{"id":16450,"date":"2019-07-15T17:50:57","date_gmt":"2019-07-15T09:50:07","guid":{"rendered":"https:\/\/swarma.org\/?p=16450"},"modified":"2019-07-15T17:50:14","modified_gmt":"2019-07-15T09:50:14","slug":"0448c0bcce","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=16450","title":{"rendered":"\u65af\u5766\u798fICLR2019\u56fe\u7f51\u7edc\u6700\u65b0\u8bba\u6587\uff1a\u56fe\u795e\u7ecf\u7f51\u7edc\u7684\u8868\u5f81\u80fd\u529b\u6709\u591a\u5f3a\uff1f"},"content":{"rendered":"
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\"\u96c6\u667a\"<\/p>\n

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\u5bfc\u8bed<\/span><\/strong><\/span><\/section>\n
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\u6df1\u5ea6\u5b66\u4e60\u9886\u57df\u5173\u4e8e\u56fe\u795e\u7ecf\u7f51\u7edc(Graph Neural Networks\uff0cGNN)\u7684\u7814\u7a76\u70ed\u60c5\u65e5\u76ca\u9ad8\u6da8\uff0c\u56fe\u7f51\u7edc\u5df2\u7ecf\u6210\u4e3a2019\u5e74\u5404\u5927\u6df1\u5ea6\u5b66\u4e60\u9876\u4f1a\u7684\u7814\u7a76\u70ed\u70b9\u3002GNN \u5904\u7406\u975e\u7ed3\u6784\u5316\u6570\u636e\u65f6\u7684\u51fa\u8272\u80fd\u529b\u4f7f\u5176\u5728\u7f51\u7edc\u6570\u636e\u5206\u6790\u3001\u63a8\u8350\u7cfb\u7edf\u3001\u7269\u7406\u5efa\u6a21\u3001\u81ea\u7136\u8bed\u8a00\u5904\u7406\u548c\u56fe\u4e0a\u7684\u7ec4\u5408\u4f18\u5316\u95ee\u9898\u65b9\u9762\u90fd\u53d6\u5f97\u4e86\u65b0\u7684\u7a81\u7834\u3002\u4f46\u662f\uff0c\u5927\u90e8\u5206\u7684\u56fe\u7f51\u7edc\u6846\u67b6\u7684\u5efa\u7acb\u90fd\u662f\u57fa\u4e8e\u7814\u7a76\u8005\u7684\u5148\u9a8c\u6216\u542f\u53d1\u6027\u77e5\u8bc6\uff0c\u7f3a\u5c11\u6e05\u6670\u7684\u7406\u8bba\u652f\u6491\u3002<\/span><\/p>\n

\n

\u672c\u6587\u4ecb\u7ecdICLR2019\u7684\u4e00\u7bc7\u8bba\u6587\uff0c\u63d0\u51fa\u57fa\u4e8eWL\u56fe\u540c\u6784\u6d4b\u8bd5\u7684\u7406\u8bba\u6846\u67b6\uff0c\u4e3a\u4f17\u591a\u7684GNN\u6846\u67b6\u7ed9\u51fa\u4e86\u7cbe\u5f69\u7684\u7406\u8bba\u5206\u6790\uff0c\u5e76\u63d0\u51fa\u4e86\u4e00\u4e2a\u7b80\u5355\u4f46\u662f\u5f3a\u5927\u7684\u56fe\u7f51\u7edc\u6846\u67b6 GIN(Graph Isomorphism Networks)\uff0c\u5e76\u9a8c\u8bc1\u4e86GIN\u5728\u56fe\u5206\u7c7b\u4efb\u52a1\u4e0a\u7684\u5353\u8d8a\u6027\u80fd\u3002<\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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\u5728\u521a\u521a\u8fc7\u53bb\u7684ICLR 2019\u4f1a\u8bae\u4e2d\uff0c\u4e00\u7bc7 Oral \u7684\u4f1a\u8bae\u6587\u7ae0\u56de\u7b54\u4e86\u5f88\u591a\u56fe\u7f51\u7edc\u7814\u7a76\u8005\u90fd\u5728\u601d\u8003\u7684\u4e00\u4e2a\u95ee\u9898\uff1a\u56fe\u795e\u7ecf\u7f51\u7edc\u5230\u5e95\u6709\u591a\u5389\u5bb3 ( How Powerful are Graph Neural Networks) \uff1f<\/span><\/p>\n

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\u672c\u6587\u662f\u65af\u5766\u798f\u5927\u5b66\u590d\u6742\u7f51\u7edc\u6570\u636e\u5206\u6790\u5927\u4f6c Jure Leskovec \u6559\u6388\u56e2\u961f\u7684\u6700\u65b0\u529b\u4f5c(Node2Vec\u3001GraphSAGE\u7b49\u7ecf\u5178\u5de5\u4f5c\u4e5f\u662f\u51fa\u81ea\u8be5\u56e2\u961f)\u3002\u81ea\u8be5\u5de5\u4f5c\u516c\u5f00\u4ee5\u6765\uff0c\u5df2\u7ecf\u6709\u4e86\u8fd170\u7684citations\uff0c\u8868\u660e\u56fe\u7f51\u7edc\u793e\u533a\u5bf9\u8be5\u5de5\u4f5c\u7684\u5173\u6ce8\u5ea6\u5f88\u9ad8\u3002<\/span><\/p>\n

<\/span>\"\u96c6\u667a\" <\/span><\/p>\n

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\u8bba\u6587\u9898\u76ee\uff1a<\/span><\/p>\n

HowPowerfulareGraphNeuralNetworks?<\/span><\/p>\n

\u8bba\u6587\u5730\u5740\uff1a<\/span><\/p>\n

https:\/\/arxiv.org\/pdf\/1810.00826.pdf<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n

\n

\u4f17\u6240\u5468\u77e5\uff0c\u56fe\u7f51\u7edc(GNNs)\u7684\u65b0\u53d8\u4f53\u5c42\u51fa\u4e0d\u7a77\uff0c\u4f46\u662f\u5374\u9c9c\u6709\u5bf9\u56fe\u7f51\u7edc\u6846\u67b6\u7684\u7406\u8bba\u5206\u6790\u3002Kipf\u57282017\u5e74\u63d0\u51fa\u7684GCN\u4e2d\uff0c\u66fe\u4ece\u56fe\u4e0a\u7684\u8c31\u5206\u6790\u7684\u89d2\u5ea6\u7ed9\u51fa\u4e86GCN\u7684\u7406\u8bba\u57fa\u7840\uff1b\u8fd1\u671f\u4e5f\u6709\u65e5\u672c\u7814\u7a76\u8005\u4ece\u56fe\u4fe1\u53f7\u5904\u7406\u7684\u89d2\u5ea6\uff0c\u8868\u660eGNNs\u53ea\u662f\u4e00\u4e2a\u4f4e\u9891\u6ee4\u6ce2\u5668(arxiv.org\/abs\/1905.09550)\u3002\u800c\u672c\u6587\u5c1d\u8bd5\u4ece\u56fe\u540c\u6784\u7684\u89d2\u5ea6\u51fa\u53d1\uff0c\u4ee5Weisfeiler-Lehman Isomorphism Test (WL test)\u4e3a\u57fa\u7840\uff0c\u7ed9\u51fa\u4e86GNNs\u8868\u5f81\u80fd\u529b\u7684\u7cbe\u5f69\u7406\u8bba\u5206\u6790\uff0c\u5177\u4f53\u7684\u8d21\u732e\u603b\u7ed3\u5982\u4e0b\uff1a<\/span><\/p>\n

    \n
  1. \n

    \u4f5c\u8005\u8868\u660e\uff0c\u5728\u533a\u522b\u4e0d\u540c\u56fe\u7ed3\u6784\u65f6\uff0cGNNs\u6700\u591a\u53ea\u80fd\u53d6\u5f97\u548c WL test \u4e00\u6837\u6548\u679c\uff0c\u5373\uff0cGNNs\u8868\u5f81\u80fd\u529b\u7684\u4e0a\u9650\u662fWL test\uff1b<\/span><\/p>\n<\/li>\n

  2. \n

    \u4f5c\u8005\u4e5f\u7ed9\u51fa\u4e86\u6784\u5efaGNNs\u7684\u6761\u4ef6\uff0c\u6ee1\u8db3\u8fd9\u4e9b\u6761\u4ef6\u540e\uff0cGNNs\u7684\u8868\u5f81\u80fd\u529b\u548c WL test\u4e00\u6837\u5f3a\uff1b<\/span><\/p>\n<\/li>\n

  3. \n

    \u7ed9\u51fa\u4e86GCN\u548cGraphSAGE\u7b49\u4f20\u7edf\u56fe\u7f51\u7edc\u6846\u67b6\u4e0d\u80fd\u533a\u5206\u7684\u7f51\u7edc\u7ed3\u6784\uff1b<\/span><\/p>\n<\/li>\n

  4. \n

    \u5efa\u7acb\u4e86\u4e00\u4e2a\u7b80\u5355\u7684\u6846\u67b6GIN\uff0c\u5e76\u5728\u7406\u8bba\u4e0a\u8bc1\u660e\u4e86\u5176\u8868\u5f81\u80fd\u529b\u548c WL test\u4e00\u6837\u5f3a\u3002<\/span><\/p>\n<\/li>\n<\/ol>\n

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

    \u603b\u7ed3\u8d77\u6765\uff0c\u5168\u6587\u9700\u8981\u56de\u7b54\u4e24\u4e2a\u5173\u952e\u6027\u7684\u95ee\u9898\uff1a<\/span><\/p>\n

      \n
    1. \n

      GNNs\u8868\u5f81\u80fd\u529b\u7684\u4e0a\u9650\u662f\u4ec0\u4e48\uff1f<\/span><\/p>\n<\/li>\n

    2. \n

      \u600e\u6837\u7684GNNs \u6846\u67b6\u8bbe\u8ba1\u624d\u80fd\u8fbe\u5230\u6700\u597d\u7684\u8868\u5f81\u80fd\u529b\uff1f<\/span><\/p>\n<\/li>\n<\/ol>\n

      \n

      \u8fd9\u91cc\u7684\u8868\u5f81\u80fd\u529b\u662f\u6307\u5bf9\u56fe\u62d3\u6251\u7ed3\u6784\u7684\u8868\u5f81\u662f\u5426\u80fd\u6709\u6548\u533a\u5206\u4e0d\u540c\u7684\u56fe\u7ed3\u6784\u3002\u6240\u4ee5\uff0c\u662f\u5426\u80fd\u591f\u5224\u65ad\u56fe\u540c\u6784<\/strong>\u4fbf\u6210\u4e86GNNs\u8868\u5f81\u80fd\u529b\u7684\u5224\u65ad\u6807\u51c6\u3002\u5982\u679cGNNs\u5bf9\u56fe\u7684\u8868\u5f81\u80fd\u533a\u5206\u540c\u6784\u6216\u4e0d\u540c\u6784\u7684\u56fe\uff0c\u5219\u8868\u660e\u5176\u6709\u8f83\u5f3a\u7684\u8868\u5f81\u80fd\u529b\u3002<\/span><\/p>\n

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

      \u4f46\u56fe\u540c\u6784\u662f\u4e00\u4e2a\u975e\u5e38\u96be\u7684\u95ee\u9898\uff0c\u81f3\u4eca\u8fd8\u6ca1\u6709\u6709\u6548\u7684\u65b9\u6cd5\u5224\u65ad\u4e24\u4e2a\u56fe\u662f\u5426\u540c\u6784\uff0c\u6240\u5e78WL test\u662f\u4e00\u4e2a\u975e\u5e38\u6709\u6548\u7684\u56fe\u540c\u6784\u68c0\u9a8c\u8fd1\u4f3c\u65b9\u6cd5\uff0c\u5bf9\u56fe\u7ed3\u6784\u5177\u6709\u5f88\u5f3a\u7684\u8868\u5f81\u80fd\u529b\u3002\u90a3\u4e48\uff0cGNNs\u80fd\u5426\u5177\u6709WL test\u4e00\u6837\u7684\u8868\u5f81\u80fd\u529b\uff1f\u6709\u7684\u8bdd\uff0c\u600e\u4e48\u8bbe\u8ba1\u6846\u67b6\u600e\u6837\u8fbe\u5230\u548cWL\u4e00\u6837\u7684\u6c34\u5e73\uff1f<\/span><\/p>\n

      \n
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      <\/p>\n

      \u80cc\u666f\u77e5\u8bc6<\/p>\n

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

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

      \n

      GNNs<\/strong><\/span><\/span><\/strong><\/span><\/p>\n<\/h2>\n

      \n

      \u5927\u591a\u6570\u7684GNNs\u53ef\u4ee5\u5f52\u7ed3\u4e3a aggregation based \u6216\u8005 message-passing based \u7684\u6846\u67b6\uff0c\u4e3b\u8981\u5305\u542b\u805a\u5408\u90bb\u5c45\u4fe1\u606f\u548c\u66f4\u65b0\u8282\u70b9\u4fe1\u606f\u4e24\u6b65\uff0cAGGREGATE \u548c COMBINE\uff1a<\/span><\/p>\n

      <\/span>\"\u96c6\u667a\" <\/span><\/p>\n

      \u4e0d\u540c\u7684GNNs\u533a\u522b\u5c31\u5728\u4e0e\u91c7\u7528\u4e0d\u540c\u7684 AGGREGATE \u548c COMBINE \u51fd\u6570\u3002\u6bd4\u5982GCN\u7684 AGGREGATE \u51fd\u6570\u5c31\u662f\u91c7\u7528\u7684mean-pooling\uff0c\u800cGraphSAGE\u5219\u662f\u91c7\u7528max-pooling\u3002<\/span><\/p>\n

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      \n
      \n

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

      The Weisfeiler-Lehman Isomorphism Test<\/span><\/strong><\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

      \n

      WL test\u662f\u4e00\u79cd\u6709\u6548\u7684\u68c0\u9a8c\u4e24\u4e2a\u56fe\u662f\u5426\u540c\u6784\u7684\u8fd1\u4f3c\u65b9\u6cd5\u3002\u5f53\u6211\u4eec\u8981\u5224\u65ad Graph1 \u548c Graph2 \u662f\u5426\u540c\u6784\u65f6\uff0cWL test \u7684\u4e3b\u8981\u6b65\u9aa4\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u901a\u8fc7\u805a\u5408\u8282\u70b9\u90bb\u5c45\u7684 label\uff0c\u7136\u540e\u901a\u8fc7 hash \u51fd\u6570\u5f97\u5230\u8282\u70b9\u65b0\u7684 label\uff0c\u4e0d\u65ad\u91cd\u590d\u77e5\u9053\u6bcf\u4e2a\u8282\u70b9\u7684 label \u7a33\u5b9a\u4e0d\u53d8\u3002<\/span> <\/p>\n

      \n

      <\/span>\"\u96c6\u667a\"<\/p>\n

      \n

      \u7a33\u5b9a\u540e\uff0c\u7edf\u8ba1\u4e24\u5f20\u56fe\u7684label\u7684\u5206\u5e03\uff0c\u5982\u679c\u5206\u5e03\u76f8\u540c\uff0c\u5219\u4e00\u822c\u8ba4\u4e3a\u4e24\u5f20\u56fe\u65f6\u540c\u6784\u7684\u3002<\/span><\/span><\/p>\n

      \"\u96c6\u667a\" <\/span><\/p>\n

      \u6211\u4eec\u53ef\u4ee5\u53d1\u73b0\uff0cWL test \u65b9\u6cd5\u7684\u6b65\u9aa4\u548cGNNs\u5177\u6709\u5f02\u66f2\u540c\u5de5\u4e4b\u5999\uff0c\u90fd\u662f\u901a\u8fc7\u4e0d\u65ad\u805a\u5408\u90bb\u5c45\u4fe1\u606f\uff0c\u5f97\u5230\u8282\u70b9\u7684\u65b0\u8868\u793a\uff0c\u8fd9\u4e5f\u662f\u4e3a\u4ec0\u4e48Kipf\u57282017\u5e74GCN\u7684\u8bba\u6587\u4e2d\u5355\u72ec\u8ba8\u8bba\u548cGCN\u548cWL test\u5173\u7cfb\u7684\u539f\u56e0\u3002\u800c\u6b63\u662f\u8fd9\u79cd\u7edf\u4e00\u6027\uff0c\u624d\u4f7f\u5f97\u672c\u6587\u80fd\u4ee5 WL test \u4e3a\u57fa\u7840\u6765\u5206\u6790GNNs\u6846\u67b6\u3002<\/span><\/p>\n

      \n

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

      \u4e3b\u8981\u7684\u7406\u8bba\u7ed3\u679c<\/span><\/strong><\/span><\/p>\n

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

      \n

      \u672c\u6587\u4f5c\u8005\u57fa\u4e8eWL test\u548cGNNs\u6846\u67b6\u7684\u76f8\u4f3c\u6027\uff0c\u5c42\u5c42\u63a8\u8fdb\uff0c\u7ed9\u51fa\u4e86\u4e00\u7cfb\u5217\u91cd\u8981\u7684\u7ed3\u679c\u3002<\/span><\/p>\n

      \u9996\u5148\uff0c\u4f5c\u8005\u8bf4\u660eGNNs\u6846\u67b6\u7684\u8868\u5f81\u80fd\u529b\u4e0d\u4f1a\u8d85\u8fc7WL test\uff1a<\/span><\/span><\/p>\n

      \"\u96c6\u667a\" <\/span><\/p>\n

      \u5bf9\u4e8e\u4e24\u4e2a\u4e0d\u540c\u6784\u7684\u56fe\uff0c\u5982\u679cGNNs\u80fd\u5c06\u5176map\u5230\u4e0d\u540cembs\uff0c\u90a3\u4e48WL test\u4e5f\u4f1a\u5f97\u51fa\u4e0d\u540c\u6784\u7684\u7ed3\u8bba\u3002\u65e2\u7136GNNs\u4e0d\u80fd\u8d85\u8fc7WL test\uff0c \u90a3\u4e48\u5982\u4f55\u624d\u80fd\u548cWL test\u4e00\u6837\u6709\u6548\u5462\uff1f<\/span><\/span><\/p>\n

      \"\u96c6\u667a\" <\/span><\/p>\n

      \u4e0a\u56fe\u5c55\u73b0\u4e86WL test\u4e0eGNNs\u5728\u8868\u5f81\u7f51\u7edc\u7ed3\u6784\u65f6\u7684\u5171\u540c\u70b9\uff1a\u4e00\u4e2a\u8282\u70b9\u7684\u8868\u5f81\u90fd\u662f\u7531\u4ee5\u8be5\u8282\u70b9\u4e3a\u7236\u8282\u70b9\u7684\u5b50\u6811\u4fe1\u606f\u805a\u5408\u5f97\u5230(\u4e2d\u95f4\u56fe)\u3002\u800c\u5728\u805a\u5408\u7684\u8fc7\u7a0b\u4e2d\uff0cWL test\u6700\u5927\u7684\u7279\u70b9\u662f\u5176\u805a\u5408\u51fd\u6570\u91c7\u7528\u7684\u662f\u5355\u5c04(injective)\u7684 hash \u51fd\u6570\u3002\u90a3\u4e48\uff0c\u662f\u5426\u5c06 GNNs \u7684\u7684\u805a\u5408\u51fd\u6570\u4e5f\u6539\u6210\u5355\u5c04(injective)\u51fd\u6570 \u5c31\u80fd\u8fbe\u5230\u548cWL test\u4e00\u6837\u7684\u6548\u679c\u5462\uff1f\u4f5c\u8005\u7ed9\u51fa\u4e86\u80af\u5b9a\u7684\u7b54\u6848\uff1a<\/span><\/span><\/p>\n

      \"\u96c6\u667a\" <\/span><\/p>\n

      \u8be5\u7ed3\u8bba\u8bf4\u660e\uff1a\u5982\u679cGNNs\u7684\u805a\u5408\u51fd\u6570\u662f\u5b9a\u4e49\u5728multiset\u4e0a\u7684\u5355\u5c04\u51fd\u6570\uff0c\u90a3\u4e48GNNs\u548cWL\u7684\u8868\u5f81\u80fd\u529b\u4e00\u6837\u3002\u4e5f\u7ed9\u51fa\u4e86\u8bbe\u8ba1 powerful \u7684 GNNs \u6846\u67b6\u7684\u9996\u8981\u6761\u4ef6\uff1ainjective\u3002<\/span><\/p>\n

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

      \u4f46\u662f\uff0c\u4e0a\u8ff0\u7ed3\u8bba\u867d\u7136\u7ed9\u51fa\u4e86\u8bbe\u8ba1\u6709\u6548GNNs\u6846\u67b6\u7684\u5145\u5206\u6761\u4ef6\uff0c\u4f46\u662f\u5e76\u6ca1\u6709\u7ed9\u51fa\u5177\u4f53\u7684\u8bbe\u8ba1\u6307\u5357\uff0c\u6211\u4eec\u4ecd\u7136\u4e0d\u77e5\u9053\u5982\u4f55\u624d\u80fd\u627e\u5230\u5177\u6709\u5355\u5c04\u6027\u8d28\u7684\u805a\u5408\u51fd\u6570\u3002\u800c\u5982\u4e0b\u7684\u7ed3\u8bba\u5f88\u597d\u7684\u7ed9\u51fa\u4e86\u7b54\u6848\uff1a<\/span><\/span><\/p>\n

      <\/span>\"\u96c6\u667a\" <\/span><\/p>\n

      \u4e0a\u8ff0\u7ed3\u8bba\u8868\u660e\uff0c\u5982\u679c\u6211\u4eec\u628a\u8282\u70b9\u4e0a\u4e00\u5c42\u7684\u8868\u5f81\u8868\u793a\u4e3ac\uff0c\u5176\u90bb\u5c45\u7684\u8868\u5f81\u7684\u96c6\u5408\u8868\u793a\u4e3aX\uff0c\u90a3\u4e48\u4efb\u610f\u5173\u4e8e c \u4e0e X \u7684\u51fd\u6570 g (\u5f53\u7136\u5305\u62ec\u5355\u5c04\u51fd\u6570) \u90fd\u53ef\u4ee5\u8868\u793a\u4e3aphi \u4e0e f \u7684\u590d\u5408\u5f62\u5f0f\u3002\u800c\u8be5\u590d\u5408\u51fd\u6570\u53ef\u4ee5\u7528\u4e07\u80fd\u62df\u5408\u51fd\u6570MLPs\u6765\u62df\u5408\uff0c\u81f3\u6b64\uff0c\u4f5c\u8005\u4eec\u5c31\u5f97\u5230\u4e86\u4e00\u4e2a\u975e\u5e38\u7b80\u5355\u7684GNNs\u6846\u67b6\uff1a<\/span><\/span><\/p>\n

      \"\u96c6\u667a\" <\/span><\/p>\n

      \u79f0\u4e4b\u4e3aGIN (Graph Isomorphism Networks)\uff0c \u8be5\u6846\u67b6\u6700\u5927\u7684\u7279\u70b9\u5c31\u662f\u7b80\u5355\uff0c\u5e76\u4e14\u5176\u6709\u6548\u6027\u5177\u6709\u7406\u8bba\u4fdd\u8bc1\u3002\u5728\u56fe\u5206\u7c7b\u7684\u5b9e\u9a8c\u4e2d\uff0c\u8be5\u6846\u67b6\u4e5f\u8868\u73b0\u51fa\u4e86SOTA\u7684\u6027\u80fd\u3002<\/span><\/p>\n

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

      \u5bf9\u4e8e\u4f20\u7edfGNNs\u7684\u5206\u6790<\/span><\/strong><\/span><\/p>\n

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

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

      \u5f88\u8fc7\u7ecf\u5178\u7684GNNs\u6846\u67b6\u91c7\u7528 mean-pooling \u6216\u8005 max-pooling\u7684\u65b9\u6cd5\uff0c\u800c\u4f5c\u8005\u63d0\u51fa\uff0c\u8fd9\u4e9b\u805a\u5408\u65b9\u6cd5\u5e76\u4e0d\u662f\u5355\u5c04\u51fd\u6570\uff0c\u5176\u4e0d\u80fd\u533a\u5206\u4e00\u4e9b\u4e0d\u540c\u7684\u5c40\u90e8\u7ed3\u6784\uff0c\u4ece\u800c\u5bfc\u81f4\u6846\u67b6\u7684\u8868\u5f81\u80fd\u529b\u4e0b\u964d\uff1a<\/span><\/p>\n

      <\/span> \"\u96c6\u667a\" <\/span><\/p>\n

      \u6bd4\u5982\u4e0a\u56fe\u6240\u793a\uff1a\u76f8\u540c\u7684\u989c\u8272\u4ee3\u8868\u76f8\u540c\u7684\u8282\u70b9\u5c5e\u6027\u3002\u5728\u56fea, b, c\u4e2d\uff0c\u8282\u70b9 v \u4e0e v\u2018 \u7684\u5c40\u90e8\u7ed3\u6784\u5747\u4e0d\u76f8\u540c\uff0c\u4f46\u662fMean \u548c Max \u5374\u4e0d\u80fd\u6709\u6548\u533a\u5206\uff0c\u4f1a\u5bfc\u81f4\u4e24\u79cd\u5c40\u90e8\u7ed3\u6784\u5f97\u5230\u76f8\u540c\u7684\u8282\u70b9\u8868\u5f81\uff0c\u4ece\u800c\u4e22\u5931\u4e86\u7f51\u7edc\u7684\u7ed3\u6784\u4fe1\u606f\u3002<\/span><\/p>\n

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

      \u4f46\u662f\u91c7\u7528Mean\u548cMax-poling\u7684\u6846\u67b6(GCN\uff0cGraphSAGE)\u8868\u73b0\u90fd\u5f88\u597d\uff0c\u90a3\u4e48\u4ed6\u4eec\u5b66\u5230\u4e86\u4ec0\u4e48\u5462\uff1f<\/span><\/strong><\/p>\n

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

      \u4f5c\u8005\u8ba4\u4e3a\uff1a<\/span><\/p>\n

      Mean-pooling \u81f4\u529b\u4e8e\u5b66\u4e60\u8282\u70b9 feature \u7684\u5206\u5e03\uff1a\u6240\u4ee5\uff0c\u5728\u4e0b\u8ff0\u60c5\u51b5\u4e2d\uff0cMean\u4e5f\u80fd\u8868\u73b0\u7684\u5f88\u597d\uff1a<\/span><\/p>\n

        \n
      1. \n

        \u5f53\u6211\u4eec\u7684\u4efb\u52a1\u4e4b\u548c\u8282\u70b9feature\u7684\u5206\u5e03\u6709\u5173\uff0c\u800c\u4e0e\u5177\u4f53\u7684\u5c40\u90e8\u7ed3\u6784\u65e0\u5173\u65f6<\/span><\/p>\n<\/li>\n

      2. \n

        \u5f53\u8282\u70b9\u7684\u5177\u6709\u4e30\u5bcc\u7684feature\uff0c\u5f88\u5c11\u91cd\u590d\u65f6<\/span><\/p>\n

        <\/span><\/p>\n<\/li>\n<\/ol>\n

        \u8fd9\u5c31\u89e3\u91ca\u4e86\u4e3a\u4ec0\u4e48GCN\u5728\u505a\u8282\u70b9\u5206\u7c7b\u65f6\uff0c\u4e3a\u4ec0\u4e48\u4f1a\u6709\u90a3\u4e48\u597d\u7684\u6548\u679c\uff1a\u56e0\u4e3a\u6bcf\u4e2a\u8282\u70b9\u7684\u7279\u5f81\u5f88\u96be\u4f1a\u91cd\u590d\u3002<\/span><\/p>\n

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

        Max \u5b66\u7684\u662f underlying set\uff1aMax\u5904\u7406Multiset\u65f6\uff0c\u53ea\u5173\u5fc3\u5176\u5bf9\u5e94\u7684underlying set\u3002\u6240\u4ee5\uff0cMax\u65e2\u6ca1\u6709\u5b66\u5230\u5c40\u90e8\u7ed3\u6784\uff0c\u4e5f\u6ca1\u6709\u5b66\u5230\u5206\u5e03\u3002\u5f53\u6211\u4eec\u5173\u5fc3Representative element\u6216\u8005\u201cskeleton\u201d\u65f6\uff0cMax\u4f1a\u6709\u597d\u6548\u679c\u3002<\/span><\/p>\n

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

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

        \u5b9e\u9a8c<\/p>\n

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

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

        \u672c\u6587\u4e3a\u4e86\u4f53\u73b0GIN\u5728\u8868\u5f81\u7f51\u7edc\u7ed3\u6784\u4fe1\u606f\u7684\u7684\u51fa\u8272\u80fd\u529b\uff0c\u9009\u62e9\u7528\u7f51\u7edc\u5206\u7c7b\u5b9e\u9a8c\u6765\u9a8c\u8bc1\u5176\u6709\u6548\u6027\u3002<\/span><\/p>\n

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

        \n

        Training Set Accuracy<\/strong><\/span><\/span><\/strong><\/span><\/p>\n

        <\/span><\/strong><\/p>\n<\/h2>\n

        \u6211\u4eec\u9700\u8981\u5f3a\u8c03\u7684\u4e00\u70b9\u65f6\uff0c\u6587\u4e2d\u5bf9GNNs\u8868\u5f81\u80fd\u529b\u7684\u5206\u6790\u53ea\u5173\u7cfb\u5176\u62df\u5408\u80fd\u529b\uff0c\u5373\u662f\u5426\u80fd\u5bf9\u8bad\u7ec3\u6570\u636e\u8fdb\u884c\u5145\u5206\u7684\u62df\u5408\uff0c\u8fd9\u4e00\u70b9\u53ef\u4ee5\u7531\u8bad\u7ec3\u8fc7\u7a0b\u7684 training set accuracy \u6765\u9a8c\u8bc1\uff1a<\/span><\/span><\/p>\n

        \"\u96c6\u667a\" <\/span><\/p>\n

        \u4e0a\u56fe\u8868\u660e\uff0c\u57285\u4e2a\u6570\u636e\u96c6\u4e0a\uff0cGIN\u7684\u8bad\u7ec3\u7cbe\u5ea6\u90fd\u662f\u6700\u9ad8\uff0c\u8bf4\u660e\u5176\u62df\u5408\u80fd\u529b\u6700\u597d\uff0c\u5373\u5176\u5bf9\u7f51\u7edc\u7ed3\u6784\u7684\u8868\u5f81\u80fd\u529b\u6700\u5f3a\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0cGIN\u7684\u8bad\u7ec3\u7cbe\u5ea6\u6700\u9ad8\u4e5f\u6ca1\u6709\u8d85\u8fc7WL subtree kernel\u7684\u7cbe\u5ea6\uff0c\u8fd9\u6837\u9a8c\u8bc1\u4e86\u6587\u4e2d\u7684\u7406\u8bba\u7ed3\u679c\uff1aGIN\u548c WL \u4e00\u6837\u5f3a\uff0c\u4f46\u662f\u4e0d\u4f1a\u8d85\u8fc7WL\u3002<\/span><\/p>\n

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

        \n

        Test Set Accuracy<\/strong><\/span><\/span><\/strong><\/p>\n

        <\/span><\/p>\n<\/h2>\n

        \u5728\u7f51\u7edc\u5206\u7c7b\u5b9e\u9a8c\u7684\u6d4b\u8bd5\u96c6\u4e0a\uff0cGIN\u5728\u591a\u4e2a\u6570\u636e\u96c6\u4e0a\u5747\u53d6\u5f97\u4e86SOTA\u7684\u6210\u7ee9\uff0c\u8868\u660eGIN\u6846\u67b6\u4e0d\u4ec5\u6709\u6700\u5f3a\u7684\u62df\u5408\u80fd\u529b\uff0c\u8fd8\u5177\u6709\u4f18\u79c0\u7684\u6cdb\u5316\u80fd\u529b\u3002<\/span><\/span><\/p>\n

        <\/span>\"\u96c6\u667a\" <\/span><\/p>\n

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

        \u5c0f\u7ed3<\/span><\/strong><\/span><\/p>\n

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

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

        \u8be5\u8bba\u6587\u5bf9\u57fa\u4e8e\u805a\u5408\u7684GNN\u505a\u4e86\u975e\u5e38\u7cbe\u5f69\u7684\u7406\u8bba\u5206\u6790\uff0c\u7ed9\u51fa\u4e86GNNs\u7684\u8868\u5f81\u80fd\u529b\u7684\u4e0a\u754c\uff0c\u540c\u65f6\u7ed9\u51fa\u4e86\u5982\u4f55\u8bbe\u8ba1GNNs\u624d\u80fd\u4f7f\u5176\u8868\u5f81\u80fd\u529b\u6700\u5f3a\u7684\u6761\u4ef6\u3002\u5728\u6b64\u57fa\u7840\u4e0a\uff0c\u8bbe\u8ba1\u4e86\u4e00\u4e2a\u5f02\u5e38\u7b80\u5355\u7684\u56fe\u7f51\u7edc\u6846\u67b6GIN\uff0c\u4f46\u662f\u5374\u975e\u5e38\u7684\u6709\u6548\uff0c\u5728\u56fe\u5206\u7c7b\u4efb\u52a1\u4e0a\u53d6\u5f97\u4e86SOTA\u7684\u6210\u7ee9\u3002\u8fd9\u7bc7\u5de5\u4f5c\u8868\u660e\u4e86\u57fa\u4e8e\u7406\u8bba\u5206\u6790\u7684\u6846\u67b6\u6784\u5efa\u662f\u591a\u4e48\u7684\u6709\u6548\uff0c\u4f7f\u6211\u4eec\u5fc5\u987b\u627f\u8ba4\uff0c\u5bf9\u66f4\u52a0\u5e7f\u4e49\u7684GNNs\u7684\u7406\u8bba\u5206\u6790\u662f\u56fe\u7f51\u7edc\u793e\u533a\u7684\u57fa\u7840\u6027\u4efb\u52a1\u3002<\/span><\/p>\n

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

        \u5176\u4ed6\u94fe\u63a5<\/p>\n

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

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

        CLR 2019 OpenReview (\u63a8\u8350\u9605\u8bfb):<\/span><\/p>\n

        https:\/\/openreview.net\/forum?id=ryGs6iA5Km<\/span><\/p>\n

        \u8bba\u6587\u7684Github\u9875\u9762:<\/span><\/p>\n

        https:\/\/github.com\/weihua916\/powerful-gnns<\/span><\/p>\n

        \u76f8\u5173\u535a\u5ba2\uff1a<\/span><\/p>\n

        https:\/\/asail.gitbook.io\/hogwarts\/graph\/how_powerful<\/span><\/p>\n

        https:\/\/www.davidbieber.com\/post\/2019-05-10-weisfeiler-lehman-isomorphism-test\/<\/span><\/p>\n

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

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

        \u8bfe\u7a0b\u63a8\u8350<\/p>\n

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

        \n

        \n

        \u5f55\u64ad\u5730\u5740\uff1a<\/strong><\/span><\/p>\n

        http:\/\/campus.swarma.org\/play\/coursedetail?id=10936<\/span><\/p>\n

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

        \n

        \n
        \n
        \u4f5c\u8005\uff1a\u9ad8\u98de<\/span><\/section>\n
        \u7f16\u8f91\uff1a\u5f20\u723d<\/span><\/section>\n<\/section>\n<\/blockquote>\n
        \n
        \n
        \n
        \n

        \n

        \n
        \"\u96c6\u667a\"<\/div>\n

        \n

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

        \u96c6\u667a\u4ff1\u4e50\u90e8QQ\u7fa4\uff5c877391004<\/span><\/strong><\/p>\n

        \u5546\u52a1\u5408\u4f5c\u53ca\u6295\u7a3f\u8f6c\u8f7d\uff5cswarma@swarma.org<\/span><\/strong><\/p>\n

        \n

        \u25c6<\/span>\u25c6<\/span>\u25c6<\/span><\/span><\/strong><\/strong><\/h1>\n<\/section>\n

        \u641c\u7d22\u516c\u4f17\u53f7\uff1a\u96c6\u667a\u4ff1\u4e50\u90e8<\/span><\/strong><\/span><\/p>\n

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

        \u52a0\u5165\u201c\u6ca1\u6709\u56f4\u5899\u7684\u7814\u7a76\u6240\u201d<\/span><\/strong><\/span><\/p>\n

        \n
        \"\u96c6\u667a\"<\/div>\n<\/section>\n

        \u8ba9\u82f9\u679c\u7838\u5f97\u66f4\u731b\u70c8\u4e9b\u5427\uff01<\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

        \n

        \u539f\u6587\u59cb\u53d1\u4e8e\u5fae\u4fe1\u516c\u4f17\u53f7\uff08\u96c6\u667a\u4ff1\u4e50\u90e8\uff09\uff1a\u96c6\u667a<\/a><\/p>\n<\/blockquote>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

        \u5bfc\u8bed \u6df1\u5ea6\u5b66\u4e60\u9886\u57df\u5173\u4e8e\u56fe\u795e\u7ecf\u7f51\u7edc(Graph Neural Networks\uff0cGNN)\u7684\u7814\u7a76\u70ed\u60c5\u65e5\u76ca\u9ad8\u6da8\uff0c\u56fe\u7f51\u7edc\u5df2\u7ecf\u6210\u4e3a2019\u5e74\u5404\u5927\u6df1\u5ea6\u5b66\u4e60\u9876\u4f1a\u7684\u7814\u7a76\u70ed\u70b9\u3002GNN \u5904\u7406\u975e\u7ed3\u6784\u5316\u6570\u636e\u65f6\u7684\u51fa\u8272\u80fd\u529b\u4f7f\u5176\u5728\u7f51\u7edc\u6570\u636e\u5206\u6790\u3001\u63a8\u8350\u7cfb\u7edf\u3001\u7269\u7406\u5efa\u6a21\u3001\u81ea\u7136\u8bed\u8a00\u5904\u7406\u548c\u56fe\u4e0a\u7684\u7ec4\u5408\u4f18\u5316\u95ee\u9898\u65b9\u9762\u90fd\u53d6\u5f97\u4e86\u65b0\u7684\u7a81\u7834\u3002\u4f46\u662f\uff0c\u5927\u90e8\u5206…<\/p>\n","protected":false},"author":1,"featured_media":16455,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"special":[],"_links":{"self":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/16450"}],"collection":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=16450"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/16450\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/16455"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=16450"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=16450"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=16450"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=16450"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}