a\u4fdd\u6301\u3002<\/p>\n

        \u56fe\u6ce8\u610f\u7f51\u7edc<\/h3>\n

        \u53e6\u4e00\u79cd\u5728\u56fe\u5c5e\u6027\u4e4b\u95f4\u4f20\u9012\u4fe1\u606f\u7684\u65b9\u6cd5\u662f\u901a\u8fc7\u6ce8\u610f\u529b\u673a\u5236\u3002\u4f8b\u5982\uff0c\u5f53\u6211\u4eec\u8003\u8651\u8282\u70b9\u53ca\u51761\u5ea6\u76f8\u90bb\u8282\u70b9\u7684\u6c47\u603b\u65f6\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u8003\u8651\u4f7f\u7528\u52a0\u6743\u548c\u3002\u6b64\u65f6\u7684\u6311\u6218\u5728\u4e8e\u4ee5\u4e00\u79cd\u6392\u5217\u4e0d\u53d8\u7684\u65b9\u5f0f\u5173\u8054\u6743\u91cd\u3002\u4e00\u79cd\u65b9\u6cd5\u662f\u8003\u8651\u4e00\u4e2a\u6807\u91cf\u8bc4\u5206\u51fd\u6570\uff0c\u5b83\u57fa\u4e8e\u8282\u70b9\u5bf9 \ud835\udc53(\ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52_\ud835\udc56,\ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52_\ud835\udc57)<\/code>\u5206\u914d\u6743\u91cd\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u8bc4\u5206\u51fd\u6570\u53ef\u4ee5\u89e3\u91ca\u4e3a\u8861\u91cf\u76f8\u90bb\u8282\u70b9\u4e0e\u4e2d\u5fc3\u8282\u70b9\u7684\u5173\u8054\u6027\u7684\u51fd\u6570\u3002\u6743\u91cd\u53ef\u4ee5\u88ab\u5f52\u4e00\u5316\uff0c\u4f8b\u5982\u901a\u8fc7 softmax<\/code> \u51fd\u6570\uff0c\u4ee5\u4fbf\u5c06\u5927\u90e8\u5206\u6743\u91cd\u96c6\u4e2d\u5728\u4e0e\u4efb\u52a1\u76f8\u5173\u7684\u76f8\u90bb\u8282\u70b9\u4e0a\u3002\u8fd9\u4e2a\u6982\u5ff5\u662f\u56fe\u6ce8\u610f\u529b\u7f51\u7edc\uff08Graph Attention Networks\uff0cGAT\uff09 [53] \u548c\u96c6\u5408\u53d8\u6362\u5668\uff08Set Transformers\uff09[54]\u7684\u57fa\u7840\u3002\u7531\u4e8e\u8bc4\u5206\u662f\u5728\u8282\u70b9\u5bf9\u4e0a\u8fdb\u884c\u7684\uff0c\u6392\u5217\u4e0d\u53d8\u6027\u5f97\u4ee5\u4fdd\u6301\u3002\u5e38\u89c1\u7684\u8bc4\u5206\u51fd\u6570\u662f\u5185\u79ef\uff08inner product\uff09\uff0c\u5e76\u4e14\u901a\u5e38\u5728\u8bc4\u5206\u4e4b\u524d\uff0c\u8282\u70b9\u4f1a\u901a\u8fc7\u7ebf\u6027\u6620\u5c04\u8f6c\u5316\u4e3a\u67e5\u8be2\u548c\u952e\u5411\u91cf\uff0c\u4ee5\u589e\u52a0\u8bc4\u5206\u673a\u5236\u7684\u8868\u8fbe\u80fd\u529b\u3002\u6b64\u5916\uff0c\u4e3a\u4e86\u53ef\u89e3\u91ca\u6027\uff0c\u8bc4\u5206\u6743\u91cd\u53ef\u4ee5\u7528\u4f5c\u8861\u91cf\u8fb9\u5bf9\u4efb\u52a1\u7684\u91cd\u8981\u6027\u7684\u6307\u6807\u3002<\/p>\n

        \"image-20230915171146224\"<\/p>\n

        \u5bf9\u4e8e\u4e00\u4e2a\u8282\u70b9\uff0c\u76f8\u5bf9\u4e8e\u5176\u76f8\u90bb\u8282\u70b9\u7684\u6ce8\u610f\u529b\u793a\u610f\u56fe\u3002\u5bf9\u4e8e\u6bcf\u6761\u8fb9\uff0c\u8ba1\u7b97\u4e00\u4e2a\u4ea4\u4e92\u5f97\u5206\uff0c\u5bf9\u5176\u8fdb\u884c\u5f52\u4e00\u5316\uff0c\u5e76\u7528\u4e8e\u52a0\u6743\u8282\u70b9\u5d4c\u5165\u3002<\/em><\/p>\n

        \u6b64\u5916\uff0c\u53ef\u4ee5\u5c06\u53d8\u538b\u5668\u89c6\u4e3a\u5e26\u6709\u6ce8\u610f\u529b\u673a\u5236\u7684GNN\u3002\u4ece\u8fd9\u4e2a\u89d2\u5ea6\u6765\u770b\uff0c\u53d8\u538b\u5668\u5c06\u591a\u4e2a\u5143\u7d20\uff08\u4f8b\u5982\u5b57\u7b26\u6807\u8bb0\uff09\u5efa\u6a21\u4e3a\u4e00\u4e2a\u5168\u8fde\u63a5\u56fe\u4e2d\u7684\u8282\u70b9\uff0c\u5e76\u4e14\u6ce8\u610f\u529b\u673a\u5236\u5c06\u4e3a\u6bcf\u5bf9\u8282\u70b9\u5206\u914d\u8fb9\u5d4c\u5165\uff0c\u8fd9\u4e9b\u8fb9\u5d4c\u5165\u7528\u4e8e\u8ba1\u7b97\u6ce8\u610f\u529b\u6743\u91cd\u3002\u4e24\u8005\u7684\u533a\u522b\u5728\u4e8e\u5b83\u4eec\u5bf9\u5b9e\u4f53\u4e4b\u95f4\u8fde\u63a5\u6a21\u5f0f\u7684\u5047\u8bbe\uff0cGNN \u5047\u5b9a\u7a00\u758f\u8fde\u63a5\u6a21\u5f0f\uff0c\u800c\u53d8\u538b\u5668\u5219\u6a21\u62df\u4e86\u6240\u6709\u8fde\u63a5\u3002<\/p>\n

        \u56fe\u89e3\u91ca\u548c\u5f52\u56e0<\/h3>\n

        \u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u6211\u4eec\u53ef\u80fd\u5173\u5fc3\u6a21\u578b\u7684\u53ef\u89e3\u91ca\u6027\uff0c\u4ee5\u5efa\u7acb\u53ef\u4fe1\u5ea6\u3001\u8c03\u8bd5\u6216\u8fdb\u884c\u79d1\u5b66\u53d1\u73b0\u3002\u6211\u4eec\u5173\u5fc3\u7684\u56fe\u6982\u5ff5\u56e0\u4e0a\u4e0b\u6587\u800c\u5f02\u3002\u4f8b\u5982\uff0c\u5728\u5206\u5b50\u9886\u57df\uff0c\u6211\u4eec\u53ef\u80fd\u5173\u5fc3\u7279\u5b9a\u5b50\u56fe\u7684\u5b58\u5728\u6216\u7f3a\u5931\uff0c\u800c\u5728\u5f15\u6587\u7f51\u7edc\u4e2d\uff0c\u6211\u4eec\u53ef\u80fd\u5173\u5fc3\u6587\u7ae0\u7684\u8fde\u63a5\u7a0b\u5ea6\u3002\u7531\u4e8e\u56fe\u6982\u5ff5\u7684\u591a\u6837\u6027\uff0c\u6709\u8bb8\u591a\u65b9\u6cd5\u53ef\u4ee5\u6784\u5efa\u89e3\u91ca\u3002GNNExplainer \u5c06\u8fd9\u4e2a\u95ee\u9898\u89c6\u4e3a\u63d0\u53d6\u5bf9\u4efb\u52a1\u91cd\u8981\u7684\u6700\u76f8\u5173\u7684\u5b50\u56fe\u3002\u5f52\u56e0\u6280\u672f\u4e3a\u56fe\u7684\u90e8\u5206\u5206\u914d\u4e86\u6392\u540d\u7684\u91cd\u8981\u6027\u503c\uff0c\u8fd9\u4e9b\u90e8\u5206\u4e0e\u4efb\u52a1\u76f8\u5173\u3002\u7531\u4e8e\u53ef\u4ee5\u5408\u6210\u5177\u6709\u73b0\u5b9e\u6027\u548c\u6311\u6218\u6027\u7684\u56fe\u95ee\u9898\uff0c\u56e0\u6b64 GNN \u53ef\u4ee5\u4f5c\u4e3a\u4e00\u4e2a\u4e25\u683c\u4e14\u53ef\u91cd\u590d\u7684\u6d4b\u8bd5\u5e73\u53f0\uff0c\u7528\u4e8e\u8bc4\u4f30\u5f52\u56e0\u6280\u672f\u3002<\/p>\n

        \"image-20230915171329185\"<\/p>\n

        \u56fe\u4e2d\u5c55\u793a\u4e86\u4e00\u4e9b\u56fe\u89e3\u91ca\u6280\u672f\u7684\u793a\u610f\u56fe\u3002\u5f52\u56e0\u6280\u672f\u4e3a\u56fe\u5c5e\u6027\u5206\u914d\u4e86\u6392\u540d\u7684\u503c\u3002\u8fd9\u4e9b\u6392\u540d\u53ef\u4ee5\u7528\u4f5c\u63d0\u53d6\u4e0e\u4efb\u52a1\u76f8\u5173\u7684\u8fde\u63a5\u5b50\u56fe\u7684\u57fa\u7840\u3002<\/em><\/p>\n

        \u751f\u6210\u6a21\u578b<\/h3>\n

        \u9664\u4e86\u5728\u56fe\u4e0a\u5b66\u4e60\u9884\u6d4b\u6a21\u578b\u5916\uff0c\u6211\u4eec\u53ef\u80fd\u8fd8\u5173\u5fc3\u5728\u56fe\u4e0a\u5b66\u4e60\u751f\u6210\u6a21\u578b\u3002\u901a\u8fc7\u751f\u6210\u6a21\u578b\uff0c\u6211\u4eec\u53ef\u4ee5\u4ece\u5b66\u4e60\u5230\u7684\u5206\u5e03\u4e2d\u8fdb\u884c\u91c7\u6837\u6216\u5728\u7ed9\u5b9a\u4e00\u4e2a\u8d77\u59cb\u70b9\u7684\u60c5\u51b5\u4e0b\u751f\u6210\u65b0\u7684\u56fe\u3002\u4e00\u4e2a\u76f8\u5173\u7684\u5e94\u7528\u662f\u5728\u8bbe\u8ba1\u65b0\u836f\u7269\u65f6\uff0c\u9700\u8981\u5177\u6709\u7279\u5b9a\u5c5e\u6027\u7684\u65b0\u5206\u5b50\u56fe\u4f5c\u4e3a\u6cbb\u7597\u75be\u75c5\u7684\u5019\u9009\u8005\u3002<\/p>\n

        \u56fe\u751f\u6210\u6a21\u578b\u7684\u4e00\u4e2a\u5173\u952e\u6311\u6218\u5728\u4e8e\u5efa\u6a21\u56fe\u7684\u62d3\u6251\u7ed3\u6784\uff0c\u5b83\u7684\u5927\u5c0f\u53ef\u80fd\u4f1a\u53d1\u751f\u663e\u8457\u53d8\u5316\uff0c\u5e76\u4e14\u5177\u6709 \ud835\udc41^2_{\ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52\ud835\udc60}<\/code> \u9879\u3002\u4e00\u4e2a\u89e3\u51b3\u65b9\u6848\u662f\u76f4\u63a5\u50cf\u5904\u7406\u56fe\u50cf\u4e00\u6837\u6765\u5bf9\u5f85\u90bb\u63a5\u77e9\u9635\uff0c\u91c7\u7528\u81ea\u52a8\u7f16\u7801\u5668\u6846\u67b6\u3002[60]\u5c06\u5b58\u5728\u6216\u4e0d\u5b58\u5728\u8fb9\u7684\u9884\u6d4b\u89c6\u4e3a\u4e8c\u5143\u5206\u7c7b\u4efb\u52a1\u3002\u53ef\u4ee5\u901a\u8fc7\u4ec5\u9884\u6d4b\u5df2\u77e5\u7684\u8fb9\u4ee5\u53ca\u4e0d\u5b58\u5728\u7684\u90e8\u5206\u8fb9\u6765\u907f\u514d \ud835\udc41^2_{\ud835\udc5b\ud835\udc5c\ud835\udc51\ud835\udc52\ud835\udc60}<\/code> \u9879\u3002\u56fe\u5f62\u53d8\u5206\u81ea\u52a8\u7f16\u7801\u5668 (graphVAE) \u5b66\u4f1a\u4e86\u5bf9\u90bb\u63a5\u77e9\u9635\u4e2d\u7684\u8fde\u63a5\u6027\u548c\u90e8\u5206\u975e\u8fde\u63a5\u6027\u6a21\u5f0f\u8fdb\u884c\u5efa\u6a21\u3002<\/p>\n

        \u53e6\u4e00\u79cd\u65b9\u6cd5\u662f\u901a\u8fc7\u4ece\u4e00\u4e2a\u56fe\u5f00\u59cb\uff0c\u7136\u540e\u8fed\u4ee3\u5730\u5e94\u7528\u8bf8\u5982\u6dfb\u52a0\u6216\u5220\u9664\u8282\u70b9\u548c\u8fb9\u7b49\u79bb\u6563\u52a8\u4f5c\u6765\u9010\u6b65\u6784\u5efa\u56fe\u3002\u4e3a\u4e86\u907f\u514d\u4e3a\u79bb\u6563\u52a8\u4f5c\u4f30\u8ba1\u68af\u5ea6\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u7b56\u7565\u68af\u5ea6\u3002\u8fd9\u53ef\u4ee5\u901a\u8fc7\u81ea\u56de\u5f52\u6a21\u578b\uff08\u5982 RNN\uff09[61] \u6765\u5b9e\u73b0\uff0c\u6216\u8005\u5728\u5f3a\u5316\u5b66\u4e60\u573a\u666f\u4e2d[62] \u8fdb\u884c\u3002\u6b64\u5916\uff0c\u6709\u65f6\u53ef\u4ee5\u5c06\u56fe\u5f62\u5efa\u6a21\u4e3a\u5177\u6709\u8bed\u6cd5\u5143\u7d20\u7684\u5e8f\u5217[63][64]\u3002<\/p>\n

        \u6700\u540e\u7684\u601d\u8003<\/h2>\n

        \u56fe\u5f62\u662f\u4e00\u79cd\u5f3a\u5927\u4e14\u4e30\u5bcc\u7684\u7ed3\u6784\u5316\u6570\u636e\u7c7b\u578b\uff0c\u5176\u4f18\u52bf\u548c\u6311\u6218\u4e0e\u56fe\u50cf\u548c\u6587\u672c\u5b8c\u5168\u4e0d\u540c\u3002\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u6982\u8ff0\u4e86\u7814\u7a76\u4eba\u5458\u5728\u6784\u5efa\u5904\u7406\u56fe\u5f62\u7684\u57fa\u4e8e\u795e\u7ecf\u7f51\u7edc\u7684\u6a21\u578b\u65b9\u9762\u53d6\u5f97\u7684\u4e00\u4e9b\u91cc\u7a0b\u7891\u3002\u6211\u4eec\u8ba8\u8bba\u4e86\u5728\u4f7f\u7528\u8fd9\u4e9b\u67b6\u6784\u65f6\u5fc5\u987b\u505a\u51fa\u7684\u4e00\u4e9b\u91cd\u8981\u8bbe\u8ba1\u9009\u62e9\uff0c\u5e0c\u671b GNN \u5e73\u53f0\u53ef\u4ee5\u8ba9\u4f60\u5bf9\u8fd9\u4e9b\u8bbe\u8ba1\u9009\u62e9\u7684\u5b9e\u8bc1\u7ed3\u679c\u6709\u76f4\u89c2\u7684\u8ba4\u8bc6\u3002\u8fd1\u5e74\u6765 GNN \u5728\u8bb8\u591a\u9886\u57df\u53d6\u5f97\u7684\u6210\u529f\u4e3a\u89e3\u51b3\u4e00\u7cfb\u5217\u65b0\u95ee\u9898\u63d0\u4f9b\u4e86\u7edd\u4f73\u7684\u673a\u4f1a\uff0c\u6211\u4eec\u671f\u5f85\u7740\u770b\u5230\u8be5\u9886\u57df\u4f1a\u5e26\u6765\u4ec0\u4e48\u6837\u7684\u6210\u679c\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

        \u539f\u6587\u732e\uff1ahttp:\/\/distill.pub\/2021\/gnn-intro\/ \u56fe\u5377\u79ef\u4ecb\u7ecd \u795e\u7ecf\u7f51\u7edc\u5df2\u7ecf\u88ab\u8c03\u6574\u4ee5… » \u9605\u8bfb\u5168\u6587<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-296","post","type-post","status-publish","format-standard","hentry","category-dl"],"_links":{"self":[{"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/posts\/296","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/comments?post=296"}],"version-history":[{"count":12,"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/posts\/296\/revisions"}],"predecessor-version":[{"id":308,"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/posts\/296\/revisions\/308"}],"wp:attachment":[{"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/media?parent=296"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/categories?post=296"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apifj.com\/index.php\/wp-json\/wp\/v2\/tags?post=296"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}