{"id":789,"date":"2025-11-13T21:24:35","date_gmt":"2025-11-13T13:24:35","guid":{"rendered":"https:\/\/blog.heartwarming.online\/?p=789"},"modified":"2025-11-13T21:24:38","modified_gmt":"2025-11-13T13:24:38","slug":"lagnn%e8%ae%ba%e6%96%87%e8%a7%a3%e8%af%bb","status":"publish","type":"post","link":"https:\/\/blog.heartwarming.online\/index.php\/2025\/11\/13\/lagnn%e8%ae%ba%e6%96%87%e8%a7%a3%e8%af%bb\/","title":{"rendered":"LAGNN\u8bba\u6587\u89e3\u8bfb"},"content":{"rendered":"\n

Local Augmentation for Graph Neural Networks<\/h1>\n\n\n\n

\u6458\u8981<\/h2>\n\n\n\n

\u56fe\u795e\u7ecf\u7f51\u7edc\uff08GNNs\uff09\u5728\u56fe\u76f8\u5173\u4efb\u52a1\u4e0a\u53d6\u5f97\u4e86\u663e\u8457\u7684\u6027\u80fd\u3002GNNs\u7684\u6838\u5fc3\u601d\u60f3\u662f\u901a\u8fc7\u805a\u5408\u6765\u81ea\u5c40\u90e8\u90bb\u57df\u7684\u4fe1\u606f\u6765\u83b7\u5f97\u4fe1\u606f\u4e30\u5bcc\u7684\u8868\u793a\u3002\u7136\u800c\uff0c\u5bf9\u4e8e\u90bb\u5c45\u8f83\u5c11\u7684\u8282\u70b9<\/mark>\uff0c\u90bb\u57df\u4fe1\u606f\u662f\u5426\u5f97\u5230\u5145\u5206\u805a\u5408\u4ee5\u5b66\u4e60\u8868\u793a\u4ecd\u7136\u662f\u4e00\u4e2a\u5f00\u653e\u95ee\u9898\u3002\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u63d0\u51fa\u4e86\u4e00\u79cd\u7b80\u5355\u9ad8\u6548\u7684\u6570\u636e\u589e\u5f3a\u7b56\u7565\u2014\u2014\u5c40\u90e8\u589e\u5f3a<\/mark>\uff0c\u6765\u5b66\u4e60\u4ee5\u4e2d\u5fc3\u8282\u70b9\u8868\u793a\u4e3a\u6761\u4ef6\u7684\u90bb\u5c45\u8282\u70b9\u8868\u793a\u5206\u5e03\uff0c\u5e76\u901a\u8fc7\u751f\u6210\u7684\u7279\u5f81\u589e\u5f3aGNN\u7684\u8868\u8fbe\u80fd\u529b\u3002\u5c40\u90e8\u589e\u5f3a\u662f\u4e00\u4e2a\u901a\u7528\u6846\u67b6\uff0c\u53ef\u4ee5\u4ee5\u5373\u63d2\u5373\u7528<\/mark>\u7684\u65b9\u5f0f\u5e94\u7528\u4e8e\u4efb\u4f55GNN\u6a21\u578b\u3002\u5b83\u5728\u6bcf\u6b21\u8bad\u7ec3\u8fed\u4ee3\u4e2d\u4ece\u5b66\u4e60\u5230\u7684\u6761\u4ef6\u5206\u5e03\u4e2d\u91c7\u6837\u4e0e\u6bcf\u4e2a\u8282\u70b9\u76f8\u5173\u7684\u7279\u5f81\u5411\u91cf\uff0c\u4f5c\u4e3a\u9aa8\u5e72\u6a21\u578b\u7684\u989d\u5916\u8f93\u5165\u3002\u5e7f\u6cdb\u7684\u5b9e\u9a8c\u548c\u5206\u6790\u8868\u660e\uff0c\u5f53\u5e94\u7528\u4e8e\u5404\u79cdGNN\u67b6\u6784\u548c\u591a\u6837\u5316\u7684\u57fa\u51c6\u6d4b\u8bd5\u65f6\uff0c\u5c40\u90e8\u589e\u5f3a\u59cb\u7ec8\u80fd\u5e26\u6765\u6027\u80fd\u63d0\u5347\u3002\u4f8b\u5982\uff0c\u5b9e\u9a8c\u8868\u660e\uff0c\u5c06\u5c40\u90e8\u589e\u5f3a\u63d2\u5165GCN\u548cGAT\u4e2d\uff0c\u5728Cora\u3001Citeseer\u548cPubmed\u4e0a\u7684\u6d4b\u8bd5\u51c6\u786e\u7387\u5e73\u5747\u5206\u522b\u63d0\u9ad8\u4e863.4%\u548c1.6%\u3002\u6b64\u5916\uff0c\u6211\u4eec\u5728\u5927\u578b\u56fe\uff08OGB\uff09\u4e0a\u7684\u5b9e\u9a8c\u7ed3\u679c\u8868\u660e\uff0c\u6211\u4eec\u7684\u6a21\u578b\u76f8\u5bf9\u4e8e\u9aa8\u5e72\u7f51\u7edc\u59cb\u7ec8\u80fd\u6539\u5584\u6027\u80fd\u3002\u4ee3\u7801\u53ef\u5728 https:\/\/github.com\/SongtaoLiu0823\/LAGNN<\/a> \u83b7\u53d6\u3002<\/p>\n\n\n\n

note<\/h3>\n\n\n\n

\u4f20\u7edf\u7684GNNs\u4ed6\u5c31\u662f\u4f9d\u9760\u4ece\u76f4\u63a5\u90bb\u5c45\u8282\u70b9\u83b7\u53d6\u4fe1\u606f\uff0c\u4f46\u662f\u8fd9\u6837\u5c31\u4f1a\u6709\u4e00\u4e2a\u95ee\u9898\uff0c\u4e07\u4e00\u6709\u7684\u8282\u70b9\u53ea\u6709\u4e00\u4e24\u4e2a\u90bb\u5c45\uff0c\u6216\u8005\u5e72\u8106\u6ca1\u6709\u90bb\u5c45\uff0c\u90a3\u4ed6\u4ece\u54ea\u91cc\u83b7\u53d6\u4fe1\u606f\u5462\uff0c\u53ea\u6709\u81ea\u8eab\uff1f\u90a3\u80af\u5b9a\u4e0d\u591f\uff0c\u6240\u4ee5\u8fd9\u4f1a\u5bfc\u81f4\u4e00\u4e9b\u8282\u70b9\u5b66\u4e60\u5230\u7684\u4fe1\u606f\u5f88\u5c11\uff0c\u4e0d\u5145\u5206\uff0c\u8fd9\u4f1a\u4f7f\u5f97\u6a21\u578b\u6574\u4f53\u62c9\u80ef\u8d77\u6765\uff0c\u597d\u50cf\u4e00\u9897\u8001\u9f20\u5c4e\u574f\u4e86\u4e00\u9505\u6c64\u3002\u6240\u4ee5\u8fd9\u7bc7\u6587\u7ae0\u5c31\u63d0\u51fa\u4e86\u4e00\u79cd\u65b0\u7684\u65b9\u6cd5\uff0c\u5c40\u90e8\u589e\u5f3a\uff0c\u4f20\u7edf\u7684GNNs\u662f\u4f9d\u9760\u90bb\u5c45\uff0c\u5c40\u90e8\u589e\u5f3a\u4e5f\u662f\u8981\u4f9d\u9760\u90bb\u5c45\uff0c\u53ea\u662f\u8bf4\u4ed6\u4e0d\u4f46\u4f9d\u9760\u76f4\u63a5\u771f\u7684\u90bb\u5c45\uff0c\u4e5f\u4f1a\u4f9d\u9760\u865a\u5047\u7684\u90bb\u5c45\uff08\u865a\u62df\u90bb\u5c45\uff09\u6765\u83b7\u53d6\u4fe1\u606f\uff0c\u8fd9\u6837\u5c31\u53ef\u4ee5\u89e3\u51b3\u4e00\u4e9b\u8282\u70b9\u6ca1\u6709\u5f88\u591a\u90bb\u5c45\u7684\u95ee\u9898\u4e86\uff0c\u4f46\u662f\u8fd9\u6837\u80af\u5b9a\u53c8\u6709\u95ee\u9898\u4e86\uff0c\u865a\u62df\u90bb\u5c45\u600e\u4e48\u751f\u6210\u5462\uff1f\u6211\u4e5f\u4e0d\u77e5\u9053\uff0c\u9700\u8981\u5f80\u4e0b\u770b\u3002<\/p>\n\n\n\n

\u5f15\u8a00<\/h2>\n\n\n\n

\u56fe\u795e\u7ecf\u7f51\u7edc\uff08GNNs\uff09\u53ca\u5176\u53d8\u4f53\uff08Kipf & Welling, 2017; Hamilton et al., 2017; Veli\u010dkovi\u0107 et al., 2018\uff09\u5728\u5404\u79cd\u57fa\u4e8e\u56fe\u7684\u4efb\u52a1\u4e0a\u53d6\u5f97\u4e86\u6700\u5148\u8fdb\u7684\u6027\u80fd\uff0c\u5305\u62ec\u63a8\u8350\u7cfb\u7edf\uff08Ying et al., 2018\uff09\u3001\u836f\u7269\u53d1\u73b0\uff08Dai et al., 2019\uff09\u548c\u4ea4\u901a\u9884\u6d4b\uff08Guo et al., 2019\uff09\u3002GNNs\u7684\u6838\u5fc3\u662f\u91c7\u7528\u6d88\u606f\u4f20\u9012\u673a\u5236\uff0c\u4f20\u9012\u548c\u805a\u5408\u6765\u81ea\u5c40\u90e8\u90bb\u57df\u7684\u4fe1\u606f\u4ee5\u751f\u6210\u4fe1\u606f\u4e30\u5bcc\u7684\u8868\u793a\u3002<\/mark>\u6df1\u5ea6GNNs\u7684\u6700\u65b0\u53d1\u5c55\uff0c\u5982JKnet\uff08Xu et al., 2018\uff09\u3001GCNII\uff08Chen et al., 2020b\uff09\u548cRevGNNDeep\uff08Li et al., 2021\uff09\uff0c\u901a\u8fc7\u6b8b\u5dee\u5f0f<\/mark>\u8bbe\u8ba1\u5c06\u6d45\u5c42\u7684\u8f93\u51fa\u6dfb\u52a0\u5230\u6df1\u5c42\uff0c\u4ee5\u4fdd\u7559\u8282\u70b9\u8868\u793a\u7684\u5c40\u90e8\u4fe1\u606f\uff08Chen et al., 2020b\uff09\u3002\u6b64\u5916\uff0c\u6700\u8fd1\u7684\u7814\u7a76\uff08Zeng et al., 2021; Zhang & Li, 2021; Wijesinghe & Wang, 2022\uff09\u5229\u7528\u5c40\u90e8\u90bb\u57df\u7684\u7ed3\u6784\u4fe1\u606f\u8bbe\u8ba1\u9ad8\u6548\u7684\u6d88\u606f\u4f20\u9012\u805a\u5408\u65b9\u6848\uff0c\u4ee5\u589e\u5f3aGNNs\u7684\u8868\u8fbe\u80fd\u529b\u3002\u8fd9\u4e9b\u5de5\u4f5c\u8868\u660e\uff0c\u5c40\u90e8\u4fe1\u606f\u5728\u8bad\u7ec3GNN\u6a21\u578b\u548c\u8bbe\u8ba1\u5f3a\u5927\u7684GNNs\u4e2d\u8d77\u7740\u91cd\u8981\u4f5c\u7528\u3002<\/p>\n\n\n\n

note<\/h3>\n\n\n\n

\u6ca1\u6709\u7528\u6b8b\u5dee\u7684GNNs,\u8fd9\u4f1a\u5bfc\u81f4\u4e00\u4e2a\u95ee\u9898\uff0c\u5982\u679c\u56fe\u6709\u591a\u5c42\uff0c\u90a3\u4e48\u7ecf\u8fc7\u591a\u6b21\u7684\u4fe1\u606f\u6d41\u52a8\uff0c\u8d8a\u9760\u8fd1\u521a\u5f00\u59cb\u521d\u59cb\u5c42\u7684\u4fe1\u606f\u8d8a\u6765\u8d8a\u88ab\u6de1\u5316\uff0c\u540e\u9762\u5c42\u6b21\u6240\u83b7\u53d6\u5230\u7684\u4fe1\u606f\u90fd\u9010\u6e10\u5e73\u5747\u5316\uff0c\u5927\u5bb6\u7684\u4fe1\u606f\u90fd\u5feb\u76f8\u540c\u4e86\uff0c\u6ca1\u6709\u4fdd\u7559\u5230\u5404\u81ea\u7279\u6709\u7684\u4fe1\u606f\uff0c\u6b8b\u5dee\u5c31\u662f\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u7684\uff0c\u6b8b\u5dee\u5f88\u7b80\u5355\u7684\u7406\u89e3\u5c31\u662f\u6211\u8fd9\u4e00\u5c42\u52a0\u4e0a\u4e0a\u4e00\u5c42\u7684\u4fe1\u606f\uff0c\u8fd9\u6837\u53ef\u4ee5\u4fdd\u8bc1\u6bcf\u6b21\u90fd\u662fnew+old\uff0c\u5373\u4f7f\u4e0d\u505c\u7684\u5411\u4e0a\u6d41\u52a8\uff0c\u7b2c\u4e00\u5c42\u7684\u4fe1\u606f\u4f9d\u7136\u53ef\u4ee5\u88ab\u5e26\u5230\u4e0a\u5c42\u53bb\uff0c\u8fd9\u6837\u5c31\u53ef\u4ee5\u89e3\u51b3\u5e73\u6ed1\u95ee\u9898\u3002<\/p>\n\n\n\n

# \u4f20\u7edfGNN\uff1a\u4fe1\u606f\u9010\u6e10\u5e73\u5747\u5316
def traditional_gnn_problem():
    # \u7b2c1\u5c42\uff1a\u6bcf\u4e2a\u8282\u70b9\u8fd8\u4fdd\u7559\u81ea\u5df1\u7684\u7279\u8272
    layer1 = {
        \"\u8282\u70b9A\": \"\u539f\u59cb\u7279\u5f81A + \u90bb\u5c451\u4fe1\u606f\",
        \"\u8282\u70b9B\": \"\u539f\u59cb\u7279\u5f81B + \u90bb\u5c452\u4fe1\u606f\", 
        \"\u8282\u70b9C\": \"\u539f\u59cb\u7279\u5f81C + \u90bb\u5c453\u4fe1\u606f\"
    }
    
    # \u7b2c2\u5c42\uff1a\u5f00\u59cb\u5e73\u5747\u5316
    layer2 = {
        \"\u8282\u70b9A\": \"\u5e73\u5747\u5316\u4fe1\u606f + \u66f4\u591a\u90bb\u5c45\u4fe1\u606f\",
        \"\u8282\u70b9B\": \"\u5e73\u5747\u5316\u4fe1\u606f + \u66f4\u591a\u90bb\u5c45\u4fe1\u606f\",
        \"\u8282\u70b9C\": \"\u5e73\u5747\u5316\u4fe1\u606f + \u66f4\u591a\u90bb\u5c45\u4fe1\u606f\"
    }
    
    # \u7b2c3\u5c42\uff1a\u4e25\u91cd\u5e73\u5747\u5316
    layer3 = {
        \"\u8282\u70b9A\": \"\u51e0\u4e4e\u76f8\u540c\u7684\u5168\u5c40\u4fe1\u606f\",
        \"\u8282\u70b9B\": \"\u51e0\u4e4e\u76f8\u540c\u7684\u5168\u5c40\u4fe1\u606f\",  # \u4e0eA\u51e0\u4e4e\u4e00\u6837
        \"\u8282\u70b9C\": \"\u51e0\u4e4e\u76f8\u540c\u7684\u5168\u5c40\u4fe1\u606f\"   # \u4e0eA\u3001B\u51e0\u4e4e\u4e00\u6837
    }
    
    # \u7ed3\u679c\uff1a\u6240\u6709\u8282\u70b9\u5931\u53bb\u72ec\u7279\u6027\uff01
    # \u6b8b\u5deeGNN\uff1anew + old \u4fdd\u6301\u72ec\u7279\u6027
def residual_gnn_solution():
    # \u7b2c1\u5c42\uff1anew + old
    layer1 = {
        \"\u8282\u70b9A\": \"\u65b0\u5b66\u5230\u7684\u4fe1\u606fA + \u539f\u59cb\u7279\u5f81A\",
        \"\u8282\u70b9B\": \"\u65b0\u5b66\u5230\u7684\u4fe1\u606fB + \u539f\u59cb\u7279\u5f81B\",
        \"\u8282\u70b9C\": \"\u65b0\u5b66\u5230\u7684\u4fe1\u606fC + \u539f\u59cb\u7279\u5f81C\"
    }
    
    # \u7b2c2\u5c42\uff1anew + old\uff08old\u5305\u542b\u4e86\u7b2c1\u5c42\u7684\u4fe1\u606f\uff09
    layer2 = {
        \"\u8282\u70b9A\": \"\u65b0\u5b66\u5230\u7684\u4fe1\u606fA + \u7b2c1\u5c42\u4fe1\u606fA\",
        \"\u8282\u70b9B\": \"\u65b0\u5b66\u5230\u7684\u4fe1\u606fB + \u7b2c1\u5c42\u4fe1\u606fB\", 
        \"\u8282\u70b9C\": \"\u65b0\u5b66\u5230\u7684\u4fe1\u606fC + \u7b2c1\u5c42\u4fe1\u606fC\"
    }
    
    # \u7b2c3\u5c42\uff1anew + old\uff08old\u5305\u542b\u4e86\u524d\u9762\u6240\u6709\u5c42\u7684\u4fe1\u606f\uff09
    layer3 = {
        \"\u8282\u70b9A\": \"\u65b0\u5b66\u5230\u7684\u4fe1\u606fA + \u524d\u9762\u6240\u6709\u5c42\u4fe1\u606fA\",
        \"\u8282\u70b9B\": \"\u65b0\u5b66\u5230\u7684\u4fe1\u606fB + \u524d\u9762\u6240\u6709\u5c42\u4fe1\u606fB\",
        \"\u8282\u70b9C\": \"\u65b0\u5b66\u5230\u7684\u4fe1\u606fC + \u524d\u9762\u6240\u6709\u5c42\u4fe1\u606fC\"
    }
    
    # \u7ed3\u679c\uff1a\u6bcf\u4e2a\u8282\u70b9\u90fd\u4fdd\u6301\u72ec\u7279\u6027\uff01<\/pre>\n\n\n\n
\u5c3d\u7ba1GNNs\u5728\u4ece\u5c40\u90e8\u90bb\u57df\u5b66\u4e60\u8282\u70b9\u8868\u793a\u65b9\u9762\u53d6\u5f97\u4e86\u8fdb\u5c55\uff0c\u4f46\u5c40\u90e8\u90bb\u57df\u4fe1\u606f\u662f\u5426\u8db3\u4ee5\u83b7\u5f97\u6709\u6548\u7684\u8282\u70b9\u8868\u793a\uff0c\u7279\u522b\u662f\u5bf9\u4e8e\u90bb\u5c45\u6570\u91cf\u6709\u9650\u7684\u8282\u70b9\uff0c\u4ecd\u7136\u662f\u4e00\u4e2a\u5f00\u653e\u95ee\u9898\u3002\u6211\u4eec\u8ba4\u4e3a\uff0c\u5c40\u90e8\u90bb\u57df\u4e2d\u6709\u9650\u7684\u90bb\u5c45\u6570\u91cf\u9650\u5236\u4e86GNNs\u7684\u8868\u8fbe\u80fd\u529b\u5e76\u963b\u788d\u4e86\u5b83\u4eec\u7684\u6027\u80fd\uff0c\u7279\u522b\u662f\u5728\u6837\u672c\u7a00\u7f3a\u7684\u60c5\u51b5\u4e0b\uff0c\u67d0\u4e9b\u8282\u70b9\u53ea\u6709\u5f88\u5c11\u7684\u90bb\u5c45\u3002\u5806\u53e0\u56fe\u5c42<\/mark>\u4ee5\u6269\u5927\u611f\u53d7\u91ce\u53ef\u4ee5\u878d\u5165\u591a\u8df3\u90bb\u57df\u4fe1\u606f\uff0c\u4f46\u4f1a\u5bfc\u81f4\u8fc7\u5e73\u6ed1\uff08Li et al., 2018\uff09<\/mark>\uff0c\u800c\u6ca1\u6709\u4e0e\u8f93\u5165\u7684\u6b8b\u5dee\u8fde\u63a5\uff0c\u8fd9\u4e0d\u662f\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u7684\u76f4\u63a5\u65b9\u6848\u3002\u73b0\u6709\u7684GNN\u6a21\u578b\u67b6\u6784\u5de5\u4f5c\u65e0\u6cd5\u89e3\u51b3\u975e\u5e38\u6709\u9650\u7684\u90bb\u5c45\u4e0d\u5229\u4e8e\u5b66\u4e60\u8282\u70b9\u8868\u793a\u7684\u95ee\u9898\u3002\u56e0\u6b64\uff0c\u8fd9\u91cc\u6211\u4eec\u4e13\u6ce8\u4e8e\u4e30\u5bcc\u4f4e\u5ea6\u8282\u70b9\u7684\u5c40\u90e8\u4fe1\u606f\u4ee5\u83b7\u5f97\u6709\u6548\u7684\u8868\u793a\u3002<\/p>\n\n\n\n
note<\/h3>\n\n\n\n
\u4ec0\u4e48\u662f\u5806\u53e0\u56fe\u5c42\uff1f\u5806\u53e0\u56fe\u5c42\u6d45\u663e\u7684\u4ece\u5b57\u9762\u610f\u601d\u6765\u8bb2\uff0c\u5c31\u662f\u628a\u4e00\u5c42\u5806\u5728\u53e6\u4e00\u5c42\u4e0a\u9762\uff0cGNN\u6709\u591a\u5c42\uff0c\u6211\u8ba1\u7b97\u7b2c\u4e8c\u5c42\u5c31\u5c06\u7b2c\u4e00\u5c42\u7684\u8f93\u51fa\u4f5c\u4e3a\u8f93\u5165\uff0c\u8ba1\u7b97\u7b2c\u4e09\u5c42\uff0c\u5c31\u5c06\u7b2c\u4e8c\u5c42\u7684\u8f93\u51fa\u4f5c\u4e3a\u8f93\u5165\uff0c\u6ce8\u610f\uff0c\u8fd9\u91cc\u662f\u4e0a\u4e00\u5c42\u7684\u8f93\u51fa\u4f5c\u4e3a\u8f93\u5165\uff0c\u4e0d\u662f\u5c06\u4e0a\u4e00\u5c42\uff0c\u6240\u4ee5\u6bcf\u4e00\u5c42\u7684\u8f93\u51fa\u90fd\u4f1a\u5728\u4e00\u5b9a\u5c42\u5ea6\u4e0a\u4fee\u6539\u4e86\u3002<\/p>\n\n\n\n
\u4ec0\u4e48\u662f\u611f\u53d7\u91ce\uff1f\u611f\u53d7\u91ce\u5c31\u662f\u4e00\u4e2a\u8282\u70b9\u53ef\u4ee5\u201c\u770b\u5230\u201d\u7684\u5176\u4ed6\u8282\u70b9\u7684\u8303\u56f4\uff0c\u5c31\u6bd4\u5982A\u6709\u90bb\u5c45B\u548cC\uff0cA\u7b2c\u4e00\u6b21\u662f\u53ea\u80fd\u770b\u5230\u81ea\u5df1\u7684\u76f4\u63a5\u90bb\u5c45B\u548cC\u7684\uff0c\u770b\u4e0d\u5230B\u548cC\u7684\u76f4\u63a5\u90bb\u5c45\u7684\uff0c\u4f46\u662f\u6269\u5927\u611f\u53d7\u91ce\u5c31\u53ef\u4ee5\u7136A\u9010\u6e10\u770b\u5230B\u548cC\u7684\u90bb\u5c45\uff0c\u6bcf\u6b21\u6269\u5927\uff0c\u53ef\u4ee5\u591a\u770b\u5230\u4e00\u5c42\u90bb\u5c45\uff0c\u8fd9\u5f88\u50cf\u8ba1\u7b97\u673a\u7f51\u7edc\u4e2d\u7684\u4e00\u4e2a\u7b97\u6cd5\uff0c\u597d\u50cf\u662f\u6d2a\u6c34\u704c\u6e89\uff0c\u90a3\u4e3a\u5565\u4f1a\u5bfc\u81f4\u8fc7\u5e73\u6ed1\u5462\uff0c\u5f88\u660e\u663e\uff0c\u540e\u9762\u7684\u8282\u70b9\u770b\u5230\u7684\u90fd\u4e00\u6837\u4e86\uff0c\u90a3\u5404\u81ea\u7684\u4fe1\u606f\u4e0d\u5c31\u5dee\u4e0d\u591a\u4e86\uff0c\u5e73\u5747\u5316\u4e86\uff0c\u81ea\u7136\u5c31\u8fc7\u5e73\u6ed1\u4e86\u3002\u8be6\u7ec6\u53ef\u4ee5\u770b\u4e0b\u9762\u7684\u4ee3\u7801<\/p>\n\n\n\n
# \u611f\u53d7\u91ce = \u4e00\u4e2a\u8282\u70b9\u80fd\u591f\"\u770b\u5230\"\u7684\u5176\u4ed6\u8282\u70b9\u7684\u8303\u56f4
def receptive_field():
    # \u7b2c1\u5c42\uff1a\u6bcf\u4e2a\u8282\u70b9\u53ea\u80fd\u770b\u5230\u76f4\u63a5\u90bb\u5c45\uff081\u8df3\uff09
    layer1_receptive_field = {
        \"\u8282\u70b9A\": [\"\u90bb\u5c451\", \"\u90bb\u5c452\"],
        \"\u8282\u70b9B\": [\"\u90bb\u5c453\", \"\u90bb\u5c454\", \"\u90bb\u5c455\"]
    }
    
    # \u7b2c2\u5c42\uff1a\u6bcf\u4e2a\u8282\u70b9\u53ef\u4ee5\u770b\u5230\u90bb\u5c45\u7684\u90bb\u5c45\uff082\u8df3\uff09
    layer2_receptive_field = {
        \"\u8282\u70b9A\": [\"\u90bb\u5c451\", \"\u90bb\u5c452\", \"\u90bb\u5c451\u7684\u90bb\u5c45\", \"\u90bb\u5c452\u7684\u90bb\u5c45\"],
        \"\u8282\u70b9B\": [\"\u90bb\u5c453\", \"\u90bb\u5c454\", \"\u90bb\u5c455\", \"\u90bb\u5c453\u7684\u90bb\u5c45\", \"\u90bb\u5c454\u7684\u90bb\u5c45\", \"\u90bb\u5c455\u7684\u90bb\u5c45\"]
    }
    
    # \u7b2c3\u5c42\uff1a\u6bcf\u4e2a\u8282\u70b9\u53ef\u4ee5\u770b\u52303\u8df3\u8303\u56f4\u5185\u7684\u6240\u6709\u8282\u70b9
    layer3_receptive_field = {
        \"\u8282\u70b9A\": [\"1\u8df3\u90bb\u5c45\", \"2\u8df3\u90bb\u5c45\", \"3\u8df3\u90bb\u5c45\"],
        \"\u8282\u70b9B\": [\"1\u8df3\u90bb\u5c45\", \"2\u8df3\u90bb\u5c45\", \"3\u8df3\u90bb\u5c45\"]
    }
    # \u8fc7\u5e73\u6ed1\u73b0\u8c61
def over_smoothing_example():
    # \u521d\u59cb\u72b6\u6001\uff1a\u6bcf\u4e2a\u8282\u70b9\u6709\u72ec\u7279\u7279\u5f81
    initial_features = {
        \"\u8282\u70b9A\": [1, 0, 0, 0],  # \u79d1\u6280\u7231\u597d\u8005
        \"\u8282\u70b9B\": [0, 1, 0, 0],  # \u65f6\u5c1a\u8fbe\u4eba
        \"\u8282\u70b9C\": [0, 0, 1, 0],  # \u8fd0\u52a8\u7231\u597d\u8005
        \"\u8282\u70b9D\": [0, 0, 0, 1]   # \u7f8e\u98df\u5bb6
    }
    
    # \u7b2c1\u5c42\u540e\uff1a\u5f00\u59cb\u6df7\u5408
    layer1_features = {
        \"\u8282\u70b9A\": [0.7, 0.1, 0.1, 0.1],
        \"\u8282\u70b9B\": [0.1, 0.7, 0.1, 0.1],
        \"\u8282\u70b9C\": [0.1, 0.1, 0.7, 0.1],
        \"\u8282\u70b9D\": [0.1, 0.1, 0.1, 0.7]
    }
    
    # \u7b2c3\u5c42\u540e\uff1a\u4e25\u91cd\u5e73\u5747\u5316
    layer3_features = {
        \"\u8282\u70b9A\": [0.3, 0.3, 0.2, 0.2],  # \u5931\u53bb\u72ec\u7279\u6027
        \"\u8282\u70b9B\": [0.3, 0.3, 0.2, 0.2],  # \u4e0eA\u51e0\u4e4e\u76f8\u540c
        \"\u8282\u70b9C\": [0.3, 0.3, 0.2, 0.2],  # \u4e0eA\u3001B\u51e0\u4e4e\u76f8\u540c
        \"\u8282\u70b9D\": [0.3, 0.3, 0.2, 0.2]   # \u4e0eA\u3001B\u3001C\u51e0\u4e4e\u76f8\u540c
    }<\/pre>\n\n\n\n
\u4e00\u4e2a\u6709\u524d\u666f\u7684\u89e3\u51b3\u65b9\u6848\u662f\u901a\u8fc7\u6570\u636e\u589e\u5f3a\u5728\u5c40\u90e8\u90bb\u57df\u4e2d\u751f\u6210\u66f4\u591a\u6837\u672c\u3002\u6570\u636e\u589e\u5f3a\u5728\u8ba1\u7b97\u673a\u89c6\u89c9\uff08Shorten & Khoshgoftaar, 2019; Cubuk et al., 2019; Zhao et al., 2019; Dong et al., 2022\uff09\u548c\u81ea\u7136\u8bed\u8a00\u5904\u7406\uff08Fadaee et al., 2017; \u015eahin & Steedman, 2019; Xia et al., 2019\uff09\u4e2d\u5f97\u5230\u4e86\u5145\u5206\u7814\u7a76\uff0c\u4f46\u5728\u56fe\u7ed3\u6784\u6570\u636e\u4e0a\u4ecd\u7136\u63a2\u7d22\u4e0d\u8db3\u3002\u73b0\u6709\u7684\u56fe\u6570\u636e\u589e\u5f3a\u65b9\u6cd5\u53ea\u4ece\u5168\u5c40\u89d2\u5ea6\u5728\u62d3\u6251\u7ea7\u522b\u548c\u7279\u5f81\u7ea7\u522b\u8fdb\u884c\u6270\u52a8\uff0c\u53ef\u4ee5\u5206\u4e3a\u4e24\u7c7b\uff1a\u62d3\u6251\u7ea7\u522b\u589e\u5f3a\uff08Rong et al., 2020; Zhao et al., 2021\uff09\u548c\u7279\u5f81\u7ea7\u522b\u589e\u5f3a\uff08Deng et al., 2019; Feng et al., 2019; Kong et al., 2020; Fang et al., 2021\uff09\u3002\u62d3\u6251\u7ea7\u522b\u589e\u5f3a\u6270\u52a8\u90bb\u63a5\u77e9\u9635\uff0c\u4ea7\u751f\u4e0d\u540c\u7684\u56fe\u7ed3\u6784\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u73b0\u6709\u7684\u7279\u5f81\u7ea7\u522b\u589e\u5f3a\uff08Deng et al., 2019; Feng et al., 2019; Kong et al., 2020\uff09\u5229\u7528\u5bf9\u6297\u8bad\u7ec3\u6307\u5bfc\u7684\u8282\u70b9\u5c5e\u6027\u6270\u52a8\u6765\u63d0\u5347\u6cdb\u5316\u80fd\u529b\u3002\u8fd9\u4e9b\u589e\u5f3a\u6280\u672f\u6709\u4e00\u4e2a\u7a81\u51fa\u7684\u7f3a\u70b9\uff1a\u5b83\u4eec\u4e13\u6ce8\u4e8e\u5173\u4e8e\u6574\u4e2a\u56fe\u5206\u5e03\u5c5e\u6027\u7684\u5168\u5c40\u589e\u5f3a\uff0c\u800c\u4e0d\u662f\u5355\u4e2a\u8282\u70b9\uff0c\u5ffd\u7565\u4e86\u90bb\u57df\u7684\u5c40\u90e8\u4fe1\u606f\u3002<\/p>\n\n\n\n
\u5f53\u524d\u5de5\u4f5c\u3002\u5728\u8fd9\u9879\u5de5\u4f5c\u4e2d\uff0c\u4e3a\u4e86\u901a\u8fc7\u5c40\u90e8\u90bb\u57df\u4e2d\u66f4\u591a\u751f\u6210\u7684\u6837\u672c\u6765\u4fc3\u8fdb\u805a\u5408\u65b9\u6848\uff0c\u6211\u4eec\u63d0\u51fa\u4e86\u4e00\u4e2a\u65b0\u9896\u9ad8\u6548\u7684\u6570\u636e\u589e\u5f3a\u6846\u67b6\uff1a\u56fe\u795e\u7ecf\u7f51\u7edc\u7684\u5c40\u90e8\u589e\u5f3a\uff08LA-GNNs\uff09\u3002\u672f\u8bed”\u5c40\u90e8\u589e\u5f3a”\u6307\u7684\u662f\u901a\u8fc7\u4ee5\u5c40\u90e8\u7ed3\u6784\u548c\u8282\u70b9\u7279\u5f81\u4e3a\u6761\u4ef6\u7684\u751f\u6210\u6a21\u578b\u751f\u6210\u90bb\u57df\u7279\u5f81\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u6211\u4eec\u63d0\u51fa\u7684\u6846\u67b6\u5305\u62ec\u4e00\u4e2a\u9884\u8bad\u7ec3\u6b65\u9aa4\uff0c\u8be5\u6b65\u9aa4\u901a\u8fc7\u751f\u6210\u6a21\u578b\u5b66\u4e60\u7ed9\u5b9a\u4e00\u4e2a\u4e2d\u5fc3\u8282\u70b9\u7279\u5f81\u7684\u8fde\u63a5\u90bb\u5c45\u8282\u70b9\u7279\u5f81\u7684\u6761\u4ef6\u5206\u5e03\u3002\u5982\u56fe1\u6240\u793a\uff0c\u6211\u4eec\u7136\u540e\u5229\u7528\u8fd9\u4e2a\u5206\u5e03\u5728\u6bcf\u6b21\u8bad\u7ec3\u8fed\u4ee3\u4e2d\u751f\u6210\u4e0e\u6b64\u4e2d\u5fc3\u8282\u70b9\u76f8\u5173\u7684\u7279\u5f81\u5411\u91cf\u4f5c\u4e3a\u989d\u5916\u8f93\u5165\u3002\u6b64\u5916\uff0c\u6211\u4eec\u5c06\u751f\u6210\u6a21\u578b\u7684\u9884\u8bad\u7ec3\u548c\u4e0b\u6e38GNN\u8bad\u7ec3\u89e3\u8026\uff0c\u5141\u8bb8\u6211\u4eec\u7684\u6570\u636e\u589e\u5f3a\u6a21\u578b\u4ee5\u5373\u63d2\u5373\u7528\u7684\u65b9\u5f0f\u5e94\u7528\u4e8e\u4efb\u4f55GNN\u6a21\u578b\u3002<\/p>\n\n\n\n
\u6211\u4eec\u5728\u4e09\u4e2a\u6807\u51c6\u5f15\u7528\u7f51\u7edc\uff08Cora\u3001Citeseer\u3001Pubmed\uff09\u548c\u5f00\u653e\u56fe\u57fa\u51c6\uff08OGB\uff09\uff08Hu et al., 2020\uff09\u4e0a\u9a8c\u8bc1\u4e86LA-GNNs\u7684\u6709\u6548\u6027\u3002\u534a\u76d1\u7763\u8282\u70b9\u5206\u7c7b\u7684\u5e7f\u6cdb\u5b9e\u9a8c\u7ed3\u679c\u8868\u660e\uff0c\u6211\u4eec\u7684\u5c40\u90e8\u589e\u5f3a\u5b9e\u73b0\u4e86\u65b0\u7684\u6700\u5148\u8fdb\u6027\u80fd\uff1aLAGCN\u548cLAGAT\u5728Cora\u3001Citeseer\u548cPubmed\u4e0a\u5206\u522b\u6bd4GCN\u548cGAT\u5e73\u5747\u63d0\u9ad8\u4e863.4%\u548c1.6%\u7684\u6d4b\u8bd5\u51c6\u786e\u7387\u3002LAGNN\u5728\u5927\u89c4\u6a21OGB\u6570\u636e\u96c6\u4e0a\u4e5f\u83b7\u5f97\u4e86\u4f18\u8d8a\u7684\u6027\u80fd\u3002\u6211\u4eec\u8868\u660e\uff0c\u6211\u4eec\u7684\u6a21\u578b\u5728Pubmed\u4e0a\u5bf9\u4e8e\u5ea6\u5728[2,5]\u548c[6,20]\u8303\u56f4\u5185\u7684\u8282\u70b9\u5206\u522b\u63d0\u9ad8\u4e861.7%\u548c0.2%\u7684\u6d4b\u8bd5\u51c6\u786e\u7387\u3002\u6b64\u5916\uff0c\u6211\u4eec\u7684\u5c40\u90e8\u589e\u5f3a\u6a21\u578b\u5728\u8282\u70b9\u5206\u7c7b\u4efb\u52a1\u4e0a\u4f18\u4e8e\u5176\u4ed6\u7279\u5f81\/\u62d3\u6251\u7ea7\u522b\u589e\u5f3a\u6a21\u578b\uff0c\u5982G-GNN\uff08Zhu et al., 2020\uff09\u3001DropEdge\uff08Rong et al., 2020\uff09\u3001GRAND\uff08Feng et al., 2020\uff09\u548cGAUG\uff08Zhao et al., 2021\uff09\uff0c\u8fd9\u8bc1\u660e\u4e86\u6211\u4eec\u6a21\u578b\u7684\u4f18\u8d8a\u6027\u3002<\/p>\n\n\n\n
\u8d21\u732e\uff1a<\/p>\n\n\n\n
    \n
  • \u6211\u4eec\u63d0\u51fa\u4e86\u4e00\u79cd\u901a\u7528\u7684\u589e\u5f3a\u7b56\u7565\uff0c\u5728\u5c40\u90e8\u90bb\u57df\u4e2d\u751f\u6210\u66f4\u591a\u7279\u5f81\u4ee5\u589e\u5f3a\u73b0\u6709GNNs\u7684\u8868\u8fbe\u80fd\u529b\uff1b<\/li>\n\n\n\n
  • \u6211\u4eec\u63a2\u7d22\u4e86\u4e3a\u56fe\u9884\u8bad\u7ec3\u751f\u6210\u6a21\u578b\u4ee5\u63d0\u9ad8\u4e0b\u6e38\u4efb\u52a1\u6027\u80fd\u7684\u65b0\u65b9\u5411\uff1b<\/li>\n\n\n\n
  • \u6211\u4eec\u63d0\u51fa\u7684\u6846\u67b6\u662f\u7075\u6d3b\u7684\uff0c\u53ef\u4ee5\u5e94\u7528\u4e8e\u5404\u79cd\u6d41\u884c\u7684\u9aa8\u5e72\u7f51\u7edc\u3002\u5e7f\u6cdb\u7684\u5b9e\u9a8c\u7ed3\u679c\u8868\u660e\uff0c\u6211\u4eec\u63d0\u51fa\u7684\u6846\u67b6\u53ef\u4ee5\u6539\u5584GNN\u53d8\u4f53\u5728\u4e0d\u540c\u57fa\u51c6\u6570\u636e\u96c6\u4e0a\u7684\u6027\u80fd\u3002<\/li>\n<\/ul>\n\n\n\n
    2. \u9884\u5907\u77e5\u8bc6<\/h2>\n\n\n\n
    \u7b26\u53f7\u8868\u793a<\/h3>\n\n\n\n
    \u8bbe \u200b \u8868\u793a\u56fe\uff0c\u5176\u4e2d \u200b \u662f\u9876\u70b9\u96c6\u5408 \u200b\uff0c\u200b\uff0c\u200b \u662f\u8fb9\u96c6\u5408\u3002\u90bb\u63a5\u77e9\u9635\u5b9a\u4e49\u4e3a \u200b\uff0c\u5f53\u4e14\u4ec5\u5f53 \u200b \u65f6 \u200b\u3002\u8bbe \u200b \u8868\u793a\u8282\u70b9 \u200b \u7684\u90bb\u57df\uff0c\u200b \u8868\u793a\u5bf9\u89d2\u5ea6\u77e9\u9635\uff0c\u5176\u4e2d \u200b\u3002\u7279\u5f81\u77e9\u9635\u8868\u793a\u4e3a \u200b\uff0c\u5176\u4e2d\u6bcf\u4e2a\u8282\u70b9 \u200b \u4e0e\u4e00\u4e2a \u200b \u7ef4\u7279\u5f81\u5411\u91cf \u200b \u76f8\u5173\u8054\u3002\u200b \u8868\u793a\u72ec\u70ed\u6807\u7b7e\u77e9\u9635\uff0c\u5176\u4e2d \u200b \u662f\u72ec\u70ed\u5411\u91cf\uff0c\u5bf9\u4e8e\u4efb\u4f55 \u200b\uff0c\u200b\u3002<\/p>\n\n\n\n
    note<\/h3>\n\n\n\n
    \u4ec0\u4e48\u662f\u72ec\u70ed\u5411\u91cf\uff1f\u4ec0\u4e48\u662f\u72ec\u70ed\u77e9\u9635\uff1f\u72ec\u70ed\u72ec\u70ed\uff0c\u5b57\u9762\u4e0a\u6765\u770b\u5c31\u662f\u552f\u72ec\u4ed6\u662f\u70ed\u7684\uff0c\u8ba1\u7b97\u673a\u91cc\u90fd\u662f0,1,0,1\uff0c\u6240\u4ee5\u72ec\u70ed\u5411\u91cf\uff0c\u5c31\u662f\u4e00\u4e2a\u5411\u91cf\u4e2d\uff0c\u53ea\u6709\u4e00\u4e2a\u5143\u7d20\u662f1\uff0c\u5176\u4ed6\u5143\u7d20\u90fd\u662f0\uff0c\u53ef\u4ee5\u770b\u4e0b\u9762\u7684\u4f8b\u5b50\uff1a<\/p>\n\n\n\n
    # \u5047\u8bbe\u67094\u4e2a\u7c7b\u522b\uff1a\u79d1\u6280\u3001\u65f6\u5c1a\u3001\u8fd0\u52a8\u3001\u7f8e\u98df
    \u200b
    # \u72ec\u70ed\u5411\u91cf\u793a\u4f8b
    tech_vector = [1, 0, 0, 0]      # \u79d1\u6280\u7c7b\u522b
    fashion_vector = [0, 1, 0, 0]   # \u65f6\u5c1a\u7c7b\u522b
    sports_vector = [0, 0, 1, 0]    # \u8fd0\u52a8\u7c7b\u522b
    food_vector = [0, 0, 0, 1]      # \u7f8e\u98df\u7c7b\u522b
    \u200b
    # \u7279\u70b9\uff1a
    # 1. \u53ea\u6709\u4e00\u4e2a\u4f4d\u7f6e\u662f1
    # 2. \u5176\u4ed6\u4f4d\u7f6e\u90fd\u662f0
    # 3. \u6240\u6709\u5143\u7d20\u7684\u548c\u7b49\u4e8e1<\/pre>\n\n\n\n
    \u90a3\u72ec\u70ed\u77e9\u9635\u5c31\u597d\u7406\u89e3\u4e86\uff0c\u5c31\u662f\u7531\u591a\u4e2a\u72ec\u70ed\u5411\u91cf\u6784\u6210\u7684\u77e9\u9635\u561b<\/p>\n\n\n\n
    # \u5047\u8bbe\u67094\u4e2a\u7528\u6237\uff0c3\u4e2a\u7c7b\u522b\uff1a\u79d1\u6280\u7231\u597d\u8005\u3001\u65f6\u5c1a\u8fbe\u4eba\u3001\u8fd0\u52a8\u7231\u597d\u8005
    label_matrix = [
        [1, 0, 0],    # \u7528\u62371: \u79d1\u6280\u7231\u597d\u8005
        [0, 1, 0],    # \u7528\u62372: \u65f6\u5c1a\u8fbe\u4eba
        [0, 0, 1],    # \u7528\u62373: \u8fd0\u52a8\u7231\u597d\u8005
        [1, 0, 0]     # \u7528\u62374: \u79d1\u6280\u7231\u597d\u8005
    ]
    \u200b
    # \u77e9\u9635\u5f62\u72b6: 4\u00d73 (4\u4e2a\u8282\u70b9\uff0c3\u4e2a\u7c7b\u522b)<\/pre>\n\n\n\n
    \u56fe\u795e\u7ecf\u7f51\u7edc<\/h3>\n\n\n\n
    \u8bb8\u591a\u6d41\u884c\u7684\u56fe\u795e\u7ecf\u7f51\u7edc\uff08GNNs\uff09\u76f4\u63a5\u5728\u56fe\u7ed3\u6784\u4e0a\u64cd\u4f5c\uff0c\u5e76\u901a\u8fc7\u56fe\u4e2d\u8282\u70b9\u4e4b\u95f4\u7684\u6d88\u606f\u4f20\u9012\u6765\u6355\u83b7\u56fe\u7684\u4f9d\u8d56\u6027\u3002\u5b83\u4eec\u91cd\u590d\u805a\u5408\u8282\u70b9 \u200b \u7684\u76f4\u63a5\u90bb\u5c45 \u200b \u7684\u8868\u793a\uff0c\u5e76\u5c06\u805a\u5408\u7684\u4fe1\u606f\u4e0e\u5176\u8868\u793a\u5411\u91cf\u7ed3\u5408\u4ee5\u83b7\u5f97\u8868\u793a\u5411\u91cf \u200b\u3002GNN\u6d88\u606f\u4f20\u9012\u65b9\u6848\u7684\u7b2c \u200b \u5c42\u662f\uff1a<\/p>\n\n\n\n
    \u200b<\/p>\n\n\n\n
    \u5176\u4e2d \u200b \u548c \u200b \u5206\u522b\u8868\u793aCOMBINE\u548cAGGREGATE\u51fd\u6570\uff0c\u200b \u662f\u8282\u70b9 \u200b \u5728\u7b2c \u200b \u5c42\u7684\u8868\u793a\u5411\u91cf\uff0c\u200b \u662f\u8282\u70b9 \u200b \u548c \u200b \u4e4b\u95f4\u7684\u8fb9\u5411\u91cf\u3002\u5177\u4f53\u5730\uff0c\u200b\u3002<\/p>\n\n\n\n
    note<\/h3>\n\n\n\n
    AGG\u8868\u793a\u805a\u5408\u51fd\u6570AGGREGAT\uff0c\u805a\u5408\u805a\u5408\u5c31\u662f\u5c06\u591a\u4e2a\u5411\u91cf\u5408\u6210\u4e00\u4e2a\uff0c\u6bd4\u5982\u5f53\u524d\u4e2d\u5fc3\u8282\u70b9\u6709\u4e09\u4e2a\u90bb\u5c45\u5411\u91cfA[1,2,3],B[2,3,4],C[3,4,5],\u90a3\u4e48AGG([A,B,C]) = [1+2+3,2+3+4,3+4+5] ( \u5047\u8bbe\u662f\u6c42\u548c\u805a\u5408) \uff0c\u5e38\u89c1\u7684\u805a\u5408\u8fd8\u6709\u6700\u5927\u503c\u805a\u5408\uff0c\u6ce8\u610f\u529b\u805a\u5408\uff0c\u6ce8\u610f\u529b\u805a\u5408\u66f4\u50cf\u662f\u52a0\u6743\u805a\u5408\u4e00\u6837\u7684\uff0c\u53ef\u80fd\u6211\u7406\u89e3\u7684\u6709\u8bef\u3002<\/p>\n\n\n\n
    COMBINE\u51fd\u6570\u7684\u4f5c\u7528\u662f\u5c06\u8282\u70b9\u81ea\u8eab\u7684\u4fe1\u606f\u4e0e\u805a\u5408\u7684\u90bb\u5c45\u4fe1\u606f\u7ed3\u5408\u8d77\u6765\uff0c\u751f\u6210\u65b0\u7684\u8282\u70b9\u8868\u793a\u3002\u90a3COMBINE\u5982\u4f55\u5c06\u4e0d\u540c\u4fe1\u606f\u7ed3\u5408\u8d77\u6765\u5462\uff0c\u6211\u67e5\u4e86\u4e00\u4e0b\uff0c\u8fd9\u91cc\u6709\u4e00\u4e9b\u5e38\u89c1\u7684\uff0c\u5982\u62fc\u63a5+\u7ebf\u6027\u53d8\u6362\uff0c\u52a0\u6743\u5e73\u5747\uff0c\u95e8\u63a7\u673a\u5236\uff0c\u6b8b\u5dee\u8fde\u63a5\u7b49\u7b49\uff0c\u5177\u4f53\u53ef\u4ee5\u770b\u4e0b\u9762\u7684\u4ee3\u7801\uff1a<\/p>\n\n\n\n
    def concat_combine(self_info, neighbor_info):
        # \u62fc\u63a5\u81ea\u8eab\u4fe1\u606f\u548c\u90bb\u5c45\u4fe1\u606f
        combined = concatenate(self_info, neighbor_info)
        # combined = [1, 0, 0, 0, 0.5, 0.5]
        
        # \u901a\u8fc7\u7ebf\u6027\u53d8\u6362\u964d\u7ef4
        output = linear_transform(combined)
        # output = [0.7, 0.2, 0.1]  # \u65b0\u7684\u8868\u793a
        
        return output
    def weighted_combine(self_info, neighbor_info, alpha=0.5):
        # \u52a0\u6743\u7ed3\u5408\u81ea\u8eab\u4fe1\u606f\u548c\u90bb\u5c45\u4fe1\u606f
        output = alpha * self_info + (1 - alpha) * neighbor_info
        
        return output
    def gated_combine(self_info, neighbor_info):
        # \u5b66\u4e60\u4e00\u4e2a\u95e8\u63a7\u5411\u91cf\uff0c\u51b3\u5b9a\u4fdd\u7559\u591a\u5c11\u81ea\u8eab\u4fe1\u606f
        gate = sigmoid(linear_transform(self_info + neighbor_info))
        
        # \u95e8\u63a7\u7ed3\u5408
        output = gate * self_info + (1 - gate) * neighbor_info
        
        return output
    def residual_combine(self_info, neighbor_info):
        # \u6b8b\u5dee\u8fde\u63a5\uff1a\u81ea\u8eab\u4fe1\u606f + \u90bb\u5c45\u4fe1\u606f
        output = self_info + neighbor_info
        
        return output
    \u200b<\/pre>\n\n\n\n
    \u90a3\u516c\u5f0f\u662f\u4ec0\u4e48\u610f\u601d\u5462\uff0c\u516c\u5f0f\u5c31\u662f\u8868\u793a\u8ba1\u7b97\u8282\u70b9v\u5728\u7b2ck\u5c42\u7684\u8868\u793a = COMBINE(v\u5728\u7b2ck-1\u5c42\u7684\u8868\u793a,AGG(\u6240\u6709\u90bb\u5c45\u8282\u70b9\u5728k-1\u5c42\u7684\u8868\u793a)),\u770b\u4e0b\u9762\u7684\u4f8b\u5b50\u5c31\u4f1a\u6e05\u695a\u5f88\u591a\u4e86\uff1a<\/p>\n\n\n\n
    def gnn_layer_computation():
        # \u5047\u8bbe\u8282\u70b9v\u67093\u4e2a\u90bb\u5c45\uff1au1, u2, u3
        
        # \u8f93\u5165
        h_v_prev = [1, 0, 0]      # \u8282\u70b9v\u4e0a\u4e00\u5c42\u7684\u8868\u793a
        h_u1_prev = [0, 1, 0]     # \u90bb\u5c45u1\u4e0a\u4e00\u5c42\u7684\u8868\u793a
        h_u2_prev = [0, 0, 1]     # \u90bb\u5c45u2\u4e0a\u4e00\u5c42\u7684\u8868\u793a
        h_u3_prev = [1, 1, 0]     # \u90bb\u5c45u3\u4e0a\u4e00\u5c42\u7684\u8868\u793a
        
        # \u6b65\u9aa41\uff1a\u805a\u5408\u90bb\u5c45\u4fe1\u606f
        neighbor_features = [h_u1_prev, h_u2_prev, h_u3_prev]
        aggregated = mean_aggregate(neighbor_features)  # \u5047\u8bbe\u4f7f\u7528\u5e73\u5747\u805a\u5408
        # aggregated = [0.33, 0.67, 0.33]
        
        # \u6b65\u9aa42\uff1a\u7ec4\u5408\u81ea\u8eab\u4fe1\u606f\u548c\u805a\u5408\u4fe1\u606f
        h_v_new = combine(h_v_prev, aggregated)
        # h_v_new = [0.67, 0.33, 0.17]  # \u65b0\u7684\u8868\u793a
        
        return h_v_new<\/pre>\n\n\n\n
    \u56fe\u795e\u7ecf\u7f51\u7edc\u7684\u5c40\u90e8\u589e\u5f3a\uff08LAGNN\uff09<\/h2>\n\n\n\n
    \u5728\u672c\u8282\u4e2d\uff0c\u6211\u4eec\u9996\u5148\u4ecb\u7ecd\u5982\u4f55\u901a\u8fc7\u751f\u6210\u6a21\u578b\u5728\u5c40\u90e8\u90bb\u57df\u4e2d\u751f\u6210\u66f4\u591a\u6837\u672c\u3002\u7136\u540e\u6211\u4eec\u4ece\u6982\u7387\u89d2\u5ea6\u5c55\u793a\u5982\u4f55\u89e3\u8026\u751f\u6210\u6a21\u578b\u7684\u9884\u8bad\u7ec3\u548c\u4e0b\u6e38GNN\u8bad\u7ec3\uff0c\u4f7f\u5f97\u6211\u4eec\u7684\u5c40\u90e8\u589e\u5f3a\u6a21\u578b\u53ef\u4ee5\u4ee5\u5373\u63d2\u5373\u7528\u7684\u65b9\u5f0f\u5e94\u7528\u4e8e\u4efb\u4f55GNN\u6a21\u578b\u3002\u63a5\u7740\u6211\u4eec\u4ecb\u7ecdLA-GNNs\u7684\u67b6\u6784\u548c\u8bad\u7ec3\u7ec6\u8282\u3002\u6574\u4f53\u6846\u67b6\u5982\u56fe1\u6240\u793a\u3002<\/p>\n\n\n\n
    \"image.png\"\/<\/div><\/figure>\n\n\n\n
    \u56fe1. \u6211\u4eec\u5c40\u90e8\u589e\u5f3a\u7684\u793a\u610f\u56fe\u3002\u56fe\u4e0a\u7684\u9ec4\u8272\u5706\u5708\u5bf9\u5e94\u90bb\u5c45\u8282\u70b9\u3002\u5047\u8bbe\u6211\u4eec\u5df2\u7ecf\u5b66\u4e60\u4e86\u5c40\u90e8\u90bb\u57df\u7684\u5206\u5e03\u3002\u6211\u4eec\u4ece\u5c40\u90e8\u90bb\u57df\u5206\u5e03\u751f\u6210\u7279\u5f81\u3002\u7136\u540e\u6211\u4eec\u5c06\u539f\u59cb\u7279\u5f81\u548c\u751f\u6210\u7684\u7279\u5f81\u4f5c\u4e3a\u4e0b\u6e38GNNs\u7684\u8f93\u5165\u3002<\/p>\n\n\n\n
    note<\/h3>\n\n\n\n
    \u8fd9\u5f20\u56fe\u4e2d\u9009\u4e86\u4e94\u4e2a\u4e0d\u540c\u989c\u8272\u7684\u70b9\uff0c\u5047\u8bbe\u8fd9\u51e0\u4e2a\u70b9\u7684\u90bb\u5c45\u6bd4\u8f83\u5c11\uff0c\u4fe1\u606f\u4e0d\u8db3\uff0c\u6240\u4ee5\u6211\u4eec\u8981\u91c7\u53d6\u5c40\u90e8\u589e\u5f3a\uff0c\u4e3a\u8fd9\u4e94\u4e2a\u4e0d\u540c\u989c\u8272\u7684\u70b9\u6dfb\u52a0\u865a\u62df\u90bb\u5c45\uff0c\u56fe\u4e2d\u5de6\u4e0a\u65b9\u5c31\u662f\u8868\u793a\u539f\u59cb\u8fd9\u4e94\u4e2a\u70b9\u7684\u7279\u5f81\u5411\u91cf\uff0c\u7136\u540e\u5de6\u4e0b\u65b9\u7684\u56fe\u5c31\u662f\u8868\u793a\u5bf9\u8fd9\u4e94\u4e2a\u8282\u70b9\u8fdb\u884c\u751f\u6210\u865a\u62df\u90bb\u5c45\u7684\u64cd\u4f5c\uff0c\u6bcf\u4e2a\u8282\u70b9\u751f\u6210\u4e00\u5b9a\u6570\u91cf\u7684\u865a\u62df\u90bb\u5c45\uff0c\u9ec4\u8272\u8282\u70b9\u5c31\u662f\u8868\u793a\u865a\u62df\u90bb\u5c45\uff0c\u7136\u540e\u518d\u5c06\u771f\u5b9e\u7684\u7279\u5f81\u5411\u91cf\u4e0e\u751f\u6210\u7684\u865a\u62df\u7279\u5f81\u5411\u91cf\u8fdb\u884c\u7ed3\u5408\uff0c\u4e00\u8d77\u4f20\u9012\u7ed9\u4e0b\u6e38\u7684GNN\u8bad\u7ec3\uff0c\u8fd9\u5f20\u56fe\u5c31\u662f\u9610\u8ff0\u4e86LAGNN\u7684\u6838\u5fc3\u601d\u60f3\u3002<\/p>\n\n\n\n
    3.1. \u5c40\u90e8\u589e\u5f3a\u52a8\u673a<\/h2>\n\n\n\n
    \u73b0\u6709\u7684GNNs\u4e13\u6ce8\u4e8e\u8bbe\u8ba1\u6d88\u606f\u4f20\u9012\u65b9\u6848\u6765\u5229\u7528\u5c40\u90e8\u4fe1\u606f\u4ee5\u83b7\u5f97\u8282\u70b9\u8868\u793a\u3002\u6211\u4eec\u63a2\u7d22\u4e86\u4e00\u4e2a\u65b0\u65b9\u5411\uff0c\u5373\u6211\u4eec\u53ef\u4ee5\u5728\u5c40\u90e8\u90bb\u57df\u4e2d\u751f\u6210\u66f4\u591a\u6837\u672c\uff0c\u7279\u522b\u662f\u5bf9\u4e8e\u90bb\u5c45\u8f83\u5c11\u7684\u8282\u70b9\uff0c\u4ee5\u589e\u5f3a\u5404\u79cdGNNs\u7684\u8868\u8fbe\u80fd\u529b\u3002\u4e3a\u4e86\u5728\u8282\u70b9v\u7684\u90bb\u57df\u200b\u4e2d\u4ea7\u751f\u66f4\u591a\u6837\u672c\uff0c\u6211\u4eec\u9700\u8981\u77e5\u9053\u5176\u90bb\u5c45\u8282\u70b9\u8868\u793a\u7684\u6982\u7387\u5206\u5e03\u3002\u7531\u4e8e\u8fd9\u4e2a\u5206\u5e03\u4e0e\u4e2d\u5fc3\u8282\u70b9v\u76f8\u5173\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u751f\u6210\u6a21\u578b\u4ee5\u4e2d\u5fc3\u8282\u70b9\u7684\u8868\u793a\u4e3a\u6761\u4ef6\u6765\u5b66\u4e60\u5b83\u3002<\/p>\n\n\n\n
    \u4f18\u52bf<\/strong>\u3002\u4e0e\u4e3a\u6bcf\u4e2a\u8282\u70b9\u8bad\u7ec3\u751f\u6210\u6a21\u578b\u76f8\u6bd4\uff0c\u4e3a\u6240\u6709\u8282\u70b9\u8bad\u7ec3\u5355\u4e2a\u751f\u6210\u6a21\u578b\u6709\u4e09\u4e2a\u4f18\u52bf\uff1a1\uff09\u901a\u8fc7\u751f\u6210\u6a21\u578b\u5b66\u4e60\u56fe\u4e2d\u6240\u6709\u8282\u70b9\u7684\u6761\u4ef6\u5206\u5e03\u964d\u4f4e\u4e86\u8ba1\u7b97\u6210\u672c\u30022\uff09\u5728\u751f\u6210\u9636\u6bb5\uff0c\u6211\u4eec\u53ef\u4ee5\u5e94\u7528\u7279\u5b9a\u8282\u70b9\u7684\u7279\u5f81\u5411\u91cf\u4f5c\u4e3a\u8f93\u5165\uff08\u6761\u4ef6\uff09\u5e76\u751f\u6210\u4e0e\u6b64\u8282\u70b9\u76f8\u5173\u7684\u7279\u5f81\u5411\u91cf\u30023\uff09\u5b83\u5177\u6709\u66f4\u597d\u7684\u53ef\u6269\u5c55\u6027\u548c\u6cdb\u5316\u6027\u3002\u5bf9\u4e8e\u6dfb\u52a0\u5230\u52a8\u6001\u56fe\u4e2d\u7684\u65b0\u8282\u70b9\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u751f\u6210\u7279\u5f81\u5411\u91cf\u800c\u65e0\u9700\u91cd\u65b0\u8bad\u7ec3\u65b0\u7684\u751f\u6210\u6a21\u578b\uff0c\u56e0\u4e3a\u751f\u6210\u6a21\u578b\u5305\u542b\u8fd9\u79cd\u6cdb\u5316\u4fe1\u606f\u3002\u56e0\u6b64\u6211\u4eec\u7684\u5c40\u90e8\u589e\u5f3a\u6a21\u578b\u53ef\u4ee5\u5e94\u7528\u4e8e\u5f52\u7eb3\u5b66\u4e60\u4efb\u52a1\uff0c\u5982\u56fe\u5206\u7c7b\u3002<\/p>\n\n\n\n
    note<\/h3>\n\n\n\n
    \u7b2c\u4e00\u4e2a\u4f18\u52bf\u5728\u4e8e\u4ed6\u6280\u672f\u9009\u62e9\u4e0a\uff0c\u5728\u751f\u6210\u6a21\u578b\u4e2d\uff0c\u4e0d\u662f\u7ed9\u6bcf\u4e2a\u4e2d\u5fc3\u8282\u70b9\u90fd\u521b\u5efa\u4e00\u4e2a\u8bad\u7ec3\u6a21\u578b\uff0c\u800c\u662f\u8bad\u7ec3\u4e00\u4e2a\u7edf\u4e00\u7684\u6a21\u578b\uff0c\u6211\u521a\u5f00\u59cb\u7406\u89e3\u9519\u4e86\uff0c\u4ee5\u4e3a\u662f\u4f20\u7edfGNN VS LAGNN,\u7ed3\u679c\u95eeAI\u8bf4\u662f\u4e0a\u9762\u7684\u610f\u601d\u3002 \u7b2c\u4e8c\u4e2a\u4f18\u52bf\u5c31\u662f\uff0c\u4ed6\u662f\u5229\u7528\u4e2d\u5fc3\u8282\u70b9\u751f\u6210\u865a\u62df\u7279\u5f81\u5411\u91cf\u7528\u4e0e\u5b66\u4e60\uff0c\u4ed6\u8fd9\u91cc\u5206\u4e3a\u4e86\u4e24\u4e2a\u9636\u6bb5\uff0c\u7b2c\u4e00\u4e2a\u9636\u6bb5\u662f\u9884\u8bad\u7ec3\u9636\u6bb5\uff0c\u662f\u5c06\u56fe\u771f\u5b9e\u7684\u4fe1\u606f\uff0c\u5373\u5404\u4e2a\u4e2d\u5fc3\u8282\u70b9\uff0c\u771f\u5b9e\u7684\u90bb\u5c45\u5206\u5e03\u7528\u4e0e\u8bad\u7ec3\uff1b\u7b2c\u4e8c\u4e2a\u9636\u6bb5\uff0c\u5c31\u662f\u4f7f\u7528\u865a\u62df\u90bb\u5c45\u589e\u5f3aGNN\uff0c\u8fd9\u65f6\u5019\uff0c\u9884\u8bad\u7ec3\u7684\u6a21\u578b\u662f\u77e5\u9053\u6b64\u4e2d\u5fc3\u8282\u70b9\u7684\u90bb\u5c45\u5206\u5e03\u7684\uff0c\u7136\u540e\u518d\u6839\u636e\u81ea\u8eab\u7684\u7279\u5f81\u5411\u91cf\u8fdb\u884c\u751f\u6210\uff0c\u865a\u62df\u90bb\u5c45\u7684\u8bde\u751f\u5176\u5b9e\u662f\u201c\u53c2\u8003\u201d\u4e86\u90bb\u5c45\u7684\u3002\u7b2c\u4e09\u4e2a\u4f18\u52bf\u5c31\u662f\u5f53\u56fe\u4e2d\u52a0\u5165\u4e86\u65b0\u7684\u8282\u70b9\u65f6\uff0c\u6a21\u578b\u65e2\u53ef\u4ee5\u5c06\u65b0\u8282\u70b9\u7684\u7279\u5f81\u5411\u91cf\u52a0\u5165\u8bad\u7ec3\uff0c\u4e5f\u53ef\u4ee5\u751f\u6210\u865a\u62df\u90bb\u5c45\u7279\u5f81\u5411\u91cf\uff0c\u8fd9\u6837\u4f1a\u66f4\u4e30\u5bcc\uff0c\u800c\u4f20\u7edf\u7684GNN\u53ea\u80fd\u5c06\u65b0\u8282\u70b9\u7684\u7279\u5f81\u5411\u91cf\u548c\u90bb\u5c45\u4fe1\u606f\u52a0\u5165\u8bad\u7ec3\uff0c\u8fd9\u6837\u53ef\u80fd\u4f1a\u4e0d\u591f\u51c6\u786e\u3002<\/p>\n\n\n\n
    \n\n\n\n
    \u65b9\u6cd5<\/strong>\u3002\u6211\u4eec\u5229\u7528\u6761\u4ef6\u53d8\u5206\u81ea\u7f16\u7801\u5668\uff08CVAE\uff09\uff08Kingma & Welling, 2013; Sohn et al., 2015\uff09\u6765\u5b66\u4e60\u7ed9\u5b9a\u4e2d\u5fc3\u8282\u70b9v\u7684\u8fde\u63a5\u90bb\u5c45u\uff08u \u2208 \u200b\uff09\u7684\u8282\u70b9\u7279\u5f81\u7684\u6761\u4ef6\u5206\u5e03\u3002\u5728\u6211\u4eec\u7684CVAE\u8bbe\u7f6e\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528\u200b\u4f5c\u4e3a\u6761\u4ef6\uff0c\u56e0\u4e3a\u200b\uff08u \u2208 \u200b\uff09\u7684\u5206\u5e03\u4e0e\u200b\u76f8\u5173\u3002\u9075\u5faaSohn et al. (2015)\uff0c\u6f5c\u5728\u53d8\u91cfz\u4ece\u5148\u9a8c\u5206\u5e03\u200b(z|\u200b)\u751f\u6210\uff0c\u6570\u636e\u200b\u901a\u8fc7\u4ee5z\u548c\u200b\u4e3a\u6761\u4ef6\u7684\u751f\u6210\u5206\u5e03\u200b(X|\u200b, z)\u751f\u6210\uff1az \u223c p\u03b8(z|\u200b),\u200b \u223c \u200b(X|\u200b, zv)\u3002\u8bbe\u03c6\u8868\u793a\u53d8\u5206\u53c2\u6570\uff0c\u03b8\u8868\u793a\u751f\u6210\u53c2\u6570\uff0c\u6211\u4eec\u6709\uff1a<\/p>\n\n\n\n
    \u200b<\/p>\n\n\n\n
    \u200b<\/p>\n\n\n\n
    \u8bc1\u636e\u4e0b\u754c\uff08ELBO\uff09\u53ef\u4ee5\u5199\u4e3a\uff1a<\/p>\n\n\n\n
    \u200b<\/p>\n\n\n\n
    \u5176\u4e2dz^(l) = g\u03c6(\u200b, \u200b, \u03b5(l))\uff0c\u03b5<\/sup>(l) \u223c N(0, I)\uff0cL\u662f\u8282\u70b9v\u7684\u90bb\u5c45\u6570\u91cf\u3002\u6ce8\u610f\uff0c\u6b63\u5982\u6211\u4eec\u4e4b\u524d\u8ba8\u8bba\u7684\uff0c\u6211\u4eec\u53ea\u4e3a\u6240\u6709\u8282\u70b9\u8bad\u7ec3\u4e00\u4e2aCVAE\u3002\u5728\u8bad\u7ec3\u9636\u6bb5\uff0c\u76ee\u6807\u662f\u4f7f\u7528\u90bb\u5c45\u5bf9(\u200b, \u200b, u \u2208\u200b)\u4f5c\u4e3a\u8f93\u5165\u6765\u6700\u5927\u5316ELBO\uff0c\u5373\u65b9\u7a0b(2)\u3002\u5728\u751f\u6210\u9636\u6bb5\uff0c\u6211\u4eec\u4f7f\u7528\u8282\u70b9\u7279\u5f81Xv\u4f5c\u4e3a\u6761\u4ef6\uff0c\u5e76\u91c7\u6837\u6f5c\u5728\u53d8\u91cfz \u223c N(0, I)\u4f5c\u4e3a\u89e3\u7801\u5668\u7684\u8f93\u5165\u3002\u7136\u540e\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u4e0e\u8282\u70b9v\u76f8\u5173\u7684\u751f\u6210\u7279\u5f81\u5411\u91cfXv\u3002<\/p>\n\n\n\n
    note<\/h3>\n\n\n\n
    \u4ec0\u4e48\u662fKL\u6563\u5ea6\uff0cKL\u6563\u5ea6\u662f\u8861\u91cf\u4e24\u4e2a\u6982\u7387\u5206\u5e03\u4e4b\u95f4\u7684\u5dee\u5f02\u7684\u5ea6\u91cf\uff0c\u5c31\u662f\u8bf4\u8fd9\u4e24\u4e2a\u6982\u7387\u4e4b\u95f4\u7684\u201c\u8ddd\u79bb\u201d\u95ee\u9898\uff0c\u4ed6\u4eec\u76f8\u4f3c\u5ea6\uff0c\u4f60\u548c\u6211\u957f\u7684\u50cf\u5417\uff1fKL\u503c\u8d8a\u5c0f\u8868\u793a\u5206\u5e03\u4e4b\u95f4\u8d8a\u76f8\u4f3c\uff0c\u4f60\u6211\u957f\u5f97\u633a\u50cf\uff1bKL\u503c\u8d8a\u5927\u8868\u793a\u5206\u5e03\u4e4b\u95f4\u8d8a\u4e0d\u540c\uff0c\u4f60\u548c\u6211\u957f\u5f97\u5f88\u4e0d\u4e00\u6837\u3002<\/p>\n\n\n\n
    \u5148\u770b\u4e00\u4e0b\u8bc1\u636e\u4e0b\u754c\u8fd9\u4e2a\u516c\u5f0f\uff0c\u4ed6\u5206\u4e3a\u4e24\u4e2a\u90e8\u5206\uff0c\u524d\u534a\u90e8\u5206\u662fKL\u6563\u5ea6\u7684\u8d1f\u6570\uff0c\u4ed6\u662f\u5e0c\u671bKL\u6563\u5ea6\u8d8a\u5c0f\uff0c\u5219-KL\u5c31\u8d8a\u5927\uff0cKL\u6563\u5ea6\u8d8a\u5c0f\uff0c\u8868\u793a\u7f16\u7801\u5668\u8f93\u51fa\u7684\u5206\u5e03\u4e0e\u5148\u9a8c\u5206\u5e03\u4e4b\u95f4\u7684\u76f8\u4f3c\u7a0b\u5ea6\u8d8a\u5927\uff0c\u8fd9\u6b63\u662f\u6211\u4eec\u60f3\u8981\u7684\u7ed3\u679c\uff0c\u540e\u534a\u90e8\u5206\u662f\u6307\u5f53\u524d\u4e2d\u5fc3\u8282\u70b9\u7684\u4e0d\u540c\u90bb\u5c45\u751f\u6210\u90bb\u5c45\u7279\u5f81\u7684\u8d28\u91cf\u8bc4\u4f30\uff0c\u6570\u503c\u8d8a\u9ad8\uff0c\u8868\u793a\u7279\u5f81\u8d28\u91cf\u8d8a\u597d\u3002<\/p>\n\n\n\n
    \u518d\u770b\u4e00\u4e0b\u4e0a\u9762\u7684\u516c\u5f0f\uff0c\u4e0a\u9762\u7684\u516c\u5f0f\u5176\u5b9e\u524d\u534a\u90e8\u5206\u5c31\u662f\u4e0b\u754cELBO\uff0c\u53ea\u662f\u4e0a\u9762\u662f\u7406\u8bba\u516c\u5f0f\uff0c\u9700\u8981\u4f7f\u7528\u590d\u6742\u7684\u79ef\u5206\uff0c\u8fd9\u96be\u4ee5\u5b9e\u73b0\uff0c\u800c\u4e0b\u9762\u662f\u6211\u4eec\u5b9e\u9645\u4ee3\u7801\u4e2d\u5b9e\u73b0\u7684\u7ed3\u679c\uff0c\u4e24\u8005\u662f\u7b49\u4ef7\u7684\uff0c\u8fd9\u4e2a\u516c\u5f0f\u662f\u53d8\u5206\u63a8\u7406\u7684\u6838\u5fc3\uff0c\u5b83\u544a\u8bc9\u6211\u4eec\u65e0\u6cd5\u8ba1\u7b97\u7684\u76ee\u6807\u53ef\u4ee5\u7528\u53ef\u8ba1\u7b97\u7684\u4e0b\u754c\u6765\u8fd1\u4f3c\uff0c\u901a\u8fc7\u6700\u5927\u5316\u4e0b\u754c\uff0c\u6211\u4eec\u53ef\u4ee5\u95f4\u63a5\u6700\u5927\u5316\u771f\u5b9e\u76ee\u6807\u3002<\/p>\n\n\n\n
    \n\n\n\n
    \u8ba8\u8bba\u3002\u5728\u5b66\u4e60\u4ee5\u4e2d\u5fc3\u8282\u70b9\u4e3a\u6761\u4ef6\u7684\u90bb\u5c45\u7279\u5f81\u5206\u5e03\u65f6\uff0c\u6211\u4eec\u6ca1\u6709\u8003\u8651\u8fde\u63a5\u5230\u6bcf\u4e2a\u90bb\u5c45\u7684\u5176\u4ed6\u8282\u70b9\u5bf9\u90bb\u5c45\u7279\u5f81\u7684\u5f71\u54cd\u3002\u5982\u679c\u6211\u4eec\u5c06\u4e2d\u5fc3\u8282\u70b9\u89c6\u4e3a\u7236\u8282\u70b9\uff0c\u5c06\u5176\u90bb\u5c45\u89c6\u4e3a\u4e2d\u5fc3\u8282\u70b9\u7684\u5b50\u8282\u70b9\uff0c\u90a3\u4e48\u6211\u4eec\u7684\u5047\u8bbe\u7c7b\u4f3c\u4e8e\u8d1d\u53f6\u65af\u7f51\u7edc\u4e2d\u7684\u56e0\u679c\u9a6c\u5c14\u53ef\u592b\u6761\u4ef6\uff08<\/mark>Hausman & Woodward, 1999\uff09\uff1a\u7ed9\u5b9a\u5176\u7236\u8282\u70b9\uff0c\u90bb\u5c45\u7279\u5f81\u7684\u5206\u5e03\u4e0e\u5176\u975e\u540e\u4ee3\u8282\u70b9\u72ec\u7acb\u3002\u8fd9\u4e2a\u5047\u8bbe\u5728\u6982\u7387\u56fe\u6a21\u578b\u7684\u6587\u732e\u4e2d\u662f\u91cd\u8981\u4e14\u5e38\u89c1\u7684\u3002\u4f18\u52bf\u662f\u8fd9\u4e2a\u5047\u8bbe\u907f\u514d\u4e86\u5bf9\u591a\u8df3\u90bb\u5c45\u6761\u4ef6\u7684\u6307\u6570\u590d\u6742\u5ea6\uff0c\u663e\u8457\u63d0\u9ad8\u4e86\u53ef\u6269\u5c55\u6027\u3002\u6211\u4eec\u7684\u5b9e\u9a8c\u7ed3\u679c\u8868\u660e\uff0c\u7531\u4e8e\u6df1\u5ea6\u751f\u6210\u6a21\u578b\u7684\u8868\u8fbe\u80fd\u529b\uff08\u7c7b\u4f3c\u4e8e\u53d8\u5206\u63a8\u7406\u7684\u5047\u8bbe\u5728\u771f\u5b9e\u6570\u636e\u96c6\u4e2d\u4e0d\u9650\u5236\u6df1\u5ea6VAEs\u7684\u6027\u80fd\uff09\uff0c\u6211\u4eec\u7684\u65b9\u6cd5\u5728\u6240\u6709\u57fa\u51c6\u6d4b\u8bd5\u4e2d\u4ecd\u7136\u53d6\u5f97\u4e86\u663e\u8457\u7684\u6027\u80fd\u3002<\/p>\n\n\n\n
    note<\/h3>\n\n\n\n
    \u4ec0\u4e48\u662f\u8d1d\u53f6\u65af\u7f51\u7edc\uff0c\u8d1d\u53f6\u65af\u7f51\u7edc\u7ed3\u6784\u5c31\u662f\u5f88\u5e38\u89c1\u7684\u7f51\u7edc\u7ed3\u6784\uff0c\u5c31\u662f\u7236\u8282\u70b9->\u5b50\u8282\u70b9->\u5b59\u8282\u70b9\u8fd9\u79cd\u7ed3\u6784\uff0c\u8fd9\u8ba9\u6211\u60f3\u5230\u4e86\u4e8c\u53c9\u6811\u3002\u7136\u540e\u8d1d\u53f6\u65af\u7f51\u7edc\u4e2d\u7684\u56e0\u679c\u9a6c\u5c14\u4ee3\u592b\u6761\u4ef6\u5c31\u662f\u8bf4\uff0c\u5b50\u8282\u70b9\u7684\u5b59\u8282\u70b9\u5bf9\u5b50\u8282\u70b9\u6ca1\u6709\u5f71\u54cd\uff0c\u5bf9\u5b50\u8282\u70b9\u6709\u5f71\u54cd\u7684\u53ea\u6709\u7236\u8282\u70b9\uff0c\u5047\u8bbe\u6709A->B->C, B\u7684\u7279\u5f81\u53ea\u4f1a\u53d7A\u5f71\u54cd\uff0cC\u4e0d\u4f1a\u5bf9B\u7684\u7279\u5f81\u4ea7\u751f\u5f71\u54cd\u3002\u90a3\u4e3a\u4ec0\u4e48\u5728LAGNN\u4e2d\u4f7f\u7528\u8fd9\u79cd\u5047\u8bbe\u5462\uff0c\u56e0\u4e3a\u5f88\u660e\u663e\uff0c\u5728\u4e00\u5f20\u56fe\u4e2d\uff0c\u4e00\u4e2a\u8282\u70b9\u53ef\u80fd\u4f1a\u6709\u591a\u4e2a\u90bb\u5c45\uff0c\u90bb\u5c45\u5c31\u76f8\u5f53\u4e8e\u6709\u7236\u5b50\u5173\u7cfb\uff0c\u5982\u679c\u6211\u4eec\u8003\u8651\u6240\u6709\u8282\u70b9\u4e4b\u95f4\u7684\u5f71\u54cd\uff0c\u90a3\u4e48\u4ed8\u51fa\u5bf9\u5e94\u7684\u4ee3\u4ef7\u4f1a\u5f88\u5927\uff0c\u6240\u4ee5\u6211\u4eec\u8981\u505a\u51fa\u8fd9\u79cd\u5047\u8bbe\uff0c\u53ea\u6709\u7236\u8282\u70b9\u5bf9\u5b50\u8282\u70b9\u6709\u5f71\u54cd\uff0c\u800c\u5b59\u8282\u70b9\u5bf9\u5b50\u8282\u70b9\u6ca1\u6709\u5f71\u54cd\uff0c\u8fd9\u6837\u4f1a\u51cf\u5c11\u5f88\u591a\u7684\u9ebb\u70e6\u3002<\/p>\n\n\n\n
    3.2. \u5c06\u751f\u6210\u6a21\u578b\u8bad\u7ec3\u4e0e\u4e0b\u6e38\u56fe\u5b66\u4e60\u89e3\u8026<\/h2>\n\n\n\n
    \u5927\u591a\u6570\u73b0\u6709\u7684GNN\u6a21\u578b\u9075\u5faa\u6d88\u606f\u4f20\u9012\u673a\u5236\uff08Gilmer et al., 2017\uff09\uff0c\u53ef\u4ee5\u88ab\u89c6\u4e3a\u5b66\u4e60\u5230\u7684\u5206\u7c7b\u6216\u56de\u5f52\u51fd\u6570\u3002\u4e3a\u4e86\u8fdb\u884c\u9884\u6d4b\uff0cGNN\u6a21\u578b\u9700\u8981\u4f30\u8ba1\u5173\u4e8e\u56fe\u7ed3\u6784A\u548c\u7279\u5f81\u77e9\u9635X\u7684\u540e\u9a8c\u5206\u5e03P\u0398(\u00b7|A, X)\u3002\u4f8b\u5982\uff0c\u00b7\u53ef\u4ee5\u662f\u8282\u70b9\u5206\u7c7b\u4efb\u52a1\u4e0a\u7684\u7c7b\u522b\u6807\u7b7eY\u3002\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u6700\u5927\u4f3c\u7136\u4f30\u8ba1\uff08MLE\uff09\u901a\u8fc7\u4f18\u5316\u4ee5\u4e0b\u4f3c\u7136\u51fd\u6570\u6765\u4f30\u8ba1\u53c2\u6570\u0398\uff1a<\/p>\n\n\n\n
    \u200b<\/p>\n\n\n\n
    \u5176\u4e2di\u8868\u793a\u8bad\u7ec3\u6570\u636e\u96c6\u4e2d\u7684\u7b2ci\u4e2a\u6570\u636e\u70b9\u3002\u5728\u6211\u4eec\u7684\u5c40\u90e8\u589e\u5f3a\u6a21\u578b\u4e2d\uff0c\u4e3a\u4e86\u8fdb\u4e00\u6b65\u63d0\u9ad8GNNs\u7684\u8868\u8fbe\u80fd\u529b\uff0c\u6211\u4eec\u901a\u8fc7\u4f7f\u7528Xv\u4f5c\u4e3a\u8f93\u5165\u6761\u4ef6\u5e76\u4ece\u751f\u6210\u6a21\u578b\u4e2d\u91c7\u6837\uff0c\u4e3a\u4e2d\u5fc3\u8282\u70b9v\u5f15\u5165\u4e00\u4e2a\u751f\u6210\u7684\u7279\u5f81\u5411\u91cfXv\u3002\u8bbeX\u8868\u793a\u751f\u6210\u7684\u7279\u5f81\u77e9\u9635\uff0c\u5176\u4e2d\u7b2cj\u884c\u5bf9\u5e94\u4e8e\u751f\u6210\u7684\u7279\u5f81\u5411\u91cfXj\u3002\u6211\u4eec\u5c06X\u7eb3\u5165\u65b9\u7a0b(3)\u5e76\u91cd\u5199\u5982\u4e0b\uff1a<\/p>\n\n\n\n
    \u200b<\/p>\n\n\n\n
    \u4e3a\u4e86\u8d1d\u53f6\u65af\u53ef\u5904\u7406\u6027\uff0c\u6211\u4eec\u5c06\u65b9\u7a0b(4)\u4e2d\u7684P\u0398\u5206\u89e3\u4e3a\u4e24\u4e2a\u540e\u9a8c\u6982\u7387\u7684\u4e58\u79ef\uff1a<\/p>\n\n\n\n
    \u200b<\/p>\n\n\n\n
    \u5176\u4e2dP\u0398(\u00b7|A, X, X)\u548cQ\u03a6(X|A, X)\u5206\u522b\u8868\u793a\u7531GNN\u6a21\u578b\u548c\u751f\u6210\u6a21\u578b\u8fd1\u4f3c\u7684\u6982\u7387\u5206\u5e03\uff0c\u5206\u522b\u7531\u0398\u548c\u03a6\u53c2\u6570\u5316\u3002\u901a\u8fc7\u8fd9\u6837\u505a\uff0c\u6211\u4eec\u53ef\u4ee5\u89e3\u8026\u6211\u4eec\u63d0\u51fa\u7684\u5c40\u90e8\u589e\u5f3a\u548c\u7279\u5b9a\u7684\u56fe\u5b66\u4e60\uff0c\u5141\u8bb8\u6211\u4eec\u7684\u589e\u5f3a\u6a21\u578b\u5e94\u7528\u4e8e\u5404\u79cdGNN\u6a21\u578b\uff0c\u800c\u751f\u6210\u6a21\u578b\u53ea\u9700\u8981\u4e00\u6b21\u9884\u8bad\u7ec3\u3002\u56e0\u6b64\uff0c\u5c40\u90e8\u589e\u5f3a\u53ef\u4ee5\u88ab\u89c6\u4e3aGNN\u8bad\u7ec3\u4e4b\u524d\u7684\u65e0\u76d1\u7763\u9884\u8bad\u7ec3\u6a21\u578b\u3002\u65b9\u7a0b(5)\u7684\u8868\u793a\u80fd\u529b\u4f18\u4e8e\u5355\u4e2a\u9884\u6d4b\u5668P\u0398(Yk|A, X)\uff0c\u56e0\u4e3a\u6211\u4eec\u5728\u5c40\u90e8\u90bb\u57df\u4e2d\u4e3aGNN\u6a21\u578b\u63d0\u4f9b\u4e86\u66f4\u591a\u751f\u6210\u7684\u6837\u672c\u3002<\/p>\n\n\n\n
    note<\/h3>\n\n\n\n
    \u4e0a\u9762\u7684\u516c\u5f0f\u770b\u7740\u771f\u7684\u5934\u6655\uff0c\u4f46\u662f\u900f\u8fc7\u73b0\u8c61\u770b\u672c\u8d28\uff0c\u7b2c\u4e00\u4e2a\u516c\u5f0f\u5c31\u662f\u8bf4\u4f20\u7edfGNN\u4ed6\u53ea\u4f1a\u76f4\u63a5\u8bad\u7ec3GNN\uff0c\u4f7f\u7528\u539f\u59cb\u7279\u5f81\uff0c\u800c\u7b2c\u4e8c\u4e2a\u516c\u5f0f\u8868\u793a\uff0c\u5f15\u5165\u4e86\u751f\u6210\u7279\u5f81\uff0c\u7b2c\u4e09\u4e2a\u516c\u5f0f\u5c31\u662fLAGNN\u7684\u539f\u7406\uff0c\u5206\u89e3\u8bad\u7ec3\uff0c\u200b\u8868\u793a\u751f\u6210\u865a\u62df\u90bb\u5c45\u7279\u5f81\uff0c\u200b\u8868\u793a\u5c06\u6240\u6709\u7684\u4fe1\u606f\u7528\u4e0e\u8bad\u7ec3GNN\u6a21\u578b\u3002<\/p>\n\n\n\n
    3.3. \u67b6\u6784<\/h2>\n\n\n\n
    \u5728\u672c\u8282\u4e2d\uff0c\u6211\u4eec\u8be6\u7ec6\u4ecb\u7ecd\u5982\u4f55\u4f7f\u7528\u6765\u81ea\u6211\u4eec\u5c40\u90e8\u589e\u5f3a\u6a21\u578b\u7684\u751f\u6210\u6837\u672c\u4f5c\u4e3a\u989d\u5916\u8f93\u5165\u6765\u8bad\u7ec3GNNs\u3002\u4e3a\u4e86\u8bf4\u660e\u6211\u4eec\u5c40\u90e8\u589e\u5f3a\u6a21\u578b\u7684\u6709\u6548\u6027\uff0c\u6211\u4eec\u63d0\u4f9b\u4e86\u4e24\u79cd\u4e0d\u540c\u7684\u5229\u7528\u751f\u6210\u6837\u672c\u7684\u65b9\u5f0f\uff0c\u5bfc\u81f4\u4e86\u67b6\u6784\u7684\u5e73\u5747\u548c\u62fc\u63a5\u8bbe\u8ba1\u3002<\/p>\n\n\n\n
    LAGCN\u3002\u5bf9\u4e8eGCN\uff0c\u6211\u4eec\u53ea\u5bf9\u7b2c\u4e00\u4e2a\u56fe\u5377\u79ef\u5c42\u8fdb\u884c\u5c0f\u5e45\u4fee\u6539\uff1a<\/p>\n\n\n\n
    \u200b<\/p>\n\n\n\n
    \u5176\u4e2d \u200b\u3002\u7b26\u53f7 \u200b \u8868\u793a\u5728\u7b2c\u4e8c\u7ef4\u5ea6\u4e0a\u62fc\u63a5\u77e9\u9635\u3002\u6743\u91cd\u77e9\u9635W\u4e2d\u7684\u4e0b\u6807\u548c\u4e0a\u6807\u5206\u522b\u8868\u793a\u5c42\u7684\u5e8f\u53f7\u548c\u53c2\u6570\u7684\u5e8f\u53f7\u3002\u4e3a\u4e86\u4e0d\u6539\u53d8GCN\u6a21\u578b\u7684\u53c2\u6570\u5927\u5c0f\uff0c\u200b \u548c \u200b \u7684\u7b2c\u4e8c\u7ef4\u5ea6\u4e4b\u548c\u7b49\u4e8eGCN\u7684 \u200b \u7684\u7b2c\u4e8c\u7ef4\u5ea6\u3002\u5bf9\u4e8e\u5176\u4ed6\u67b6\u6784\uff08LAGAT\u3001LASAGE\u3001LAGCNII\uff09\uff0c\u6211\u4eec\u5c06\u5728\u540e\u9762\u8ba8\u8bba\uff0c\u6211\u4eec\u5728\u7b2c\u4e00\u5c42\u4fdd\u6301\u4e0eLAGCN\u76f8\u540c\u7684\u53c2\u6570\u5927\u5c0f\u8bbe\u7f6e\u3002\u5bf9\u4e8eGraphSAGE\u548cGCNII\uff0c\u5b83\u4eec\u5177\u6709\u4e0eGCN\u76f8\u4f3c\u7684\u67b6\u6784\uff0c\u6211\u4eec\u5bf9LASAGE\u548cLAGCNII\u91c7\u7528\u4e0eLAGCN\u76f8\u540c\u7684\u4fee\u6539\u7b56\u7565\u3002\u9664\u4e86\u62fc\u63a5\u5f0f\u8bbe\u8ba1\u5916\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u5e73\u5747X\u548cX\u4f5c\u4e3aGNNs\u7684\u8f93\u5165\uff0c\u800c\u4e0d\u6539\u53d8\u67b6\u6784\u3002<\/p>\n\n\n\n
    LAGAT\u3002\u7c7b\u4f3c\u5730\uff0cLAGAT\u7684\u7b2c\u4e00\u5c42\u5b9a\u4e49\u5982\u4e0b\uff1a<\/p>\n\n\n\n
    \u200b<\/p>\n\n\n\n
    \u5176\u4e2d \u200b \u5728X\u4e0a\u8ba1\u7b97\uff08\u200b\uff09\u6216\u5728X\u4e0a\u8ba1\u7b97\uff08\u200b\uff09\u3002\u6ce8\u610f \u200b \u7684\u7b2c\u4e8c\u7ef4\u5ea6\u4e0eGAT\u76f8\u540c\u3002\u6211\u4eec\u53ea\u662f\u5c06\u4e00\u534a\u6ce8\u610f\u529b\u5934\u7684\u8f93\u5165\u66ff\u6362\u4e3aX\u3002\u6211\u4eec\u4e5f\u4e3aGAT\u63d0\u4f9b\u4e86\u5e73\u5747\u5f0f\u8bbe\u8ba1\u3002<\/p>\n\n\n\n
    3.4. \u635f\u5931\u51fd\u6570<\/h2>\n\n\n\n
    \u5728\u672c\u8282\u4e2d\uff0c\u6211\u4eec\u89e3\u91ca\u8bad\u7ec3LAGNNs\u7684\u4e24\u79cd\u635f\u5931\u51fd\u6570\u53ca\u5176\u6f5c\u5728\u52a8\u673a\uff1a\u76d1\u7763\u635f\u5931\u548c\u4e00\u81f4\u6027\u635f\u5931\u3002<\/p>\n\n\n\n
    \u76d1\u7763\u635f\u5931\u3002\u4e00\u65e6\u6211\u4eec\u5b8c\u6210\u4e86\u5c40\u90e8\u589e\u5f3a\u6a21\u578b\u7684\u9884\u8bad\u7ec3\uff0c\u6211\u4eec\u5c31\u4f7f\u7528\u5b83\u4ea7\u751f\u7684\u751f\u6210\u7279\u5f81\u77e9\u9635X\u4f5c\u4e3a\u989d\u5916\u8f93\u5165\u6765\u589e\u5f3aGNN\u6a21\u578b\u7684\u8868\u8fbe\u80fd\u529b\u3002\u7ed9\u5b9a\u8bad\u7ec3\u6807\u7b7eK\u548cS\u4e2a\u589e\u5f3a\u7279\u5f81\u77e9\u9635X^(s)\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u8282\u70b9\u5206\u7c7b\u4efb\u52a1\u7684\u76d1\u7763\u635f\u5931\u51fd\u6570\u5199\u4e3a\uff1a<\/p>\n\n\n\n
    \u200b<\/p>\n\n\n\n
    \u5176\u4e2d \u200b\u3002\u6ce8\u610f\u6211\u4eec\u53ea\u63d0\u4f9b\u4e86\u4e00\u79cd\u76d1\u7763\u635f\u5931\u51fd\u6570\u3002\u5bf9\u4e8e\u5176\u4ed6\u56fe\u5b66\u4e60\u4efb\u52a1\uff0c\u5982\u94fe\u63a5\u9884\u6d4b\u548c\u56fe\u5206\u7c7b\uff0c\u76d1\u7763\u635f\u5931\u51fd\u6570\u53ef\u4ee5\u76f8\u5e94\u8c03\u6574\u3002<\/p>\n\n\n\n
    \u4e00\u81f4\u6027\u6b63\u5219\u5316\u635f\u5931\u3002\u53d7\u5230\u4e00\u81f4\u6027\u8bad\u7ec3\u5728\u534a\u76d1\u7763\u5b66\u4e60\u4efb\u52a1\u4e0a\u5de8\u5927\u6210\u529f\u7684\u542f\u53d1\uff08Wang et al., 2020c; Feng et al., 2020; Sajjadi et al., 2016; Samuli & Timo, 2017; Berthelot et al., 2019; Verma et al., 2019\uff09\uff0c\u6211\u4eec\u4e3a\u7279\u5b9a\u7684GNNs\u548c\u56fe\u5b66\u4e60\u4efb\u52a1\u63d0\u4f9b\u4e86\u4e00\u4e2a\u53ef\u9009\u7684\u635f\u5931\u51fd\u6570\u3002\u76f4\u89c2\u4e0a\uff0c\u4e00\u81f4\u6027\u6b63\u5219\u5316\u9f13\u52b1\u5728\u6bcf\u4e2a\u8bad\u7ec3\u8fed\u4ee3\u4e2d\u5bf9\u4e0d\u540c\u8f93\u5165\u7684\u4e0d\u53d8\u9884\u6d4b\uff08Verma et al., 2019\uff09\u3002\u5177\u4f53\u5730\uff0c\u4e00\u81f4\u6027\u6b63\u5219\u5316\u635f\u5931\u51fd\u6570\u5177\u6709\u4ee5\u4e0b\u5f62\u5f0f\uff1a<\/p>\n\n\n\n
    \u200b<\/p>\n\n\n\n
    \u5176\u4e2d \u200b\uff0c\u200b \u662f\u9510\u5316\u6280\u5de7\uff08Berthelot et al., 2019\uff09\uff0cT\u662f\u8c03\u6574\u8fd9\u4e2a\u5206\u7c7b\u5206\u5e03”\u6e29\u5ea6”\u7684\u8d85\u53c2\u6570\u3002\u9510\u5316\u6280\u5de7\u53ef\u4ee5\u51cf\u5c11\u9884\u6d4b\u7684\u71b5\u3002<\/p>\n\n\n\n
    \u8bad\u7ec3\u548c\u63a8\u7406\u3002\u6211\u4eec\u8bad\u7ec3\u548c\u63a8\u7406\u8fc7\u7a0b\u7684\u7ec6\u8282\u5728\u7b97\u6cd51\u4e2d\u6982\u8ff0\u3002\u9996\u5148\uff0c\u6211\u4eec\u8bad\u7ec3CVAE\uff0c\u5373\u6211\u4eec\u7684\u5c40\u90e8\u589e\u5f3a\u6a21\u578b\u3002\u7136\u540e\u6211\u4eec\u5728\u6bcf\u4e2a\u8bad\u7ec3\u8fed\u4ee3\u4e2d\u91c7\u6837\u7531CVAE\u751f\u6210\u7684\u4e0d\u540c\u7279\u5f81\u77e9\u9635\u4f5c\u4e3a\u989d\u5916\u8f93\u5165\u6765\u8bad\u7ec3GNN\u6a21\u578b\u3002\u4f46\u5bf9\u4e8eGRAND\uff08Feng et al., 2020\uff09\uff0c\u6211\u4eec\u5728\u8bad\u7ec3\u9636\u6bb5\u53ea\u91c7\u6837\u4e00\u4e2a\u7279\u5f81\u77e9\u9635\uff0c\u56e0\u4e3a\u6211\u4eec\u53d1\u73b0\u4f7f\u7528\u8fd9\u6837\u7684\u91c7\u6837\u7b56\u7565\u53ef\u4ee5\u83b7\u5f97\u66f4\u597d\u7684\u6027\u80fd\u3002\u76d1\u7763\u635f\u5931\u51fd\u6570\u5728\u521d\u59cb\u7279\u5f81\u77e9\u9635X\u548c\u751f\u6210\u7279\u5f81\u77e9\u9635X\u4e0a\u8ba1\u7b97\u3002\u6b64\u5916\uff0c\u6211\u4eec\u53ef\u9009\u5730\u57fa\u4e8e\u200b\u4e3a\u7279\u5b9a\u4efb\u52a1\u8ba1\u7b97\u4e00\u81f4\u6027\u6b63\u5219\u5316\u635f\u5931\u51fd\u6570\u200b\u3002\u6b64\u5916\uff0c\u6211\u4eec\u5728\u6bcf\u4e2a\u8bad\u7ec3\u8fed\u4ee3\u4e2d\u91cd\u65b0\u91c7\u6837\u53e6\u4e00\u4e2a\u4e0e\u8ba1\u7b97\u8bad\u7ec3\u635f\u5931\u51fd\u6570\u4e0d\u540c\u7684\u7279\u5f81\u77e9\u9635\u6765\u8ba1\u7b97\u9a8c\u8bc1\u635f\u5931\u51fd\u6570\u548c\u9a8c\u8bc1\u51c6\u786e\u7387\u3002\u5728\u63a8\u7406\u9636\u6bb5\uff0c\u6211\u4eec\u4e0d\u9700\u8981\u518d\u6b21\u751f\u6210X\uff0c\u56e0\u4e3a\u6211\u4eec\u5728\u5f15\u7528\u6570\u636e\u96c6\uff08Cora\u3001Citeseer\u3001Pubmed\uff09\u4e0a\u9009\u62e9\u5177\u6709\u6700\u5c0f\u9a8c\u8bc1\u635f\u5931\u51fd\u6570\u7684X\uff0c\u6216\u5728OGB\u6570\u636e\u96c6\u4e0a\u9009\u62e9\u5177\u6709\u6700\u9ad8\u9a8c\u8bc1\u51c6\u786e\u7387\u7684X\u3002\u9884\u8bad\u7ec3\u548cGNN\u8bad\u7ec3\u7684\u8ba1\u7b97\u590d\u6742\u5ea6\u5206\u522b\u4e3a\u200b\u548c\u200b\uff0c\u5176\u4e2dD\u662f\u9690\u85cf\u901a\u9053\u6570\uff0cL\u662f\u5c42\u6570\u3002\u9884\u8bad\u7ec3\u8f6e\u6570\u901a\u5e38\u5c11\u4e8e10\u8f6e\uff0c\u8fd9\u8868\u660e\u9884\u8bad\u7ec3\u5f15\u5165\u7684\u8ba1\u7b97\u5f00\u9500\u5f88\u5c0f\u3002<\/p>\n\n\n\n
    note<\/h3>\n\n\n\n
    LAGNN\u7684\u4e24\u79cd\u635f\u5931\u5206\u522b\u4ee3\u8868\u5565\u5462\uff1f\u635f\u5931\u9996\u5148\u8868\u793a\u7684\u662f\u771f\u5b9e\u503c\u4e0e\u9884\u6d4b\u503c\u7684\u5dee\u8ddd\uff0c\u8fd9\u662f\u6211\u7684\u7406\u89e3\uff0c\u5728GNN\u4e2d\uff0c\u4f60\u4f1a\u8bad\u7ec3\u4e00\u4e2a\u6a21\u578b\uff0c\u7136\u540e\u7528\u8fd9\u4e2a\u6a21\u578b\u9884\u6d4b\u51fa\u4e00\u4e9b\u8f93\u51fa\uff0c\u8fd9\u4e9b\u8f93\u51fa\u4e0e\u4f7f\u7528\u8f93\u5165\u5f97\u51fa\u7684\u771f\u5b9e\u8f93\u51fa\u7684\u5dee\u8ddd\u5c31\u662f\u635f\u5931\uff0c\u635f\u5931\u5c31\u662f\u8861\u91cf\u6807\u7b7e\u4e0e\u9884\u6d4b\u4e4b\u95f4\u7684\u5dee\u8ddd\u3002\u7136\u540e\u76d1\u7763\u635f\u5931\u8868\u793a\u7684\u5c31\u662f\u6a21\u578b\u5206\u7c7b\u7684\u6548\u679c\uff0c\u8ba9\u6a21\u578b\u53ef\u4ee5\u6bd4\u8f83\u9884\u6d4b\u7ed3\u679c\u548c\u771f\u5b9e\u6807\u7b7e\uff0c\u8ba9\u6a21\u578b\u5b66\u4f1a\u6b63\u786e\u5206\u7c7b\uff0c\u635f\u5931\u592a\u5927\uff0c\u8868\u793a\u6a21\u578b\u5b66\u7684\u5206\u7c7b\u6548\u679c\u4e0d\u597d\uff0c\u635f\u5931\u5c0f\u5219\u597d\u3002\u4e00\u81f4\u6027\u635f\u5931\u662f\u4e3a\u4e86\u589e\u5f3a\u6a21\u578b\uff0c\u4f7f\u7528\u865a\u62df\u90bb\u5c45\u7279\u5f81\u6765\u589e\u5f3a\u6a21\u578b\uff0c\u8ba9\u6a21\u578b\u9884\u6d4b\u7684\u6c34\u5e73\u66f4\u9ad8\uff0c\u66f4\u7a33\u5b9a\uff0c\u8fd9\u91cc\u7684\u6838\u5fc3\u5c31\u662f\u901a\u8fc7\u865a\u62df\u90bb\u5c45\u7279\u5f81\u6765\u589e\u5f3a\u6a21\u578b\u4e86\u3002<\/p>\n\n\n\n
    \u8bad\u7ec3\u548c\u63a8\u7406<\/h2>\n\n\n\n
    \u6211\u4eec\u8bad\u7ec3\u548c\u63a8\u7406\u8fc7\u7a0b\u7684\u7ec6\u8282\u5728\u7b97\u6cd51\u4e2d\u6982\u8ff0\u3002\u9996\u5148\uff0c\u6211\u4eec\u8bad\u7ec3CVAE\uff0c\u5373\u6211\u4eec\u7684\u5c40\u90e8\u589e\u5f3a\u6a21\u578b\u3002\u7136\u540e\u6211\u4eec\u5728\u6bcf\u4e2a\u8bad\u7ec3\u8fed\u4ee3\u4e2d\u91c7\u6837\u7531CVAE\u751f\u6210\u7684\u4e0d\u540c\u7279\u5f81\u77e9\u9635\u4f5c\u4e3a\u989d\u5916\u8f93\u5165\u6765\u8bad\u7ec3GNN\u6a21\u578b\u3002\u4f46\u5bf9\u4e8eGRAND\uff08Feng et al., 2020\uff09\uff0c\u6211\u4eec\u5728\u8bad\u7ec3\u9636\u6bb5\u53ea\u91c7\u6837\u4e00\u4e2a\u7279\u5f81\u77e9\u9635\uff0c\u56e0\u4e3a\u6211\u4eec\u53d1\u73b0\u4f7f\u7528\u8fd9\u6837\u7684\u91c7\u6837\u7b56\u7565\u53ef\u4ee5\u83b7\u5f97\u66f4\u597d\u7684\u6027\u80fd\u3002<\/p>\n\n\n\n
    \u76d1\u7763\u635f\u5931\u51fd\u6570\u5728\u521d\u59cb\u7279\u5f81\u77e9\u9635X\u548c\u751f\u6210\u7279\u5f81\u77e9\u9635X\u4e0a\u8ba1\u7b97\u3002\u6b64\u5916\uff0c\u6211\u4eec\u53ef\u9009\u5730\u57fa\u4e8efLAGNN(A, X, X^(s), \u0398)\u4e3a\u7279\u5b9a\u4efb\u52a1\u8ba1\u7b97\u4e00\u81f4\u6027\u6b63\u5219\u5316\u635f\u5931\u51fd\u6570L_con\u3002\u6b64\u5916\uff0c\u6211\u4eec\u5728\u6bcf\u4e2a\u8bad\u7ec3\u8fed\u4ee3\u4e2d\u91cd\u65b0\u91c7\u6837\u53e6\u4e00\u4e2a\u4e0e\u8ba1\u7b97\u8bad\u7ec3\u635f\u5931\u51fd\u6570\u4e0d\u540c\u7684\u7279\u5f81\u77e9\u9635\u6765\u8ba1\u7b97\u9a8c\u8bc1\u635f\u5931\u51fd\u6570\u548c\u9a8c\u8bc1\u51c6\u786e\u7387\u3002<\/p>\n\n\n\n
    \u5728\u63a8\u7406\u9636\u6bb5\uff0c\u6211\u4eec\u4e0d\u9700\u8981\u518d\u6b21\u751f\u6210X\uff0c\u56e0\u4e3a\u6211\u4eec\u5728\u5f15\u7528\u6570\u636e\u96c6\uff08Cora\u3001Citeseer\u3001Pubmed\uff09\u4e0a\u9009\u62e9\u5177\u6709\u6700\u5c0f\u9a8c\u8bc1\u635f\u5931\u51fd\u6570\u7684X\uff0c\u6216\u5728OGB\u6570\u636e\u96c6\u4e0a\u9009\u62e9\u5177\u6709\u6700\u9ad8\u9a8c\u8bc1\u51c6\u786e\u7387\u7684X\u3002<\/p>\n\n\n\n
    \u9884\u8bad\u7ec3\u548cGNN\u8bad\u7ec3\u7684\u8ba1\u7b97\u590d\u6742\u5ea6\u5206\u522b\u4e3aO(|E|(FD + LD\u00b2))\u548cO(S|E|(FD + LD\u00b2))\uff0c\u5176\u4e2dD\u662f\u9690\u85cf\u901a\u9053\u6570\uff0cL\u662f\u5c42\u6570\u3002\u9884\u8bad\u7ec3\u8f6e\u6570\u901a\u5e38\u5c11\u4e8e10\u8f6e\uff0c\u8fd9\u8868\u660e\u9884\u8bad\u7ec3\u5f15\u5165\u7684\u8ba1\u7b97\u5f00\u9500\u5f88\u5c0f\u3002<\/p>\n\n\n\n
    \u7b97\u6cd51 \u56fe\u795e\u7ecf\u7f51\u7edc\u7684\u5c40\u90e8\u589e\u5f3a<\/p>\n\n\n\n
      \n
    1. \u8f93\u5165\uff1a\u90bb\u63a5\u77e9\u9635A\uff0c\u7279\u5f81\u77e9\u9635X<\/li>\n\n\n\n
    2. \u8f93\u51fa\uff1a\u9884\u6d4bZ<\/li>\n\n\n\n
    3. \u4f7f\u7528\u65b9\u7a0b(2)\u9884\u8bad\u7ec3\u751f\u6210\u6a21\u578b\u200b\uff0c\u7ed9\u5b9aA\u548cX\u4f5c\u4e3a\u8f93\u5165<\/li>\n\n\n\n
    4. while \u672a\u6536\u655b do<\/li>\n\n\n\n
    5. for s = 1 : S do<\/li>\n\n\n\n
    6. \u751f\u6210\u589e\u5f3a\u7279\u5f81\u77e9\u9635\uff1a\u200b<\/li>\n\n\n\n
    7. \u4f7f\u7528LAGNN \u200b\u83b7\u5f97\u9884\u6d4b\uff1a\u200b<\/li>\n\n\n\n
    8. end for<\/li>\n\n\n\n
    9. \u901a\u8fc7\u65b9\u7a0b(8)\u8ba1\u7b97\u76d1\u7763\u5206\u7c7b\u635f\u5931\u200b<\/li>\n\n\n\n
    10. \u53ef\u9009\u5730\u901a\u8fc7\u65b9\u7a0b(9)\u8ba1\u7b97\u4e00\u81f4\u6027\u6b63\u5219\u5316\u635f\u5931\u200b<\/li>\n\n\n\n
    11. \u901a\u8fc7\u68af\u5ea6\u4e0b\u964d\u66f4\u65b0\u53c2\u6570\u0398\uff1a\u200b<\/li>\n\n\n\n
    12. \u91cd\u65b0\u751f\u6210\u589e\u5f3a\u7279\u5f81\u77e9\u9635\uff1a\u200b<\/li>\n\n\n\n
    13. \u901a\u8fc7\u200b\u548c\u65b9\u7a0b(8)\u8ba1\u7b97\u9a8c\u8bc1\u635f\u5931\u51fd\u6570\u6216\u9a8c\u8bc1\u51c6\u786e\u7387<\/li>\n\n\n\n
    14. end while<\/li>\n\n\n\n
    15. \u901a\u8fc7\u200b\u8fdb\u884c\u9884\u6d4b\uff0c\u5176\u4e2d\u6211\u4eec\u9009\u62e9\u5177\u6709\u6700\u5c0f\u9a8c\u8bc1\u635f\u5931\u51fd\u6570\u6216\u6700\u9ad8\u9a8c\u8bc1\u51c6\u786e\u7387\u7684X<\/li>\n<\/ol>\n\n\n\n
      \u88681. \u4e09\u4e2a\u5f15\u7528\u7f51\u7edc\u4e0a\u7684\u5206\u7c7b\u7ed3\u679c\uff08%\uff09<\/h2>\n\n\n\n
      \u65b9\u6cd5<\/th>Cora<\/th>Citeseer<\/th>Pubmed<\/th><\/tr><\/thead>
      Chebyshev<\/td>81.2<\/td>69.8<\/td>74.4<\/td><\/tr>
      APPNP<\/td>83.8\u00b10.3<\/td>71.6\u00b10.5<\/td>79.7\u00b10.3<\/td><\/tr>
      MixHop<\/td>81.9\u00b10.4<\/td>71.4\u00b10.8<\/td>80.8\u00b10.6<\/td><\/tr>
      Graph U-net<\/td>84.4\u00b10.6<\/td>73.2\u00b10.5<\/td>79.6\u00b10.2<\/td><\/tr>
      GSNN-M<\/td>83.9\u00b10.5<\/td>72.2\u00b10.5<\/td>79.1\u00b10.3<\/td><\/tr>
      S2GC<\/td>83.5\u00b10.02<\/td>73.6\u00b10.09<\/td>80.2\u00b10.02<\/td><\/tr>
      GCN<\/td>81.5\u00b10.5<\/td>70.3\u00b10.7<\/td>79.0\u00b10.5<\/td><\/tr>
      G-GCN<\/td>83.7<\/td>71.3<\/td>80.9<\/td><\/tr>
      DropEdge-GCN<\/td>82.8<\/td>72.3<\/td>79.6<\/td><\/tr>
      GAUG-O-GCN<\/td>83.6\u00b10.5<\/td>73.3\u00b11.1<\/td>79.3\u00b10.4<\/td><\/tr>
      GraphSNNGCN<\/td>83.1\u00b11.8<\/td>72.3\u00b11.5<\/td>79.8\u00b11.2<\/td><\/tr>
      GRAND-GCN<\/td>84.5\u00b10.3<\/td>74.2\u00b10.3<\/td>80.0\u00b10.3<\/td><\/tr>
      LA-GCN<\/td>84.6\u00b10.5<\/td>74.7\u00b10.5<\/td>81.7\u00b10.7<\/td><\/tr>
      GAT<\/td>83.0\u00b10.7<\/td>72.5\u00b10.7<\/td>79.0\u00b10.3<\/td><\/tr>
      GAUG-O-GAT<\/td>82.2\u00b10.2<\/td>71.6\u00b11.1<\/td>OOM<\/td><\/tr>
      GraphSNNGAT<\/td>83.8\u00b11.2<\/td>73.5\u00b11.6<\/td>79.6\u00b11.4<\/td><\/tr>
      GRAND-GAT<\/td>84.3\u00b10.4<\/td>73.2\u00b10.4<\/td>79.2\u00b10.6<\/td><\/tr>
      LA-GAT<\/td>84.7\u00b10.4<\/td>73.7\u00b10.5<\/td>81.0\u00b10.4<\/td><\/tr>
      GCNII<\/td>85.5\u00b10.5<\/td>73.4\u00b10.6<\/td>80.2\u00b10.4<\/td><\/tr>
      LA-GCNII<\/td>85.7\u00b10.3<\/td>74.1\u00b10.5<\/td>80.6\u00b10.7<\/td><\/tr>
      GRAND<\/td>85.4\u00b10.4<\/td>75.4\u00b10.4<\/td>82.7\u00b10.6<\/td><\/tr>
      LA-GRAND<\/td>85.7\u00b10.3<\/td>75.8\u00b10.5<\/td>83.4\u00b10.6<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
      4. \u5b9e\u9a8c<\/h2>\n\n\n\n
      \u5728\u672c\u8282\u4e2d\uff0c\u6211\u4eec\u8bc4\u4f30\u4e86\u6211\u4eec\u7684\u5c40\u90e8\u589e\u5f3a\u6a21\u578b\u5728\u5404\u79cd\u4efb\u52a1\u4e0a\u7684\u6027\u80fd\uff0c\u5305\u62ec\u8282\u70b9\u5206\u7c7b\u3001\u94fe\u63a5\u9884\u6d4b\u548c\u56fe\u5206\u7c7b\u3002\u6240\u6709\u5b9e\u9a8c\u90fd\u5728\u5f00\u653e\u56fe\u6570\u636e\u96c6\u4e0a\u8fdb\u884c\u3002<\/p>\n\n\n\n
      4.1. \u534a\u76d1\u7763\u5b66\u4e60<\/h3>\n\n\n\n
      \u6570\u636e\u96c6\u3002\u6211\u4eec\u5229\u7528\u4e09\u4e2a\u516c\u5171\u5f15\u7528\u7f51\u7edc\u6570\u636e\u96c6Cora\u3001Citeseer\u548cPubmed\uff08Sen et al., 2008\uff09\u8fdb\u884c\u534a\u76d1\u7763\u8282\u70b9\u5206\u7c7b\u3002\u6240\u6709\u6570\u636e\u96c6\u7684\u7edf\u8ba1\u4fe1\u606f\u53ef\u4ee5\u5728\u9644\u5f55D\u4e2d\u627e\u5230\u3002<\/p>\n\n\n\n
      \u57fa\u7ebf\u6a21\u578b\u3002\u6211\u4eec\u8003\u8651\u4e09\u79cd\u6d41\u884c\u7684\u56fe\u795e\u7ecf\u7f51\u7edc\uff1aGCN\uff08Kipf & Welling, 2017\uff09\u3001GAT\uff08Veli\u010dkovi\u0107 et al., 2018\uff09\u548cGCNII\uff08Chen et al., 2020b\uff09\u4f5c\u4e3a\u6211\u4eec\u5b9e\u73b0\u7684\u9aa8\u5e72\u7f51\u7edc\u3002GCN\u548cGAT\u662f\u6700\u5148\u8fdbGNN\u67b6\u6784\u7684\u4ee3\u8868\uff0c\u800cGCNII\u662f\u5177\u6709\u8df3\u8dc3\u8fde\u63a5\u8bbe\u8ba1\u7684\u6df1\u5ea6GNN\u6a21\u578b\u3002\u5bf9\u4e8e\u8fd9\u4e9b\u9aa8\u5e72\u7f51\u7edc\u4e2d\u7684\u6bcf\u4e00\u4e2a\uff0c\u6211\u4eec\u91c7\u7528\u7b2c3.3\u8282\u4e2d\u8ba8\u8bba\u7684\u62fc\u63a5\u5f0f\u8bbe\u8ba1\u4f5c\u4e3a\u6211\u4eec\u7684LAGNN\u67b6\u6784\u3002\u4f46\u6211\u4eec\u4fdd\u6301LAGNN\u7684\u53ef\u5b66\u4e60\u6743\u91cd\u77e9\u9635\u5927\u5c0f\u4e0e\u76f8\u5e94\u7684GNN\u6a21\u578b\u76f8\u540c\uff0c\u8fd9\u5728\u9644\u5f55D\u4e2d\u6709\u8be6\u7ec6\u8bf4\u660e\u3002\u6211\u4eec\u8fd8\u5c06\u6211\u4eec\u7684\u65b9\u6cd5\u4e0e\u5176\u4ed6\u6570\u636e\u589e\u5f3a\u6a21\u578b\u2014\u2014GRAND\uff08Feng et al., 2020\uff09\u7ed3\u5408\u3002\u4e3a\u4e86\u8bc4\u4f30\u6211\u4eec\u63d0\u51fa\u7684\u6846\u67b6\uff0c\u6211\u4eec\u5c06\u6211\u4eec\u7684\u6a21\u578b\u4e0e\u56db\u7c7b\u6700\u5148\u8fdb\u7684\u6a21\u578b\u8fdb\u884c\u6bd4\u8f83\uff1a<\/p>\n\n\n\n
        \n
      • \u9aa8\u5e72\u6a21\u578b\uff1aChebyshev\uff08Defferrard et al., 2016\uff09\u3001GCN\uff08Kipf & Welling, 2017\uff09\u3001GAT\uff08Veli\u010dkovi\u0107 et al., 2018\uff09\u3001APPNP\uff08Klicpera et al., 2019\uff09\u3001Graph U-net\uff08Gao & Ji, 2019\uff09\u3001MixHop\uff08Abu-El-Haija et al., 2019\uff09\u3001GCNII\uff08Chen et al., 2020b\uff09\u3001GSNN-M\uff08Wang et al., 2020a\uff09\u548cS2GC\uff08Zhu & Koniusz, 2021\uff09<\/li>\n\n\n\n
      • \u7279\u5f81\u7ea7\u589e\u5f3a\u6a21\u578b\uff1aG-GNNs\uff08Zhu et al., 2020\uff09\u548cGRAND\uff08Feng et al., 2020\uff09<\/li>\n\n\n\n
      • \u62d3\u6251\u7ea7\u589e\u5f3a\u6a21\u578b\uff1aDropEdge\uff08Rong et al., 2020\uff09\u548cGAUG-O\uff08Zhao et al., 2021\uff09<\/li>\n\n\n\n
      • \u5b50\u56feGNN\uff1aGraphSNN\uff08Wijesinghe & Wang, 2022\uff09<\/li>\n<\/ul>\n\n\n\n
        \u57fa\u7ebf\u6a21\u578b\u7684\u9009\u62e9\u65e8\u5728\u8868\u660e\u73b0\u6709\u7684GNNs\u4ece\u6211\u4eec\u63d0\u51fa\u7684\u5c40\u90e8\u6570\u636e\u589e\u5f3a\u4e2d\u53d7\u76ca\uff0c\u5e76\u4e14\u6211\u4eec\u7684\u6a21\u578b\u4f18\u4e8e\u5176\u4ed6\u6570\u636e\u589e\u5f3a\u6a21\u578b\u3002<\/p>\n\n\n\n
        \u5b9e\u9a8c\u8bbe\u7f6e\u3002\u6211\u4eec\u5728Cora\u3001Citeseer\u548cPubmed\u4e0a\u5e94\u7528\u6807\u51c6\u56fa\u5b9a\u5206\u5272\uff08Yang et al., 2016\uff09\uff0c\u6bcf\u4e2a\u7c7b\u522b20\u4e2a\u8282\u70b9\u7528\u4e8e\u8bad\u7ec3\uff0c500\u4e2a\u8282\u70b9\u7528\u4e8e\u9a8c\u8bc1\uff0c1000\u4e2a\u8282\u70b9\u7528\u4e8e\u6d4b\u8bd5\u3002\u66f4\u591a\u5173\u4e8e\u5b9e\u9a8c\u8bbe\u7f6e\u548c\u8d85\u53c2\u6570\u7684\u8be6\u7ec6\u4fe1\u606f\u8bf7\u53c2\u89c1\u9644\u5f55D\u3002<\/p>\n\n\n\n
        \u4e0eSOTA\u7684\u6bd4\u8f83\u3002\u6211\u4eec\u5728\u88681\u4e2d\u62a5\u544a\u4e86100\u6b21\u8fd0\u884c\u540e\u7684\u5e73\u5747\u8282\u70b9\u5206\u7c7b\u51c6\u786e\u7387\u3002\u6211\u4eec\u91cd\u7528\u4e86\u76f8\u5e94\u8bba\u6587\u4e2d\u5df2\u62a5\u544a\u7684\u57fa\u7ebf\u6307\u6807\u3002\u7ed3\u679c\u8868\u660e\uff0c\u914d\u5907\u6211\u4eec\u65b9\u6cd5\u7684\u9aa8\u5e72\u6a21\u578b\u5728\u6240\u6709\u4e09\u4e2a\u6570\u636e\u96c6\u4e0a\u90fd\u53d6\u5f97\u4e86\u66f4\u597d\u7684\u6027\u80fd\u3002\u5177\u4f53\u5730\uff0c\u5c40\u90e8\u589e\u5f3a\u53ef\u4ee5\u5728Cora\u3001Citeseer\u548cPubmed\u4e0a\u5206\u522b\u6bd4GCN\u63d0\u9ad83.1%\u30014.4%\u548c2.7%\uff0c\u800cLAGAT\u76f8\u6bd4GAT\u7684\u6539\u8fdb\u5e45\u5ea6\u5206\u522b\u4e3a1.7%\u30011.2%\u548c2.0%\u3002\u6b64\u5916\uff0c\u5f53\u4e0e\u5176\u4ed6\u6570\u636e\u589e\u5f3a\u65b9\u6cd5\u2014\u2014GRAND\u7ed3\u5408\u65f6\uff0c\u6211\u4eec\u4ecd\u7136\u53ef\u4ee5\u5206\u522b\u63d0\u9ad80.3%\u30010.4%\u548c0.7%\u3002\u6b64\u5916\uff0c\u57fa\u4e8eGRAND\u548c\u6211\u4eec\u7684LA-GRAND\u5b9e\u9a8c\u7ed3\u679c\u7684\u6807\u51c6\u5dee\u4fe1\u606f\uff0c\u6211\u4eec\u901a\u8fc7t\u68c0\u9a8c\u8ba1\u7b97p\u503c\u6765\u9a8c\u8bc1\u6539\u8fdb\u3002\u9664\u4e86LA-GCN\u4e0eGRAND-GCN\u5728Cora\u4e0a\u7684\u6bd4\u8f83\uff08p\u503c\u4e3a0.046\uff09\u5916\uff0c\u6240\u6709p\u503c\u90fd\u226a0.01\uff08GRAND\u4e5f\u91c7\u7528\u4e86\u76f8\u540c\u7684\u6d4b\u8bd5\uff09\uff0c\u8fd9\u8868\u660eLA\u76f8\u6bd4GRAND\u7684\u6539\u8fdb\u5728\u7edf\u8ba1\u4e0a\u662f\u663e\u8457\u7684\u3002<\/p>\n\n\n\n
        \u4e0e\u5176\u4ed6\u6570\u636e\u589e\u5f3a\u6a21\u578b\uff08Zhu et al., 2020; Rong et al., 2020; Zhao et al., 2021\uff09\u76f8\u6bd4\uff0cLA-GNN\u5728\u4e24\u4e2a\u6d41\u884c\u7684\u9aa8\u5e72\u7f51\u7edcGCN\u548cGAT\u4e0a\u53d6\u5f97\u4e86\u6700\u4f73\u6027\u80fd\uff0c\u8868\u660e\u4ece\u5168\u5c40\u89d2\u5ea6\u6765\u770b\uff0c\u5c40\u90e8\u4fe1\u606f\u786e\u5b9e\u4f18\u4e8e\u589e\u5f3a\u65b9\u6cd5\uff0c\u5982DropEdge\uff08Rong et al., 2020\uff09\u548cGAUG\uff08Zhao et al., 2021\uff09\u3002\u6211\u4eec\u7684\u6a21\u578b\u548cGraphSNN\u90fd\u4ece\u5b50\u56fe\u7684\u89d2\u5ea6\u51fa\u53d1\u3002\u7ed3\u679c\u8868\u660e\uff0c\u5c40\u90e8\u589e\u5f3a\u5728\u6355\u83b7\u5c40\u90e8\u90bb\u57df\u7684\u7279\u5f81\u4fe1\u606f\u65b9\u9762\u6bd4GraphSNN\u66f4\u6709\u6548\uff0c\u8fd9\u8bc1\u660e\u4e86\u5728\u8bbe\u8ba1\u5b50\u56fe\u76f8\u5173\u7684GNNs\u65f6\u8003\u8651\u7279\u5f81\u548c\u7ed3\u6784\u4fe1\u606f\u66f4\u597d\u3002<\/p>\n\n\n\n
        \u88682. \u8282\u70b9\u5c5e\u6027\u9884\u6d4b\u7684\u6d4b\u8bd5\u6027\u80fd\uff08%\uff09\uff0c\u5e73\u574710\u6b21\u8fd0\u884c<\/h2>\n\n\n\n
        \u6a21\u578b<\/th>products Acc<\/th>proteins ROC-AUC<\/th>arxiv Acc<\/th><\/tr><\/thead>
        MLP<\/td>61.06\u00b10.08<\/td>72.04\u00b10.48<\/td>55.50\u00b10.23<\/td><\/tr>
        CoLinkDistMLP<\/td>62.59\u00b10.10<\/td>–<\/td>56.38\u00b10.16<\/td><\/tr>
        Node2vec<\/td>72.49\u00b10.10<\/td>68.81\u00b10.65<\/td>70.07\u00b10.13<\/td><\/tr>
        GraphZoom<\/td>74.06\u00b10.26<\/td>–<\/td>71.18\u00b10.18<\/td><\/tr>
        GCN<\/td>75.64\u00b10.21<\/td>72.51\u00b10.35<\/td>71.74\u00b10.29<\/td><\/tr>
        +FLAG<\/td>–<\/td>71.71\u00b10.50<\/td>72.04\u00b10.20<\/td><\/tr>
        +GraphSNN<\/td>–<\/td>–<\/td>72.20\u00b10.90<\/td><\/tr>
        +LA<\/td>76.11\u00b10.09<\/td>73.25\u00b10.51<\/td>72.08\u00b10.14<\/td><\/tr>
        GraphSAGE<\/td>78.70\u00b10.36<\/td>77.68\u00b10.20<\/td>71.49\u00b10.27<\/td><\/tr>
        +FLAG<\/td>79.36\u00b10.57<\/td>76.57\u00b10.75<\/td>72.19\u00b10.21<\/td><\/tr>
        +GraphSNN<\/td>–<\/td>–<\/td>71.80\u00b10.70<\/td><\/tr>
        +LA<\/td>79.44\u00b10.25<\/td>77.86\u00b10.37<\/td>72.30\u00b10.12<\/td><\/tr>
        GAT<\/td>79.45\u00b10.59<\/td>–<\/td>73.65\u00b10.11<\/td><\/tr>
        +FLAG<\/td>81.76\u00b10.45<\/td>–<\/td>73.71\u00b10.13<\/td><\/tr>
        +LA<\/td>80.46\u00b10.54<\/td>–<\/td>73.77\u00b10.12<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
        \u88683. \u94fe\u63a5\u9884\u6d4b\u7684\u6d4b\u8bd5\u6027\u80fd\uff08%\uff09\uff0c\u5e73\u574710\u6b21\u8fd0\u884c<\/h2>\n\n\n\n
        \u6a21\u578b<\/th>ogbl-collab Hits@50 (%)<\/th><\/tr><\/thead>
        MLP<\/td>19.27\u00b11.29<\/td><\/tr>
        Node2vec<\/td>48.88\u00b10.54<\/td><\/tr>
        GCN<\/td>44.75\u00b11.07<\/td><\/tr>
        +LA<\/td>47.49\u00b11.40<\/td><\/tr>
        GraphSAGE<\/td>48.10\u00b10.81<\/td><\/tr>
        +LA<\/td>49.23\u00b10.55<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
        \u88684. \u56fe\u5c5e\u6027\u9884\u6d4b\u7684\u6d4b\u8bd5\u6027\u80fd\uff08%\uff09\uff0c\u5e73\u574710\u6b21\u8fd0\u884c<\/h2>\n\n\n\n
        \u6a21\u578b<\/th>ogbg-molhiv ROC-AUC<\/th>ogbg-molpcba AP<\/th><\/tr><\/thead>
        GCN<\/td>76.06\u00b10.97<\/td>20.20\u00b10.24<\/td><\/tr>
        +LA<\/td>76.18\u00b11.11<\/td>20.28\u00b10.16<\/td><\/tr>
        GIN<\/td>75.58\u00b11.40<\/td>22.66\u00b10.28<\/td><\/tr>
        +LA<\/td>75.20\u00b11.74<\/td>22.38\u00b10.24<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
        4.2. \u5168\u76d1\u7763\u5b66\u4e60<\/h2>\n\n\n\n
        \u6570\u636e\u96c6\u3002\u4e3a\u4e86\u8bc1\u660e\u6211\u4eec\u7684\u6a21\u578b\u5728\u5927\u578b\u56fe\u4e0a\u7684\u5168\u76d1\u7763\u8282\u70b9\u548c\u94fe\u63a5\u5206\u7c7b\u4efb\u52a1\u4e2d\u7684\u6709\u6548\u6027\uff0c\u6211\u4eec\u5229\u7528\u6765\u81eaOpen Graph Benchmark (OGB)\uff08Hu et al., 2020\uff09\u7684ogbn-products\u3001ogbn-proteins\u3001ogbn-arxiv\u548cogbl-collab\u6570\u636e\u96c6\u8fdb\u884c\u8bc4\u4f30\u3002\u6240\u6709\u6570\u636e\u96c6\u7684\u7edf\u8ba1\u4fe1\u606f\u53ef\u4ee5\u5728\u9644\u5f55D\u4e2d\u627e\u5230\u3002<\/p>\n\n\n\n
        \u57fa\u7ebf\u6a21\u578b\u3002\u6211\u4eec\u8003\u8651\u56db\u79cd\u6d41\u884c\u7684\u6d88\u606f\u4f20\u9012GNNs\uff1aGCN\uff08Kipf & Welling, 2017\uff09\u3001GAT\uff08Veli\u010dkovi\u0107 et al., 2018\uff09\u548cGraphSAGE\uff08Hamilton et al., 2017\uff09\u4f5c\u4e3a\u9aa8\u5e72\u7f51\u7edc\u3002\u5bf9\u4e8e\u8fd9\u4e9b\u9aa8\u5e72\u7f51\u7edc\u4e2d\u7684\u6bcf\u4e00\u4e2a\uff0c\u6211\u4eec\u5e94\u7528\u7b2c3.3\u8282\u4e2d\u8ba8\u8bba\u7684\u62fc\u63a5\u5f0f\u6216\u5e73\u5747\u5f0f\u8bbe\u8ba1\u4f5c\u4e3a\u6211\u4eec\u7684LAGNN\u67b6\u6784\uff0c\u8fd9\u5728\u9644\u5f55D\u4e2d\u6709\u8be6\u7ec6\u8bf4\u660e\u3002\u5bf9\u4e8earxiv\u3001proteins\u548cproducts\u4e0a\u7684\u8282\u70b9\u5206\u7c7b\uff0c\u6211\u4eec\u5c06\u5176\u4e0eMLP\u3001Node2vec\uff08Grover & Leskovec, 2016\uff09\u3001GCN\u3001GAT\u3001GraphSAGE\u3001FLAG\uff08Kong et al., 2020\uff09\u3001GraphSNN\uff08Wijesinghe & Wang, 2022\uff09\u3001GraphZoom\uff08Deng et al., 2020\uff09\u548cCoLinkDistMLP\uff08Luo et al., 2021\uff09\u8fdb\u884c\u6bd4\u8f83\u3002\u6b64\u5916\uff0c\u6211\u4eec\u4f7f\u7528ogbl-collab\u6765\u8bc4\u4f30\u6211\u4eec\u7684\u6a21\u578b\u5728\u94fe\u63a5\u9884\u6d4b\u4efb\u52a1\u4e0a\u7684\u6027\u80fd\uff0c\u5e76\u5c06\u5176\u4e0eMLP\u3001Node2vec\u3001GCN\u3001GraphSAGE\u8fdb\u884c\u6bd4\u8f83\u3002<\/p>\n\n\n\n
        \u5b9e\u9a8c\u8bbe\u7f6e\u548c\u7ed3\u679c\u3002\u6211\u4eec\u9075\u5faaOGB\uff08Hu et al., 2020\uff09\u4e2d\u7684\u5b9e\u9a8c\u8bbe\u7f6e\u3002\u5bf9\u4e8e\u8be6\u7ec6\u8bbe\u7f6e\uff0c\u5982\u5206\u5272\u6bd4\u4f8b\u548c\u8bc4\u4f30\u6307\u6807\uff0c\u6211\u4eec\u53ea\u662f\u9075\u5faaOGB\u5b9e\u73b0\u4e2d\u7684\u76f8\u540c\u8bbe\u7f6e\u3002\u6ce8\u610f\uff0c\u57fa\u7ebf\u6a21\u578b\u7684\u6d4b\u8bd5\u7ed3\u679c\u6765\u81ea\u5b98\u65b9OGB\u6392\u884c\u699c\u7f51\u7ad9\u6216\u76f8\u5e94\u8bba\u6587\u3002\u4e3a\u4e86\u516c\u5e73\u6bd4\u8f83\uff0c\u6211\u4eec\u5728OGB\u4efb\u52a1\u4e0a\u4ece\u5f00\u6e90\u4ee3\u7801\u5b9e\u73b0\u6211\u4eec\u7684\u6a21\u578b\uff0c\u53ea\u4fee\u6539\u7b2c\u4e00\u5c42\u3002\u4eceOGB\u6392\u884c\u699c\u53ef\u4ee5\u770b\u51fa\uff0c\u6d4b\u8bd5\u7ed3\u679c\u5bf9\u6a21\u578b\u5927\u5c0f\u548c\u5404\u79cd\u6280\u5de7\u90fd\u5f88\u654f\u611f\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u6309\u7167\u7b2c3.3\u8282\u7684\u5efa\u8bae\u4e0d\u6539\u53d8\u9aa8\u5e72\u7f51\u7edc\u7684\u6a21\u578b\u5927\u5c0f\uff0c\u4e5f\u4e0d\u6dfb\u52a0\u5176\u4ed6\u6280\u5de7\u3002\u6211\u4eecLAGNN\u67b6\u6784\u7684\u8be6\u7ec6\u4fe1\u606f\u53ef\u4ee5\u5728\u9644\u5f55D\u4e2d\u627e\u5230\u3002\u7ed3\u679c\u603b\u7ed3\u5728\u88682\u548c\u88683\u4e2d\u3002\u9075\u5faa\u5e38\u89c1\u505a\u6cd5\uff0c\u6211\u4eec\u62a5\u544a\u4e0e\u6700\u4f73\u9a8c\u8bc1\u6027\u80fd\u76f8\u5173\u7684\u6d4b\u8bd5\u51c6\u786e\u7387\u3002\u8282\u70b9\u548c\u94fe\u63a5\u9884\u6d4b\u7684\u7ed3\u679c\u8868\u660e\uff0c\u6211\u4eec\u7684\u589e\u5f3a\u6a21\u578b\u5728\u9aa8\u5e72\u7f51\u7edc\u4e0a\u6301\u7eed\u6539\u8fdb\u4e86\u6027\u80fd\u3002<\/p>\n\n\n\n
        \u4e3b\u8981\u53d1\u73b0\uff1a<\/h3>\n\n\n\n
          \n
        1. \u8282\u70b9\u5206\u7c7b\u4efb\u52a1\uff1a<\/li>\n<\/ol>\n\n\n\n
            \n
          • \u5728ogbn-products\u6570\u636e\u96c6\u4e0a\uff0cLA\u65b9\u6cd5\u5728\u6240\u6709GNN\u53d8\u4f53\u4e0a\u90fd\u53d6\u5f97\u4e86\u6700\u4f73\u6027\u80fd<\/li>\n\n\n\n
          • \u5728ogbn-proteins\u6570\u636e\u96c6\u4e0a\uff0cLA\u65b9\u6cd5\u663e\u8457\u63d0\u5347\u4e86ROC-AUC\u5206\u6570<\/li>\n\n\n\n
          • \u5728ogbn-arxiv\u6570\u636e\u96c6\u4e0a\uff0cLA\u65b9\u6cd5\u5728GraphSAGE\u4e0a\u53d6\u5f97\u4e86\u6700\u4f73\u6027\u80fd<\/li>\n<\/ul>\n\n\n\n
              \n
            1. \u94fe\u63a5\u9884\u6d4b\u4efb\u52a1\uff1a<\/li>\n<\/ol>\n\n\n\n
                \n
              • \u5728ogbl-collab\u6570\u636e\u96c6\u4e0a\uff0cLA\u65b9\u6cd5\u5728GCN\u548cGraphSAGE\u4e0a\u90fd\u53d6\u5f97\u4e86\u663e\u8457\u7684\u6027\u80fd\u63d0\u5347<\/li>\n\n\n\n
              • LA-GraphSAGE\u8fbe\u5230\u4e86\u6700\u9ad8\u7684Hits@50\u5206\u6570\uff0849.23%\uff09<\/li>\n<\/ul>\n\n\n\n
                  \n
                1. \u65b9\u6cd5\u7684\u4e00\u81f4\u6027\uff1a<\/li>\n<\/ol>\n\n\n\n
                    \n
                  • LA\u65b9\u6cd5\u5728\u6240\u6709\u6d4b\u8bd5\u7684\u5927\u578b\u56fe\u6570\u636e\u96c6\u4e0a\u90fd\u8868\u73b0\u51fa\u4e00\u81f4\u7684\u6539\u8fdb<\/li>\n\n\n\n
                  • \u8bc1\u660e\u4e86\u5c40\u90e8\u589e\u5f3a\u65b9\u6cd5\u5728\u4e0d\u540c\u89c4\u6a21\u548c\u7c7b\u578b\u7684\u56fe\u4e0a\u7684\u6709\u6548\u6027\u548c\u901a\u7528\u6027<\/li>\n<\/ul>\n\n\n\n
                    \u8fd9\u4e9b\u7ed3\u679c\u8fdb\u4e00\u6b65\u9a8c\u8bc1\u4e86\u5c40\u90e8\u589e\u5f3a\u65b9\u6cd5\u5728\u5927\u89c4\u6a21\u56fe\u5b66\u4e60\u4efb\u52a1\u4e2d\u7684\u6709\u6548\u6027\u548c\u9c81\u68d2\u6027\u3002<\/p>\n\n\n\n
                    \u88682. \u8282\u70b9\u5c5e\u6027\u9884\u6d4b\u7684\u6d4b\u8bd5\u6027\u80fd\uff08%\uff09\uff0c\u5e73\u574710\u6b21\u8fd0\u884c<\/h2>\n\n\n\n
                    \u6a21\u578b<\/th>products Acc<\/th>proteins ROC-AUC<\/th>arxiv Acc<\/th><\/tr><\/thead>
                    MLP<\/td>61.06\u00b10.08<\/td>72.04\u00b10.48<\/td>55.50\u00b10.23<\/td><\/tr>
                    CoLinkDistMLP<\/td>62.59\u00b10.10<\/td>–<\/td>56.38\u00b10.16<\/td><\/tr>
                    Node2vec<\/td>72.49\u00b10.10<\/td>68.81\u00b10.65<\/td>70.07\u00b10.13<\/td><\/tr>
                    GraphZoom<\/td>74.06\u00b10.26<\/td>–<\/td>71.18\u00b10.18<\/td><\/tr>
                    GCN<\/td>75.64\u00b10.21<\/td>72.51\u00b10.35<\/td>71.74\u00b10.29<\/td><\/tr>
                    +FLAG<\/td>–<\/td>71.71\u00b10.50<\/td>72.04\u00b10.20<\/td><\/tr>
                    +GraphSNN<\/td>–<\/td>–<\/td>72.20\u00b10.90<\/td><\/tr>
                    +LA<\/td>76.11\u00b10.09<\/td>73.25\u00b10.51<\/td>72.08\u00b10.14<\/td><\/tr>
                    GraphSAGE<\/td>78.70\u00b10.36<\/td>77.68\u00b10.20<\/td>71.49\u00b10.27<\/td><\/tr>
                    +FLAG<\/td>79.36\u00b10.57<\/td>76.57\u00b10.75<\/td>72.19\u00b10.21<\/td><\/tr>
                    +GraphSNN<\/td>–<\/td>–<\/td>71.80\u00b10.70<\/td><\/tr>
                    +LA<\/td>79.44\u00b10.25<\/td>77.86\u00b10.37<\/td>72.30\u00b10.12<\/td><\/tr>
                    GAT<\/td>79.45\u00b10.59<\/td>–<\/td>73.65\u00b10.11<\/td><\/tr>
                    +FLAG<\/td>81.76\u00b10.45<\/td>–<\/td>73.71\u00b10.13<\/td><\/tr>
                    +LA<\/td>80.46\u00b10.54<\/td>–<\/td>73.77\u00b10.12<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
                    \u88683. \u94fe\u63a5\u9884\u6d4b\u7684\u6d4b\u8bd5\u6027\u80fd\uff08%\uff09\uff0c\u5e73\u574710\u6b21\u8fd0\u884c<\/h2>\n\n\n\n
                    \u6a21\u578b<\/th>ogbl-collab Hits@50 (%)<\/th><\/tr><\/thead>
                    MLP<\/td>19.27\u00b11.29<\/td><\/tr>
                    Node2vec<\/td>48.88\u00b10.54<\/td><\/tr>
                    GCN<\/td>44.75\u00b11.07<\/td><\/tr>
                    +LA<\/td>47.49\u00b11.40<\/td><\/tr>
                    GraphSAGE<\/td>48.10\u00b10.81<\/td><\/tr>
                    +LA<\/td>49.23\u00b10.55<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
                    \u88684. \u56fe\u5c5e\u6027\u9884\u6d4b\u7684\u6d4b\u8bd5\u6027\u80fd\uff08%\uff09\uff0c\u5e73\u574710\u6b21\u8fd0\u884c<\/h2>\n\n\n\n
                    \u6a21\u578b<\/th>ogbg-molhiv ROC-AUC<\/th>ogbg-molpcba AP<\/th><\/tr><\/thead>
                    GCN<\/td>76.06\u00b10.97<\/td>20.20\u00b10.24<\/td><\/tr>
                    +LA<\/td>76.18\u00b11.11<\/td>20.28\u00b10.16<\/td><\/tr>
                    GIN<\/td>75.58\u00b11.40<\/td>22.66\u00b10.28<\/td><\/tr>
                    +LA<\/td>75.20\u00b11.74<\/td>22.38\u00b10.24<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
                    4.3. \u5f52\u7eb3\u5b66\u4e60<\/h2>\n\n\n\n
                    \u4e3a\u4e86\u8bc4\u4f30\u6211\u4eec\u7684\u6a21\u578b\u5728\u5f52\u7eb3\u5b66\u4e60\u4efb\u52a1\u4e0a\u7684\u6709\u6548\u6027\uff0c\u6211\u4eec\u4f7f\u7528\u6765\u81eaOGB\u7684ogbg-molhiv\u548cogbg-molpcba\u6570\u636e\u96c6\u8fdb\u884c\u8bc4\u4f30\u3002\u5bf9\u4e8e\u5b9e\u9a8c\u8bbe\u7f6e\uff0c\u6211\u4eec\u9075\u5faa\u5b98\u65b9OGB\u5b9e\u73b0\u3002\u6211\u4eec\u8003\u8651GCN\u548cGIN\uff08Xu et al., 2019b\uff09\u4f5c\u4e3a\u9aa8\u5e72\u7f51\u7edc\uff0cLAGCN\u548cLAGIN\u7684\u67b6\u6784\u53ef\u4ee5\u5728\u9644\u5f55D\u4e2d\u627e\u5230\u3002\u7ed3\u679c\u603b\u7ed3\u5728\u88684\u4e2d\u3002<\/p>\n\n\n\n
                    \u5b9e\u9a8c\u7ed3\u679c\u8868\u660e\uff0c\u6211\u4eec\u7684\u6a21\u578b\u5728\u5f52\u7eb3\u5b66\u4e60\u4efb\u52a1\u4e0a\u4ecd\u7136\u9002\u7528\u4e8eGCN\u3002\u6211\u4eec\u7684\u751f\u6210\u6a21\u578b\u53ea\u5728\u8bad\u7ec3\u6570\u636e\u96c6\u4e0a\u8fdb\u884c\u8bad\u7ec3\u3002\u53ea\u8981\u6d4b\u8bd5\u6570\u636e\u96c6\u548c\u8bad\u7ec3\u6570\u636e\u96c6\u4e0a\u7684\u56fe\u5177\u6709\u76f8\u4f3c\u7684\u5206\u5e03\uff0c\u5373\u76f8\u4f3c\u7684\u5b50\u56fe\u7ed3\u6784\u548c\u7279\u5f81\u5411\u91cf\uff0c\u6211\u4eec\u7684\u751f\u6210\u6a21\u578b\u5c31\u53ef\u4ee5\u505a\u51fa\u5408\u7406\u7684\u63a8\u7406\u5e76\u751f\u6210\u6709\u6548\u7684\u589e\u5f3a\u7279\u5f81\u5411\u91cf\u3002<\/p>\n\n\n\n
                    \u4e3b\u8981\u53d1\u73b0\uff1a<\/h3>\n\n\n\n
                      \n
                    1. \u5f52\u7eb3\u5b66\u4e60\u80fd\u529b\uff1a<\/li>\n<\/ol>\n\n\n\n
                        \n
                      • LA\u65b9\u6cd5\u5728GCN\u4e0a\u53d6\u5f97\u4e86\u5c0f\u5e45\u4f46\u4e00\u81f4\u7684\u6539\u8fdb<\/li>\n\n\n\n
                      • \u5728ogbg-molhiv\u6570\u636e\u96c6\u4e0a\uff1aLA-GCN (76.18%) vs GCN (76.06%)<\/li>\n\n\n\n
                      • \u5728ogbg-molpcba\u6570\u636e\u96c6\u4e0a\uff1aLA-GCN (20.28%) vs GCN (20.20%)<\/li>\n<\/ul>\n\n\n\n
                          \n
                        1. \u6cdb\u5316\u80fd\u529b\uff1a<\/li>\n<\/ol>\n\n\n\n
                            \n
                          • \u751f\u6210\u6a21\u578b\u53ea\u5728\u8bad\u7ec3\u6570\u636e\u4e0a\u8bad\u7ec3\uff0c\u4f46\u80fd\u5728\u6d4b\u8bd5\u6570\u636e\u4e0a\u6709\u6548\u5de5\u4f5c<\/li>\n\n\n\n
                          • \u8bc1\u660e\u4e86\u5c40\u90e8\u589e\u5f3a\u65b9\u6cd5\u5177\u6709\u826f\u597d\u7684\u6cdb\u5316\u80fd\u529b<\/li>\n<\/ul>\n\n\n\n
                            \u88685. \u5728Pubmed\u6570\u636e\u96c6\u4e0a\u8bc4\u4f30\u7684LAGCN\u4e0d\u540c\u7ec4\u4ef6\u7684\u6548\u679c<\/h2>\n\n\n\n
                            \u6280\u672f<\/th>\u51c6\u786e\u7387 (%)<\/th>\u2206<\/th>\u7d2f\u79ef\u2206<\/th><\/tr><\/thead>
                            GCN<\/td>79.0<\/td>0<\/td>0<\/td><\/tr>
                            + Concatenation<\/td>79.3\u00b10.4<\/td>0.3<\/td>0.3<\/td><\/tr>
                            + Local Augmentation<\/td>81.1\u00b10.5<\/td>1.8<\/td>2.1<\/td><\/tr>
                            + Consistency Training<\/td>81.4\u00b10.5<\/td>0.3<\/td>2.4<\/td><\/tr>
                            + Sharpening Trick<\/td>81.7\u00b10.7<\/td>0.3<\/td>2.7<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
                            \u6d88\u878d\u7814\u7a76\u5206\u6790\uff1a<\/h3>\n\n\n\n
                              \n
                            1. \u67b6\u6784\u4fee\u6539\u8d21\u732e\uff1a\u4ec5\u62fc\u63a5\u539f\u59cb\u7279\u5f81\u5e26\u67650.3%\u7684\u63d0\u5347<\/li>\n\n\n\n
                            2. \u5c40\u90e8\u589e\u5f3a\u6838\u5fc3\u8d21\u732e\uff1a\u751f\u6210\u7279\u5f81\u77e9\u9635\u5e26\u67651.8%\u7684\u663e\u8457\u63d0\u5347<\/li>\n\n\n\n
                            3. \u4e00\u81f4\u6027\u8bad\u7ec3\u8d21\u732e\uff1a\u989d\u59160.3%\u7684\u63d0\u5347<\/li>\n\n\n\n
                            4. \u9510\u5316\u6280\u5de7\u8d21\u732e\uff1a\u6700\u7ec80.3%\u7684\u63d0\u5347<\/li>\n\n\n\n
                            5. \u603b\u4f53\u63d0\u5347\uff1a\u4ece79.0%\u63d0\u5347\u523081.7%\uff0c\u603b\u51712.7%\u7684\u6539\u8fdb<\/li>\n<\/ol>\n\n\n\n
                              \u88686. \u5728Citeseer\u6570\u636e\u96c6\u4e0a\u7279\u5f81\u6062\u590d\u7814\u7a76\u7684GCN\u7ed3\u679c\u603b\u7ed3\uff08\u5206\u7c7b\u51c6\u786e\u7387%\uff09<\/h2>\n\n\n\n
                              \u5c4f\u853d\u6bd4\u4f8b<\/th>0.1<\/th>0.2<\/th>0.4<\/th>0.8<\/th><\/tr><\/thead>
                              GCN<\/td>70.4(\u21910.1)<\/td>69.2(\u21931.1)<\/td>67.2(\u21933.1)<\/td>61.1(\u21939.2)<\/td><\/tr>
                              LAGCN<\/td>73.8(\u21930.9)<\/td>74.0(\u21930.7)<\/td>71.8(\u21932.9)<\/td>68.7(\u21936.0)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
                              \u9c81\u68d2\u6027\u5206\u6790\uff1a<\/h3>\n\n\n\n
                                \n
                              1. \u4f4e\u5c4f\u853d\u6bd4\u4f8b\uff080.1-0.2\uff09\uff1a<\/li>\n<\/ol>\n\n\n\n
                                  \n
                                • GCN\u6027\u80fd\u57fa\u672c\u4fdd\u6301\u6216\u7565\u6709\u4e0b\u964d<\/li>\n\n\n\n
                                • LAGCN\u6027\u80fd\u7565\u6709\u4e0b\u964d\u4f46\u4fdd\u6301\u8f83\u9ad8\u6c34\u5e73<\/li>\n<\/ul>\n\n\n\n
                                    \n
                                  1. \u9ad8\u5c4f\u853d\u6bd4\u4f8b\uff080.4-0.8\uff09\uff1a<\/li>\n<\/ol>\n\n\n\n
                                      \n
                                    • GCN\u6027\u80fd\u663e\u8457\u4e0b\u964d\uff083.1%-9.2%\uff09<\/li>\n\n\n\n
                                    • LAGCN\u6027\u80fd\u4e0b\u964d\u5e45\u5ea6\u8f83\u5c0f\uff082.9%-6.0%\uff09<\/li>\n\n\n\n
                                    • LAGCN\u5728\u4fe1\u606f\u7f3a\u5931\u65f6\u8868\u73b0\u51fa\u66f4\u5f3a\u7684\u9c81\u68d2\u6027<\/li>\n<\/ul>\n\n\n\n
                                        \n
                                      1. \u6027\u80fd\u5dee\u8ddd\u6269\u5927\uff1a<\/li>\n<\/ol>\n\n\n\n
                                          \n
                                        • \u968f\u7740\u5c4f\u853d\u6bd4\u4f8b\u589e\u52a0\uff0cLAGCN\u76f8\u6bd4GCN\u7684\u4f18\u52bf\u66f4\u52a0\u660e\u663e<\/li>\n\n\n\n
                                        • \u8bc1\u660e\u4e86\u5c40\u90e8\u589e\u5f3a\u80fd\u591f\u6709\u6548\u8865\u5145\u7f3a\u5931\u7684\u7279\u5f81\u4fe1\u606f<\/li>\n<\/ul>\n\n\n\n
                                          \u88687. \u5728Pubmed\u6570\u636e\u96c6\u4e0a\u6848\u4f8b\u7814\u7a76\u7684GCN\u548cLAGCN\u7ed3\u679c\u603b\u7ed3\uff08\u5206\u7c7b\u51c6\u786e\u7387%\uff09<\/h2>\n\n\n\n
                                          \u8282\u70b9\u5ea6<\/th>[2, 5]<\/th>[6, 20]<\/th><\/tr><\/thead>
                                          #Nodes<\/td>761<\/td>189<\/td><\/tr>
                                          GCN<\/td>78.2<\/td>82.0<\/td><\/tr>
                                          LAGCN<\/td>79.9<\/td>82.2<\/td><\/tr>
                                          \u2206<\/td>1.7<\/td>0.2<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
                                          \u6848\u4f8b\u7814\u7a76\u5206\u6790\uff1a<\/h3>\n\n\n\n
                                            \n
                                          1. \u8282\u70b9\u5206\u5e03\uff1a<\/li>\n<\/ol>\n\n\n\n
                                              \n
                                            • \u4f4e\u5ea6\u8282\u70b9\uff08\u5ea62-5\uff09\uff1a761\u4e2a\u8282\u70b9\uff0c\u536080.1%<\/li>\n\n\n\n
                                            • \u9ad8\u5ea6\u8282\u70b9\uff08\u5ea66-20\uff09\uff1a189\u4e2a\u8282\u70b9\uff0c\u536019.9%<\/li>\n<\/ul>\n\n\n\n
                                                \n
                                              1. \u6027\u80fd\u63d0\u5347\u6a21\u5f0f\uff1a<\/li>\n<\/ol>\n\n\n\n
                                                  \n
                                                • \u4f4e\u5ea6\u8282\u70b9\uff1aLAGCN\u76f8\u6bd4GCN\u63d0\u53471.7%\uff0878.2%\u219279.9%\uff09<\/li>\n\n\n\n
                                                • \u9ad8\u5ea6\u8282\u70b9\uff1aLAGCN\u76f8\u6bd4GCN\u63d0\u53470.2%\uff0882.0%\u219282.2%\uff09<\/li>\n<\/ul>\n\n\n\n
                                                    \n
                                                  1. \u5173\u952e\u6d1e\u5bdf\uff1a<\/li>\n<\/ol>\n\n\n\n
                                                      \n
                                                    • \u5c40\u90e8\u589e\u5f3a\u5bf9\u4f4e\u5ea6\u8282\u70b9\u7684\u5e2e\u52a9\u66f4\u5927<\/li>\n\n\n\n
                                                    • \u4f4e\u5ea6\u8282\u70b9\u4fe1\u606f\u4f20\u64ad\u53d7\u9650\uff0c\u5c40\u90e8\u589e\u5f3a\u63d0\u4f9b\u4e86\u989d\u5916\u7684\u90bb\u57df\u4fe1\u606f<\/li>\n\n\n\n
                                                    • \u9ad8\u5ea6\u8282\u70b9\u672c\u8eab\u5df2\u6709\u4e30\u5bcc\u4fe1\u606f\uff0c\u63d0\u5347\u7a7a\u95f4\u6709\u9650<\/li>\n<\/ul>\n\n\n\n
                                                      \u88688. \u5728Cora\u6570\u636e\u96c6\u4e0aLAGCN\u4e0eGCN\u7684MADgap\u6307\u6807\uff0810\u6b21\u8fd0\u884c\uff09<\/h2>\n\n\n\n
                                                      \u5c42\u6570<\/th>GCN<\/th>LAGCN<\/th><\/tr><\/thead>
                                                      Layer2<\/td>0.63\u00b10.02<\/td>0.68\u00b10.02<\/td><\/tr>
                                                      Layer3<\/td>0.61\u00b10.08<\/td>0.61\u00b10.07<\/td><\/tr>
                                                      Layer4<\/td>0.55\u00b10.06<\/td>0.64\u00b10.05<\/td><\/tr>
                                                      Layer5<\/td>0.39\u00b10.23<\/td>0.61\u00b10.06<\/td><\/tr>
                                                      Layer6<\/td>0.24\u00b10.47<\/td>0.31\u00b10.17<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
                                                      \u8fc7\u5e73\u6ed1\u5206\u6790\uff1a<\/h3>\n\n\n\n
                                                        \n
                                                      1. \u6d45\u5c42\uff082-3\u5c42\uff09\uff1a<\/li>\n<\/ol>\n\n\n\n
                                                          \n
                                                        • LAGCN\u7684MADgap\u6307\u6807\u4e0eGCN\u76f8\u5f53\u6216\u7565\u9ad8<\/li>\n\n\n\n
                                                        • \u8868\u660e\u5c40\u90e8\u589e\u5f3a\u5728\u6d45\u5c42\u4fdd\u6301\u4e86\u826f\u597d\u7684\u5c40\u90e8\u6027<\/li>\n<\/ul>\n\n\n\n
                                                            \n
                                                          1. \u4e2d\u5c42\uff084-5\u5c42\uff09\uff1a<\/li>\n<\/ol>\n\n\n\n
                                                              \n
                                                            • LAGCN\u7684MADgap\u6307\u6807\u660e\u663e\u9ad8\u4e8eGCN<\/li>\n\n\n\n
                                                            • \u7279\u522b\u662f\u5728\u7b2c5\u5c42\uff1aLAGCN (0.61) vs GCN (0.39)<\/li>\n<\/ul>\n\n\n\n
                                                                \n
                                                              1. \u6df1\u5c42\uff086\u5c42\uff09\uff1a<\/li>\n<\/ol>\n\n\n\n
                                                                  \n
                                                                • \u4e24\u8005\u90fd\u51fa\u73b0\u660e\u663e\u7684\u8fc7\u5e73\u6ed1\u73b0\u8c61<\/li>\n\n\n\n
                                                                • \u4f46LAGCN\u4ecd\u7136\u4fdd\u6301\u76f8\u5bf9\u8f83\u9ad8\u7684MADgap\u503c<\/li>\n<\/ul>\n\n\n\n
                                                                    \n
                                                                  1. \u5173\u952e\u53d1\u73b0\uff1a<\/li>\n<\/ol>\n\n\n\n
                                                                      \n
                                                                    • LAGCN\u80fd\u591f\u66f4\u597d\u5730\u4fdd\u6301\u8282\u70b9\u8868\u793a\u7684\u5c40\u90e8\u6027<\/li>\n\n\n\n
                                                                    • \u901a\u8fc7\u4e30\u5bcc\u5c40\u90e8\u4fe1\u606f\uff0c\u95f4\u63a5\u7f13\u89e3\u4e86\u8fc7\u5e73\u6ed1\u95ee\u9898<\/li>\n\n\n\n
                                                                    • \u5728\u6df1\u5c42\u7f51\u7edc\u4e2d\uff0cLAGCN\u7684\u8868\u793a\u8d28\u91cf\u4ecd\u7136\u4f18\u4e8eGCN<\/li>\n<\/ul>\n\n\n\n
                                                                      \u7efc\u5408\u7ed3\u8bba\uff1a<\/h3>\n\n\n\n
                                                                        \n
                                                                      1. \u5c40\u90e8\u589e\u5f3a\u662f\u6027\u80fd\u63d0\u5347\u7684\u4e3b\u8981\u6765\u6e90\uff081.8%\u7684\u8d21\u732e\uff09<\/li>\n\n\n\n
                                                                      2. \u5bf9\u4fe1\u606f\u7f3a\u5931\u5177\u6709\u5f3a\u9c81\u68d2\u6027\uff0c\u7279\u522b\u662f\u5728\u9ad8\u5c4f\u853d\u6bd4\u4f8b\u4e0b<\/li>\n\n\n\n
                                                                      3. \u7279\u522b\u6709\u52a9\u4e8e\u4f4e\u5ea6\u8282\u70b9\uff0c\u4e3a\u5176\u63d0\u4f9b\u989d\u5916\u7684\u90bb\u57df\u4fe1\u606f<\/li>\n\n\n\n
                                                                      4. \u80fd\u591f\u7f13\u89e3\u8fc7\u5e73\u6ed1\u95ee\u9898\uff0c\u4fdd\u6301\u8282\u70b9\u8868\u793a\u7684\u5c40\u90e8\u6027<\/li>\n\n\n\n
                                                                      5. \u5404\u7ec4\u4ef6\u534f\u540c\u5de5\u4f5c\uff0c\u5171\u540c\u63d0\u5347\u6a21\u578b\u6027\u80fd<\/li>\n<\/ol>\n\n\n\n
                                                                        4.4. \u6d88\u878d\u7814\u7a76<\/h2>\n\n\n\n
                                                                        \u4e3a\u4e86\u8bc1\u660e\u6211\u4eec\u63d0\u51fa\u7684\u5c40\u90e8\u589e\u5f3a\u6a21\u578b\u7684\u6709\u6548\u6027\uff0c\u6211\u4eec\u5728Pubmed\u6570\u636e\u96c6\u4e0a\u5bf9LAGCN\u8fdb\u884c\u4e86\u5b9e\u9a8c\uff0c\u5c06\u5176\u4e0e\u51e0\u4e2a\u6d88\u878d\u53d8\u4f53\u8fdb\u884c\u6bd4\u8f83\u3002\u7ed3\u679c\u5982\u88685\u6240\u793a\u3002<\/p>\n\n\n\n
                                                                        \u6d88\u878d\u7814\u7a76\u7ed3\u679c\uff1a<\/h3>\n\n\n\n
                                                                          \n
                                                                        1. “+ concatenation”\uff1a\u6211\u4eec\u53ea\u5e94\u7528\u7b2c3.3\u8282\u4e2dLAGCN\u7684\u62fc\u63a5\u5f0f\u8bbe\u8ba1\u67b6\u6784\uff0c\u5c06\u539f\u59cb\u7279\u5f81\u77e9\u9635\u4f5c\u4e3a\u989d\u5916\u7684\u62fc\u63a5\u8f93\u5165\u3002\u6539\u8fdb\u4e3a0.3%\uff0c\u8fd9\u8868\u660e\u6211\u4eec\u5bf9\u67b6\u6784\u7684\u4fee\u6539\u5bf9\u7ed3\u679c\u6ca1\u6709\u5f88\u5927\u5f71\u54cd\u3002<\/li>\n\n\n\n
                                                                        2. “+ local augmentation”\uff1a\u6211\u4eec\u4f7f\u7528\u751f\u6210\u7684\u7279\u5f81\u77e9\u9635\u4f5c\u4e3a\u989d\u5916\u7684\u62fc\u63a5\u8f93\u5165\uff0c\u4f46\u4e0d\u4f7f\u7528\u4e00\u81f4\u6027\u8bad\u7ec3\u3002\u867d\u7136\u6211\u4eec\u6ca1\u6709\u4f7f\u7528\u4e00\u81f4\u6027\u8bad\u7ec3\uff0c\u4f46\u751f\u6210\u7684\u7279\u5f81\u77e9\u9635\u4f5c\u4e3a\u989d\u5916\u8f93\u5165\u5c06GCN\u7684\u6d4b\u8bd5\u51c6\u786e\u7387\u63d0\u9ad8\u4e861.8%\u3002<\/li>\n\n\n\n
                                                                        3. \u5b8c\u6574LA\u65b9\u6cd5\uff1a\u901a\u8fc7\u4e00\u81f4\u6027\u8bad\u7ec3\u548c\u9510\u5316\u6280\u5de7\uff0c\u6211\u4eec\u53ef\u4ee5\u8fdb\u4e00\u6b65\u63d0\u5347\u6027\u80fd\u3002<\/li>\n<\/ol>\n\n\n\n
                                                                          \u5173\u952e\u6d1e\u5bdf\uff1a<\/h3>\n\n\n\n
                                                                          \u4ece\u6d88\u878d\u7814\u7a76\u4e2d\u53ef\u4ee5\u660e\u663e\u770b\u51fa\uff0c\u6027\u80fd\u63d0\u5347\u4e3b\u8981\u5f52\u56e0\u4e8e\u6211\u4eec\u63d0\u51fa\u7684\u751f\u6210\u5f0f\u5c40\u90e8\u589e\u5f3a\u6846\u67b6\uff1a<\/p>\n\n\n\n
                                                                            \n
                                                                          • \u67b6\u6784\u4fee\u6539\u7684\u8d21\u732e\uff1a\u4ec50.3%\u7684\u6539\u8fdb<\/li>\n\n\n\n
                                                                          • \u5c40\u90e8\u589e\u5f3a\u7684\u8d21\u732e\uff1a1.8%\u7684\u6539\u8fdb<\/li>\n\n\n\n
                                                                          • \u4e00\u81f4\u6027\u8bad\u7ec3\u7684\u8d21\u732e\uff1a\u989d\u5916\u7684\u6027\u80fd\u63d0\u5347<\/li>\n<\/ul>\n\n\n\n
                                                                            \u8fd9\u8bc1\u660e\u4e86\uff1a<\/p>\n\n\n\n
                                                                              \n
                                                                            1. \u5c40\u90e8\u589e\u5f3a\u662f\u6027\u80fd\u63d0\u5347\u7684\u4e3b\u8981\u6765\u6e90<\/li>\n\n\n\n
                                                                            2. \u751f\u6210\u7684\u7279\u5f81\u5411\u91cf\u786e\u5b9e\u63d0\u4f9b\u4e86\u6709\u4ef7\u503c\u7684\u4fe1\u606f<\/li>\n\n\n\n
                                                                            3. \u4e00\u81f4\u6027\u8bad\u7ec3\u8fdb\u4e00\u6b65\u7a33\u5b9a\u548c\u63d0\u5347\u4e86\u6a21\u578b\u6027\u80fd<\/li>\n\n\n\n
                                                                            4. \u6211\u4eec\u7684\u65b9\u6cd5\u5728\u4fdd\u6301\u6a21\u578b\u7b80\u6d01\u6027\u7684\u540c\u65f6\u5b9e\u73b0\u4e86\u663e\u8457\u7684\u6027\u80fd\u6539\u8fdb<\/li>\n<\/ol>\n\n\n\n
                                                                              \u8fd9\u4e9b\u7ed3\u679c\u9a8c\u8bc1\u4e86\u5c40\u90e8\u589e\u5f3a\u6846\u67b6\u5404\u4e2a\u7ec4\u4ef6\u7684\u6709\u6548\u6027\uff0c\u5e76\u8bc1\u660e\u4e86\u8be5\u65b9\u6cd5\u7684\u6838\u5fc3\u4ef7\u503c\u5728\u4e8e\u751f\u6210\u9ad8\u8d28\u91cf\u7684\u5c40\u90e8\u589e\u5f3a\u7279\u5f81\u3002<\/p>\n\n\n\n
                                                                              4.5. \u5bf9\u7f3a\u5931\u4fe1\u606f\u7684\u9c81\u68d2\u6027<\/h2>\n\n\n\n
                                                                              \u5728\u672c\u8282\u4e2d\uff0c\u6211\u4eec\u8fdb\u884c\u5b9e\u9a8c\u6765\u9a8c\u8bc1\u6211\u4eec\u63d0\u51fa\u7684\u6846\u67b6\u5bf9\u7279\u5f81\u5c5e\u6027\u4e2d\u7f3a\u5931\u4fe1\u606f\u5177\u6709\u9c81\u68d2\u6027\u3002\u5177\u4f53\u5730\uff0c\u6211\u4eec\u5c4f\u853d\u6bcf\u4e2a\u7279\u5f81\u5411\u91cf\u7684\u4e00\u5b9a\u767e\u5206\u6bd4\u7684\u5c5e\u6027\uff0c\u5e76\u4f7f\u7528\u76f8\u540c\u7684\u7ba1\u9053\u5bf9\u5c4f\u853d\u7684\u7279\u5f81\u77e9\u9635\u8fdb\u884c\u589e\u5f3a\u3002\u5982\u88686\u6240\u793a\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\uff0c\u968f\u7740\u5c4f\u853d\u6bd4\u4f8b\u7684\u589e\u52a0\uff0c\u5728Citeseer\u6570\u636e\u96c6\u4e2d\uff0cGCN\u548cLA-GCN\u4e4b\u95f4\u7684\u6027\u80fd\u5dee\u8ddd\u5728\u5927\u591a\u6570\u60c5\u51b5\u4e0b\u90fd\u4f1a\u6269\u5927\uff0c\u8fd9\u8bc1\u5b9e\u4e86\u6211\u4eec\u7684\u6d1e\u5bdf\uff1a\u6211\u4eec\u7684\u5c40\u90e8\u589e\u5f3a\u53ef\u4ee5\u8865\u5145\u5c40\u90e8\u90bb\u57df\u7684\u4e0a\u4e0b\u6587\u4fe1\u606f\u3002<\/p>\n\n\n\n
                                                                              \u4e3b\u8981\u53d1\u73b0\uff1a<\/h3>\n\n\n\n
                                                                                \n
                                                                              1. \u9c81\u68d2\u6027\u9a8c\u8bc1\uff1a<\/li>\n<\/ol>\n\n\n\n
                                                                                  \n
                                                                                • \u968f\u7740\u7279\u5f81\u5c4f\u853d\u6bd4\u4f8b\u589e\u52a0\uff0cLA-GCN\u76f8\u6bd4GCN\u7684\u4f18\u52bf\u66f4\u52a0\u660e\u663e<\/li>\n\n\n\n
                                                                                • \u8bc1\u660e\u4e86\u5c40\u90e8\u589e\u5f3a\u65b9\u6cd5\u80fd\u591f\u6709\u6548\u5904\u7406\u4e0d\u5b8c\u6574\u7684\u7279\u5f81\u4fe1\u606f<\/li>\n<\/ul>\n\n\n\n
                                                                                    \n
                                                                                  1. \u4e0a\u4e0b\u6587\u4fe1\u606f\u8865\u5145\uff1a<\/li>\n<\/ol>\n\n\n\n
                                                                                      \n
                                                                                    • \u5c40\u90e8\u589e\u5f3a\u80fd\u591f\u4ece\u90bb\u57df\u4fe1\u606f\u4e2d\u63a8\u65ad\u548c\u8865\u5145\u7f3a\u5931\u7684\u7279\u5f81<\/li>\n\n\n\n
                                                                                    • \u5728\u4fe1\u606f\u7f3a\u5931\u7684\u60c5\u51b5\u4e0b\uff0c\u589e\u5f3a\u65b9\u6cd5\u663e\u793a\u51fa\u66f4\u5f3a\u7684\u9002\u5e94\u6027<\/li>\n<\/ul>\n\n\n\n
                                                                                      4.6. \u6848\u4f8b\u7814\u7a76<\/h2>\n\n\n\n
                                                                                      \u5728\u672c\u8282\u4e2d\uff0c\u6211\u4eec\u63a2\u7d22\u5e94\u7528\u6211\u4eec\u7684\u5c40\u90e8\u589e\u5f3a\u65b9\u6cd5\u540e\u4e0d\u540c\u8282\u70b9\u6d4b\u8bd5\u51c6\u786e\u7387\u7684\u53d8\u5316\u3002\u6ce8\u610f\uff0c\u6211\u4eec\u53ea\u5e94\u7528\u5c40\u90e8\u589e\u5f3a\u800c\u4e0d\u4f7f\u7528\u4e00\u81f4\u6027\u8bad\u7ec3\uff0c\u5e76\u5c06S\u8bbe\u7f6e\u4e3a1\u3002\u7ed3\u679c\u603b\u7ed3\u5728\u88687\u4e2d\u3002<\/p>\n\n\n\n
                                                                                      \u4e3b\u8981\u7ed3\u8bba\uff1a<\/h3>\n\n\n\n
                                                                                        \n
                                                                                      1. \u8282\u70b9\u5ea6\u5206\u5e03\uff1a<\/li>\n<\/ol>\n\n\n\n
                                                                                          \n
                                                                                        • Pubmed\u6d4b\u8bd5\u96c6\u4e2d\u5927\u591a\u6570\u8282\u70b9\u7684\u5ea6\u76f8\u5bf9\u8f83\u5c0f<\/li>\n\n\n\n
                                                                                        • \u5ea6\u5c0f\u4e8e6\u7684\u8282\u70b9\u7ea6\u536076.1%<\/li>\n<\/ul>\n\n\n\n
                                                                                            \n
                                                                                          1. \u6027\u80fd\u63d0\u5347\u6a21\u5f0f\uff1a<\/li>\n<\/ol>\n\n\n\n
                                                                                              \n
                                                                                            • \u5ea6\u8f83\u5c0f\u7684\u8282\u70b9\u5f80\u5f80\u5177\u6709\u8f83\u4f4e\u7684\u6d4b\u8bd5\u51c6\u786e\u7387<\/li>\n\n\n\n
                                                                                            • \u6211\u4eec\u7684\u5c40\u90e8\u589e\u5f3a\u53ef\u4ee5\u4e3a\u8fd9\u4e9b\u8282\u70b9\u4e30\u5bcc\u5c40\u90e8\u4fe1\u606f\uff0c\u4ece\u800c\u63d0\u5347\u5b83\u4eec\u7684\u6027\u80fd<\/li>\n<\/ul>\n\n\n\n
                                                                                                \n
                                                                                              1. \u5c40\u90e8\u4fe1\u606f\u589e\u5f3a\uff1a<\/li>\n<\/ol>\n\n\n\n
                                                                                                  \n
                                                                                                • \u5bf9\u4e8e\u4f4e\u5ea6\u8282\u70b9\uff0c\u5c40\u90e8\u589e\u5f3a\u63d0\u4f9b\u4e86\u989d\u5916\u7684\u90bb\u57df\u4fe1\u606f<\/li>\n\n\n\n
                                                                                                • \u8fd9\u6709\u52a9\u4e8e\u6539\u5584\u4fe1\u606f\u4f20\u64ad\u53d7\u9650\u8282\u70b9\u7684\u8868\u793a\u8d28\u91cf<\/li>\n<\/ul>\n\n\n\n
                                                                                                  4.7. \u8fc7\u5e73\u6ed1\u5206\u6790<\/h2>\n\n\n\n
                                                                                                  \u4f17\u6240\u5468\u77e5\uff0c\u5806\u53e0GNN\u5c42\u4f1a\u5bfc\u81f4\u8fc7\u5e73\u6ed1\uff08Li et al., 2018\uff09\u3002\u5728\u672c\u8282\u4e2d\uff0c\u6211\u4eec\u8ba8\u8bba\u6211\u4eec\u63d0\u51fa\u7684\u65b9\u6cd5\u5982\u4f55\u4e0e\u73b0\u6709\u65b9\u6cd5\u76f8\u6bd4\u9632\u6b62GNN\u4e2d\u7684\u8fc7\u5e73\u6ed1\u95ee\u9898\u3002\u6211\u4eec\u5229\u7528MADgap\uff08Chen et al., 2020a\uff09\u6307\u6807\u6765\u6bd4\u8f83\u6211\u4eec\u7684\u65b9\u6cd5\u4e0e\u73b0\u6709GNNs\u3002<\/p>\n\n\n\n
                                                                                                  \u4e3b\u8981\u53d1\u73b0\uff1a<\/h3>\n\n\n\n
                                                                                                    \n
                                                                                                  1. MADgap\u6307\u6807\u6bd4\u8f83\uff1a<\/li>\n<\/ol>\n\n\n\n
                                                                                                      \n
                                                                                                    • \u88688\u62a5\u544a\u4e86LAGCN\u548cGCN\u5728Cora\u6570\u636e\u96c6\u4e0a\uff08\u4e0d\u540c\u5c42\u6570\uff09\u7684MADgap\u6307\u6807<\/li>\n\n\n\n
                                                                                                    • \u53ef\u4ee5\u89c2\u5bdf\u5230\uff0cLAGCN\u7684MADgap\u6307\u6807\u5728\u4e0d\u540c\u5c42\u4e0a\u90fd\u5927\u4e8e\u6216\u7b49\u4e8eGCN<\/li>\n<\/ul>\n\n\n\n
                                                                                                        \n
                                                                                                      1. \u8fc7\u5e73\u6ed1\u7f13\u89e3\u673a\u5236\uff1a<\/li>\n<\/ol>\n\n\n\n
                                                                                                          \n
                                                                                                        • \u867d\u7136\u6211\u4eec\u7684\u65b9\u6cd5\u4e0d\u662f\u4e13\u95e8\u89e3\u51b3\u8fc7\u5e73\u6ed1\u95ee\u9898\u7684<\/li>\n\n\n\n
                                                                                                        • \u4f46\u6211\u4eec\u7684\u65b9\u6cd5\u53ef\u4ee5\u4e30\u5bcc\u5c40\u90e8\u90bb\u57df\u4fe1\u606f\uff0c\u4ece\u800c\u6539\u5584\u8282\u70b9\u8868\u793a\u7684\u5c40\u90e8\u6027<\/li>\n\n\n\n
                                                                                                        • \u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u7f13\u89e3\u8fc7\u5e73\u6ed1\u95ee\u9898<\/li>\n<\/ul>\n\n\n\n
                                                                                                            \n
                                                                                                          1. \u5c40\u90e8\u6027\u4fdd\u6301\uff1a<\/li>\n<\/ol>\n\n\n\n
                                                                                                              \n
                                                                                                            • \u5c40\u90e8\u589e\u5f3a\u901a\u8fc7\u63d0\u4f9b\u989d\u5916\u7684\u5c40\u90e8\u4fe1\u606f\uff0c\u5e2e\u52a9\u4fdd\u6301\u8282\u70b9\u8868\u793a\u7684\u5c40\u90e8\u7279\u5f81<\/li>\n\n\n\n
                                                                                                            • \u8fd9\u6709\u52a9\u4e8e\u9632\u6b62\u6df1\u5c42GNN\u4e2d\u7684\u8868\u793a\u8fc7\u5ea6\u5e73\u6ed1<\/li>\n<\/ul>\n\n\n\n
                                                                                                              \u5173\u952e\u6d1e\u5bdf\uff1a<\/h3>\n\n\n\n
                                                                                                                \n
                                                                                                              1. \u4fe1\u606f\u8865\u5145\u80fd\u529b\uff1a\u5c40\u90e8\u589e\u5f3a\u65b9\u6cd5\u5728\u7279\u5f81\u4fe1\u606f\u7f3a\u5931\u65f6\u8868\u73b0\u51fa\u66f4\u5f3a\u7684\u9c81\u68d2\u6027<\/li>\n\n\n\n
                                                                                                              2. \u4f4e\u5ea6\u8282\u70b9\u4f18\u5316\uff1a\u65b9\u6cd5\u7279\u522b\u6709\u52a9\u4e8e\u6539\u5584\u4fe1\u606f\u4f20\u64ad\u53d7\u9650\u7684\u4f4e\u5ea6\u8282\u70b9<\/li>\n\n\n\n
                                                                                                              3. \u8fc7\u5e73\u6ed1\u7f13\u89e3\uff1a\u901a\u8fc7\u4e30\u5bcc\u5c40\u90e8\u4fe1\u606f\uff0c\u95f4\u63a5\u7f13\u89e3\u4e86\u6df1\u5c42GNN\u7684\u8fc7\u5e73\u6ed1\u95ee\u9898<\/li>\n\n\n\n
                                                                                                              4. \u901a\u7528\u6027\u9a8c\u8bc1\uff1a\u8fd9\u4e9b\u5206\u6790\u8bc1\u660e\u4e86\u5c40\u90e8\u589e\u5f3a\u65b9\u6cd5\u5728\u4e0d\u540c\u573a\u666f\u4e0b\u7684\u6709\u6548\u6027\u548c\u9002\u5e94\u6027<\/li>\n<\/ol>\n\n\n\n
                                                                                                                \u8fd9\u4e9b\u5b9e\u9a8c\u4ece\u591a\u4e2a\u89d2\u5ea6\u9a8c\u8bc1\u4e86\u5c40\u90e8\u589e\u5f3a\u65b9\u6cd5\u7684\u6709\u6548\u6027\u548c\u9c81\u68d2\u6027\uff0c\u4e3a\u65b9\u6cd5\u7684\u5b9e\u9645\u5e94\u7528\u63d0\u4f9b\u4e86\u575a\u5b9e\u7684\u7406\u8bba\u57fa\u7840\u3002<\/p>\n\n\n\n
                                                                                                                5. \u76f8\u5173\u5de5\u4f5c<\/h2>\n\n\n\n
                                                                                                                5.1. \u56fe\u4e0a\u7684\u65e0\u76d1\u7763\u8868\u793a\u5b66\u4e60<\/h3>\n\n\n\n
                                                                                                                \u4e00\u822c\u6765\u8bf4\uff0c\u56fe\u4e0a\u7684\u65e0\u76d1\u7763\u8868\u793a\u5b66\u4e60\u65b9\u6cd5\u5305\u62ec\u57fa\u4e8e\u5bf9\u6bd4\u7684\u81ea\u76d1\u7763\u65b9\u6cd5\uff08Velickovic et al., 2019; Sun et al., 2020; Hassani & Khasahmadi, 2020; You et al., 2020\uff09\u3001\u56fe\u5d4c\u5165\u65b9\u6cd5\uff08Garc\u00eda-Dur\u00e1n & Niepert, 2017; Hamilton et al., 2017\uff09\u548c\u968f\u673a\u6e38\u8d70\u65b9\u6cd5\uff08Perozzi et al., 2014; Tang et al., 2015; Grover & Leskovec, 2016\uff09\u3002<\/p>\n\n\n\n
                                                                                                                \u5bf9\u6bd4\u5b66\u4e60\u65b9\u6cd5\uff08Hassani & Khasahmadi, 2020; You et al., 2020\uff09\u91c7\u7528\u5bf9\u6bd4\u635f\u5931\u51fd\u6570\u6765\u5f3a\u5236\u6700\u5c0f\u5316\u6b63\u6837\u672c\u5bf9\u7684\u8868\u793a\u8ddd\u79bb\uff0c\u6700\u5927\u5316\u8d1f\u6837\u672c\u5bf9\u7684\u8ddd\u79bb\u3002<\/p>\n\n\n\n
                                                                                                                \u968f\u673a\u6e38\u8d70\u65b9\u6cd5\u901a\u8fc7\u5728\u8282\u70b9\u95f4\u8fdb\u884c\u968f\u673a\u6e38\u8d70\u6765\u83b7\u5f97\u53e5\u5b50\uff0c\u5e76\u4f7f\u7528NLP\u8bcd\u5d4c\u5165\u6a21\u578b\u6765\u5b66\u4e60\u8282\u70b9\u8868\u793a\u3002<\/p>\n\n\n\n
                                                                                                                \u6211\u4eec\u7684\u5c40\u90e8\u589e\u5f3a\u4e5f\u662f\u4e00\u79cd\u5b66\u4e60\u5c40\u90e8\u90bb\u57df\u4fe1\u606f\u7684\u65e0\u76d1\u7763\u65b9\u6cd5\u3002<\/p>\n\n\n\n
                                                                                                                5.2. \u56fe\u751f\u6210\u6a21\u578b<\/h3>\n\n\n\n
                                                                                                                \u751f\u6210\u6a21\u578b\uff08Goodfellow et al., 2014; Kingma & Welling, 2013\uff09\u662f\u901a\u8fc7\u65e0\u76d1\u7763\u5b66\u4e60\u5b66\u4e60\u6570\u636e\u5206\u5e03\u7684\u5f3a\u5927\u5de5\u5177\u3002\u6700\u8fd1\uff0c\u7814\u7a76\u4eba\u5458\u63d0\u51fa\u4e86\u51e0\u79cd\u6709\u8da3\u7684\u56fe\u6570\u636e\u751f\u6210\u751f\u6210\u6a21\u578b\u3002<\/p>\n\n\n\n
                                                                                                                  \n
                                                                                                                • \u53d8\u5206\u56fe\u81ea\u7f16\u7801\u5668\uff08VGAE\uff09\uff08Kipf & Welling, 2016\uff09\u5229\u7528\u6f5c\u5728\u53d8\u91cf\u6765\u5b66\u4e60\u65e0\u5411\u56fe\u7684\u53ef\u89e3\u91ca\u8868\u793a<\/li>\n\n\n\n
                                                                                                                • Salha et al. (2019) \u4f7f\u7528\u7b80\u5355\u7684\u7ebf\u6027\u6a21\u578b\u66ff\u6362VGAE\u4e2d\u7684GCN\u7f16\u7801\u5668\uff0c\u964d\u4f4e\u7f16\u7801\u65b9\u6848\u7684\u590d\u6742\u5ea6<\/li>\n\n\n\n
                                                                                                                • Xu et al. (2019a) \u63d0\u51fa\u4e86\u751f\u6210GCN\u6a21\u578b\u6765\u5b66\u4e60\u589e\u957f\u56fe\u7684\u8282\u70b9\u8868\u793a<\/li>\n\n\n\n
                                                                                                                • ConDgen\uff08Yang et al., 2019\uff09\u5229\u7528GCN\u7f16\u7801\u5668\u5904\u7406\u6761\u4ef6\u7ed3\u6784\u751f\u6210\u7684\u4e0d\u53d8\u6392\u5217<\/li>\n<\/ul>\n\n\n\n
                                                                                                                  \u6b64\u5916\uff0c\u4e00\u4e9b\u65b9\u6cd5\u88ab\u63d0\u51fa\u5c06\u56fe\u751f\u6210\u6a21\u578b\u5e94\u7528\u4e8e\u5404\u79cd\u5e94\u7528\u4e2d\uff0c\u5982\u56fe\u5339\u914d\uff08Simonovsky & Komodakis, 2018\uff09\u3001\u5206\u5b50\u8bbe\u8ba1\uff08Liu et al., 2018\uff09\u3001\u9006\u5408\u6210\u9884\u6d4b\uff08Shi et al., 2020\uff09\u548c\u5316\u5b66\u8bbe\u8ba1\uff08Samanta et al., 2018\uff09\u3002<\/p>\n\n\n\n
                                                                                                                  \u4e0e\u8fd9\u4e9b\u4e3b\u8981\u5173\u6ce8\u7ed3\u6784\u751f\u6210\u7684\u65b9\u6cd5\u76f8\u6bd4\uff0c\u6211\u4eec\u7684\u6a21\u578b\u5145\u5206\u5229\u7528\u4e86\u751f\u6210\u6a21\u578b\u7684\u529b\u91cf\u8fdb\u884c\u7279\u5f81\u8868\u793a\u751f\u6210\uff0c\u53ef\u4ee5\u4f5c\u4e3a\u4e0b\u6e38\u9aa8\u5e72\u6a21\u578b\u7684\u589e\u5f3a\u6280\u672f\u3002<\/p>\n\n\n\n
                                                                                                                  5.3. \u62fc\u63a5\u5f0f\u8bbe\u8ba1<\/h3>\n\n\n\n
                                                                                                                  \u5728\u8fd9\u9879\u5de5\u4f5c\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528\u62fc\u63a5\u6765\u8fde\u63a5\u539f\u59cb\u7279\u5f81\u548c\u6bcf\u4e2a\u8bad\u7ec3\u8fed\u4ee3\u4e2d\u4e0d\u540c\u7684\u751f\u6210\u7279\u5f81\uff0c\u901a\u8fc7\u5c40\u90e8\u589e\u5f3a\u6765\u4e30\u5bcc\u90bb\u57df\u4fe1\u606f\u3002\u62fc\u63a5\u5f0f\u8bbe\u8ba1\u662f\u4e00\u79cd\u901a\u7528\u6280\u672f\uff0c\u8bb8\u591a\u5de5\u4f5c\u90fd\u91c7\u7528\u8fd9\u79cd\u65b9\u6cd5\uff0c\u5982GAT\uff08Veli\u010dkovi\u0107 et al., 2018\uff09\u548cSIGN\uff08Rossi et al., 2020\uff09\u3002<\/p>\n\n\n\n
                                                                                                                  SIGN\u4e13\u6ce8\u4e8e\u5927\u578b\u56fe\u4e0aGNN\u6a21\u578b\u7684\u53ef\u6269\u5c55\u8bad\u7ec3\uff0c\u901a\u8fc7\u90bb\u63a5\u77e9\u9635\u7684\u5e42\u6b21\u6765\u589e\u5f3a\u591a\u8df3\u4fe1\u606f\u7684\u7279\u5f81\u3002<\/p>\n\n\n\n
                                                                                                                  6. \u7ed3\u8bba<\/h2>\n\n\n\n
                                                                                                                  \u6211\u4eec\u63d0\u51fa\u4e86\u5c40\u90e8\u589e\u5f3a\uff0c\u8fd9\u662f\u4e00\u79cd\u65b0\u6280\u672f\uff0c\u5229\u7528\u751f\u6210\u6a21\u578b\u6765\u5b66\u4e60\u7ed9\u5b9a\u4e2d\u5fc3\u8282\u70b9\u7279\u5f81\u7684\u4e2d\u5fc3\u8282\u70b9\u90bb\u5c45\u7279\u5f81\u7684\u6761\u4ef6\u5206\u5e03\u3002\u6211\u4eec\u5c06\u6765\u81ea\u8bad\u7ec3\u826f\u597d\u7684\u751f\u6210\u6a21\u578b\u7684\u751f\u6210\u7279\u5f81\u77e9\u9635\u8f93\u5165\u5230\u4e00\u4e9b\u4fee\u6539\u7684\u9aa8\u5e72GNN\u6a21\u578b\u4e2d\uff0c\u4ee5\u589e\u5f3a\u5b83\u4eec\u7684\u6027\u80fd\u3002<\/p>\n\n\n\n
                                                                                                                  \u4e3b\u8981\u8d21\u732e\uff1a<\/h3>\n\n\n\n
                                                                                                                    \n
                                                                                                                  1. \u6027\u80fd\u63d0\u5347\uff1a\u5b9e\u9a8c\u8868\u660e\uff0c\u6211\u4eec\u7684\u6a21\u578b\u53ef\u4ee5\u5728\u5404\u79cdGNN\u67b6\u6784\u548c\u57fa\u51c6\u6570\u636e\u96c6\u4e0a\u63d0\u9ad8\u6027\u80fd<\/li>\n\n\n\n
                                                                                                                  2. \u6700\u5148\u8fdb\u7ed3\u679c\uff1a\u6211\u4eec\u7684\u6a21\u578b\u5728\u5404\u79cd\u534a\u76d1\u7763\u8282\u70b9\u5206\u7c7b\u4efb\u52a1\u4e0a\u53d6\u5f97\u4e86\u65b0\u7684\u6700\u5148\u8fdb\u7ed3\u679c<\/li>\n\n\n\n
                                                                                                                  3. \u901a\u7528\u6027\uff1a\u65b9\u6cd5\u9002\u7528\u4e8e\u4e0d\u540c\u7684GNN\u67b6\u6784\u548c\u6570\u636e\u96c6<\/li>\n<\/ol>\n\n\n\n
                                                                                                                    \u5c40\u9650\u6027\uff1a<\/h3>\n\n\n\n
                                                                                                                    \u6211\u4eec\u63d0\u51fa\u7684\u6846\u67b6\u7684\u4e00\u4e2a\u5c40\u9650\u6027\u662f\u6211\u4eec\u6ca1\u6709\u5229\u75282\u8df3\u90bb\u5c45\u6216\u4f7f\u7528\u968f\u673a\u6e38\u8d70\u6765\u4e3a\u4e2d\u5fc3\u8282\u70b9\u627e\u5230\u66f4\u591a\u76f8\u5173\u90bb\u5c45\u3002<\/p>\n\n\n\n
                                                                                                                    \u672a\u6765\u5de5\u4f5c\uff1a<\/h3>\n\n\n\n
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                                                                                                                    Local Augmentation for Graph Neural Networks \u6458\u8981 \u56fe\u795e\u7ecf\u7f51\u7edc\uff08G […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[57,4],"tags":[66,65],"class_list":["post-789","post","type-post","status-publish","format-standard","hentry","category-python","category-blog","tag-lagnn","tag-65"],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/blog.heartwarming.online\/index.php\/wp-json\/wp\/v2\/posts\/789","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.heartwarming.online\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.heartwarming.online\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.heartwarming.online\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.heartwarming.online\/index.php\/wp-json\/wp\/v2\/comments?post=789"}],"version-history":[{"count":1,"href":"https:\/\/blog.heartwarming.online\/index.php\/wp-json\/wp\/v2\/posts\/789\/revisions"}],"predecessor-version":[{"id":790,"href":"https:\/\/blog.heartwarming.online\/index.php\/wp-json\/wp\/v2\/posts\/789\/revisions\/790"}],"wp:attachment":[{"href":"https:\/\/blog.heartwarming.online\/index.php\/wp-json\/wp\/v2\/media?parent=789"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.heartwarming.online\/index.php\/wp-json\/wp\/v2\/categories?post=789"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.heartwarming.online\/index.php\/wp-json\/wp\/v2\/tags?post=789"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}