{"id":52106,"date":"2024-08-17T20:57:13","date_gmt":"2024-08-17T12:57:13","guid":{"rendered":"https:\/\/swarma.org\/?p=52106"},"modified":"2024-08-17T20:57:13","modified_gmt":"2024-08-17T12:57:13","slug":"%e4%bb%8e%e5%9b%be%e7%a5%9e%e7%bb%8f%e7%bd%91%e7%bb%9c%e5%88%b0%e5%87%a0%e4%bd%95%e6%b7%b1%e5%ba%a6%e5%ad%a6%e4%b9%a0%ef%bc%9aai4science%e7%9a%84%e4%b8%8b%e4%b8%80%e4%b8%aa%e9%a2%a0%e8%a6%86%e6%80%a7","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=52106","title":{"rendered":"\u4ece\u56fe\u795e\u7ecf\u7f51\u7edc\u5230\u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60\uff1aAI4Science\u7684\u4e0b\u4e00\u4e2a\u98a0\u8986\u6027\u7a81\u7834\u5728\u4f55\u5904\uff1f"},"content":{"rendered":"
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\u5728\u79d1\u5b66\u9886\u57df\uff0c\u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60<\/span>\uff08Geometric Deep Learning, GDL\uff09<\/span>\u662f\u4eba\u5de5\u667a\u80fd\u7814\u7a76\u7684\u91cd\u8981\u65b9\u5411\u3002\u81ea2022\u5e74AlphaFold 2\u5f00\u6e90\u4ee5\u6765\uff0c\u4eba\u4eec\u9010\u6e10\u8ba4\u8bc6\u5230AI\u5728\u751f\u7269\u5b66\uff0c\u7279\u522b\u662f\u7ed3\u6784\u751f\u7269\u5b66\u4e2d\u7684\u5de8\u5927\u8d21\u732e\uff0c\u5305\u62ec\u86cb\u767d\u8d28\u7ed3\u6784\u6298\u53e0\u548c\u9006\u6298\u53e0\u7b49\u5e94\u7528\u3002\u8fd9\u8fdb\u4e00\u6b65\u8bc1\u660e\u4e86AI\u5728\u79d1\u5b66\u7814\u7a76\u4e2d\u7684\u6f5c\u529b\u3002\u5728\u86cb\u767d\u8d28\u7ed3\u6784\u9884\u6d4b\u65b9\u9762\uff0cAI\u4e0d\u4ec5\u901f\u5ea6\u5feb\uff0c\u800c\u4e14\u5176\u51c6\u786e\u6027\u80fd\u591f\u4e0e\u5b9e\u9a8c\u5ba4\u6d4b\u5f97\u7ed3\u679c\u76f8\u5ab2\u7f8e\u751a\u81f3\u8d85\u8d8a\uff0c\u8fd9\u4e00\u6210\u679c\u4ee4\u4eba\u632f\u594b\u3002<\/span><\/section>\n

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\u6b64\u5916\uff0c\u5728\u6570\u5b66\u9886\u57df\uff0cDeepMind \u7684\u4e00\u7bc7 Nature \u5c01\u9762\u6587\u7ae0\u4ecb\u7ecd\u4e86\u4e00\u79cd\u5229\u7528\u56fe\u795e\u7ecf\u7f51\u7edc\u8fdb\u884c\u5feb\u901f\u4f18\u5316\u7684\u65b9\u6cd5\uff0c\u7528\u4ee5\u8bc1\u660e\u67d0\u4e9b\u6570\u5b66\u731c\u60f3\uff0c\u4f8b\u5982\u62d3\u6251\u5b66\u4e2d\u7684\u7ebd\u7ed3\u5b9a\u7406\u4ee5\u53ca\u56fe\u8868\u793a\u8bba\u4e2d\u4e00\u4e9b\u8f83\u5927\u731c\u60f3\u7684\u4f18\u5316\uff0c\u5305\u62ec\u754c\u7684\u4f18\u5316\u3002\u8fd9\u8868\u660e\u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60\uff0c\u7279\u522b\u662f\u5f53\u524d\u7684\u62d3\u6251\u6df1\u5ea6\u5b66\u4e60<\/span>\uff08Topological Deep Learning, TDL\uff09<\/span>\u5177\u6709\u91cd\u8981\u5e94\u7528\u4ef7\u503c\u3002<\/span><\/section>\n

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\u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60 Geometric Deep Learning<\/span><\/strong><\/h2>\n
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\u7b49\u53d8\u6027\uff08Equivariance\uff09\u6307\u5bf9\u4e00\u4e2a\u5bf9\u8c61\u65bd\u52a0\u4e00\u4e2a\u5e7f\u4e49\u7684\u53d8\u6362\u4ee5\u540e\uff0c\u9884\u6d4b\u7ed3\u679c\u662f\u5426\u5728\u67d0\u4e9b\u5c42\u9762\u662f\u4e00\u81f4\u7684\u3002<\/strong>\u4f8b\u5982\u5bf9\u4e8e\u8fd9\u4e2a\u5c0f\u767d\u5154<\/span> (Bunny)<\/span>\uff0c\u5b83\u7ecf\u8fc7\u4e00\u4e2a\u65cb\u8f6c\u53d8\u6362\u540e\u662f\u5426\u8fd8\u80fd\u5224\u65ad\u51fa\u5b83\u662f\u4e00\u4e2a\u5c0f\u767d\u5154\u3002\u8fd9\u79cd\u7a7a\u95f4\u4e0a\u7684\u7b49\u53d8\u6027\u5bf9\u836f\u7269\u8bbe\u8ba1\uff0c\u7279\u522b\u662f\u5927\u5206\u5b50\u836f\u7269\u8bbe\u8ba1\u3001\u6297\u4f53\u8bbe\u8ba1\u7684\u9884\u6d4b\u590d\u5408\u4f53\u7ed3\u6784\u4e2d<\/span>\uff08\u4f8b\u5982 AlphaFold 3\uff09<\/span>\u7684\u51c6\u786e\u6027\u7684\u63d0\u5347\u5341\u5206\u91cd\u8981\u3002<\/span><\/section>\n

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\u611f\u5174\u8da3\u7684\u670b\u53cb\u53ef\u4ee5\u89c2\u770b\u76f8\u5173\u5206\u4eab\u2014\u2014\u56fe\u795e\u7ecf\u7f51\u7edc\u4e0e\u7ec4\u5408\u4f18\u5316\uff1a5.\u51e0\u4f55\u56fe\u795e\u7ecf\u7f51\u7edc\u53ca\u5176\u79d1\u5b66\u5e94\u7528\uff08https:\/\/pattern.swarma.org\/study_group_issue\/485\uff09\u3002\u5e76\u4e14\uff0c\u793e\u533a\u6210\u5458\u6574\u7406\u6210\u7b14\u8bb0\uff0c\u4f9b\u5927\u5bb6\u5b66\u4e60\u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60\uff1a\u8ba9\u7269\u7406\u4e16\u754c\u62e5\u6709AI | \u9ec4\u6587\u70b3\u5206\u4eab\u6574\u7406<\/a><\/span><\/section>\n<\/section>\n<\/blockquote>\n

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Graph and Image Data<\/span><\/strong><\/span><\/h2>\n
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\u6df1\u5ea6\u5b66\u4e60\u5728\u8fc7\u53bb\u5341\u51e0\u5e74\u53d1\u5c55\u6bd4\u8f83\u6210\u529f\u7684\u4e24\u4e2a\u7f51\u7edc\u4e00\u4e2a\u662f\u56fe\u795e\u7ecf\u7f51\u7edc<\/span>\uff08Graph Neural Networks, GNNs\uff09<\/span>\uff0c\u53e6\u4e00\u4e2a\u662f\u5377\u79ef\u795e\u7ecf\u7f51\u7edc<\/span>\uff08CNN\uff09<\/span>\u3002\u73b0\u5728\u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60\u80fd\u591f\u540c\u65f6\u5173\u6ce8\u8fd9\u4e24\u79cd\u7f51\u7edc\u3002<\/strong><\/span><\/section>\n

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\u5bf9\u4e8eCNN\u6765\u8bf4\uff0c\u5728\u56fe\u7247\u7279\u5f81\u63d0\u53d6\u65f6\uff0c\u4f1a\u8003\u8651\u4e00\u4e9b\u5c40\u90e8\u7279\u5f81\uff0c\u8fd9\u4e9b\u7279\u5f81\u548c\u4f4d\u7f6e\u65e0\u5173\u3002\u800c\u56fe\u6570\u636e\u7ed3\u6784\u5219\u4f1a\u8003\u8651\u8282\u70b9\u4e4b\u95f4\u7684\u6bd4\u5982\u4e24\u539f\u5b50\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\uff0c\u8fd9\u79cd\u4f5c\u7528\u6765\u81ea\u7269\u7406\u5c5e\u6027\u6216\u8005\u751f\u5316\u5c5e\u6027\uff0c\u4f8b\u5982\u76f8\u4e92\u4f5c\u7528\u529b\u548c\u5171\u4ef7\u952e\u8fde\u63a5\u3002\u8fd9\u4e9b\u5173\u7cfb\u7279\u70b9\u662f\u81ea\u7136\u754c\u5e7f\u6cdb\u5b58\u5728\u7684\u3002<\/strong>\u6b64\u5916\u5728\u793e\u4ea4\u7f51\u7edc\u4e2d\u4e5f\u4f1a\u8003\u8651\u4eba\u548c\u4eba\u4e4b\u95f4\u7684\u8054\u7cfb\uff0c\u7528\u6237\u548c\u5546\u54c1\u4e4b\u95f4\u7684\u8054\u7cfb\uff0c\u628a\u8fd9\u4e9b\u8054\u7cfb\u62bd\u8c61\u51fa\u6765\uff0c\u5c31\u53d8\u6210\u4e86\u4e00\u4e2a\u7ed3\u6784\u6570\u636e\u6216\u8005\u5173\u7cfb\u6570\u636e\u3002\u53ef\u4ee5\u628a\u8fd9\u79cd\u5173\u7cfb\u770b\u4f5c\u56fe\u7684\u4e00\u6761\u8fb9\uff0c\u751a\u81f3\u662f\u62d3\u6251\u4e2d\u7684\u67d0\u4e9b\u51e0\u4f55\u7279\u5f81\u3002<\/span><\/section>\n

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\u8fd9\u4e9b\u6570\u636e\u548c\u5e73\u9762\u6570\u636e\u6709\u7740\u672c\u8d28\u7684\u4e0d\u540c\uff0c\u79f0\u4e3a\u975e\u6b27\u7ed3\u6784\u6570\u636e<\/strong><\/span>\uff08Non-Euclidean Structure data\uff09<\/span>\uff0c\u5e73\u9762\u6570\u636e\u6216\u8005\u56fe\u50cf\u6570\u636e\u79f0\u4e3a\u6b27\u5f0f\u7ed3\u6784\u6570\u636e<\/strong><\/span>\uff08Euclidean Structure data\uff09<\/span>\u3002\u5bf9\u8fd9\u4e24\u79cd\u6570\u636e\u7684\u7279\u5f81\u5b66\u4e60\u548c\u9884\u6d4b\u662f\u4e24\u79cd\u622a\u7136\u4e0d\u540c\u7684\u6a21\u5f0f\u3002<\/span><\/section>\n

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\u795e\u7ecf\u6d88\u606f\u4f20\u9012<\/span>\uff08Neural Message Passing\uff09<\/span>\u662f\u795e\u7ecf\u7f51\u7edc\u4e2d\u5e38\u7528\u7684\u4e00\u79cd\u6a21\u5f0f\uff0c\u5176\u6982\u5ff5\u6e90\u81ea\u7406\u8bba\u8ba1\u7b97\u673a\u79d1\u5b66\u4e2d\u7684\u6d88\u606f\u4f20\u9012\u673a\u5236\u3002\u5728\u8282\u70b9\u7279\u5f81\u66f4\u65b0\u65f6\uff0c\u4f1a\u8003\u8651\u8be5\u8282\u70b9\u4e0e\u5176\u5468\u8fb9\u8282\u70b9\u4e4b\u95f4\u7684\u7279\u5f81\u4ea4\u4e92\u5173\u7cfb\u3002<\/strong>\u4f8b\u5982\uff0c\u5728\u5206\u7c7b\u4efb\u52a1\u4e2d\uff0c\u7269\u4ee5\u7c7b\u805a\u7684\u539f\u5219\u4f7f\u5f97\u6211\u4eec\u5728\u8fdb\u884c\u5206\u7c7b\u65f6\u4f1a\u5173\u6ce8\u8fd9\u4e9b\u8054\u7cfb\uff0c\u8fd9\u4e9b\u8054\u7cfb\u53cd\u6620\u4e86\u5b83\u4eec\u4e4b\u95f4\u7684\u5171\u6027\u3002\u5982\u4f55\u5c06\u8fd9\u79cd\u5171\u6027\u7eb3\u5165\u795e\u7ecf\u6d88\u606f\u4f20\u9012\u8fc7\u7a0b\u4e2d\u81f3\u5173\u91cd\u8981\u3002<\/span><\/section>\n

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\u5b9e\u73b0\u8fd9\u4e00\u70b9\u4e3b\u8981\u4f9d\u8d56\u4e8e\u4e24\u4e2a\u6b65\u9aa4\uff1a\u9996\u5148\uff0c\u5468\u8fb9\u8282\u70b9\u53ef\u4ee5\u662f\u76f4\u63a5\u76f8\u8fde\u7684\u90bb\u5c45\uff0c\u4e5f\u53ef\u4ee5\u662f\u66f4\u5e7f\u6cdb\u8303\u56f4\u5185\u53d7\u5171\u540c\u7279\u5f81\u5f71\u54cd\u7684\u8282\u70b9\uff1b\u5176\u6b21\uff0c\u9700\u8981\u6574\u5408\u8fd9\u4e9b\u7279\u70b9\uff0c\u4f8b\u5982\u901a\u8fc7\u5168\u8fde\u63a5\u7f51\u7edc<\/span>\uff08Multilayer Perceptron, MLP\uff09\u6765<\/span>\u63d0\u53d6\u6570\u636e\u7279\u5f81\u3002\u8fd9\u4e00\u8fc7\u7a0b\u4e0d\u4ec5\u6d89\u53ca\u4e2d\u5fc3\u8282\u70b9\uff0c\u8fd8\u9700\u8003\u8651\u6bcf\u4e2a\u8282\u70b9\u53ca\u5176\u90bb\u8fd1\u8282\u70b9\u95f4\u7684\u5173\u7cfb\uff0c\u5305\u62ec\u4e0d\u540c\u5c42\u7ea7\u95f4\u70b9\u4e0e\u70b9\u4e4b\u95f4\u7684\u5173\u8054\u3002\u56e0\u6b64\uff0c\u53ef\u4ee5\u5c06\u6574\u4e2a\u7cfb\u7edf\u89c6\u4e3a\u4e00\u4e2a\u79bb\u6563\u52a8\u529b\u7cfb\u7edf\uff0c\u4f46\u5b9e\u9645\u4e0a\u7531\u4e8e\u56fe\u4e2d\u53ef\u80fd\u6709 n<\/em> \u4e2a\u8282\u70b9\uff0c\u56e0\u6b64\u5f62\u6210\u4e86 n<\/em> \u4e2a\u5b50\u7cfb\u7edf\uff0c\u4f7f\u4e4b\u6210\u4e3a\u4e00\u4e2a\u590d\u6742\u7684\u591a\u4f53\u7cfb\u7edf\u3002<\/span><\/section>\n

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\u6570\u5b66\u4e0a\u4e5f\u6709\u76f8\u5173\u7814\u7a76\uff0c\u6bd4\u5982\u7c92\u5b50\u7cfb\u7edf\u53ef\u7528\u4e8e\u6a21\u62df\u591a\u4f53\u7cfb\u7edf\uff0c\u5176\u4e2d\u7c92\u5b50\u95f4\u76f8\u4e92\u5173\u7cfb\u53ef\u89c6\u4e3a\u56fe\u4e2d\u7684\u8fb9\uff0c\u800c\u591a\u4e2a\u56fe\u4e4b\u95f4\u5219\u53ef\u770b\u4f5c\u8d85\u8fb9\u3002\u8fd9\u4e9b\u7814\u7a76\u6210\u679c\u5bf9\u63a2\u7d22\u548c\u6539\u8fdb\u795e\u7ecf\u6d88\u606f\u4f20\u9012\u65b9\u6cd5\u5177\u6709\u91cd\u8981\u610f\u4e49\uff0c\u5e76\u4e14\u8fd1\u671f\u5728\u6b64\u9886\u57df\u5df2\u6709\u8bf8\u591a\u8fdb\u5c55\u3002<\/span><\/section>\n

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Classic Message Passing: Graph Convolution Network (GCN)<\/span><\/strong><\/span><\/h2>\n
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\u7ecf\u5178\u7684\u56fe\u5377\u79ef\u7f51\u7edc<\/strong>\u662f\u4e00\u4e2a\u76f8\u5bf9\u7b80\u5355\u7684\u7cfb\u7edf\uff0c\u4ece\u5fae\u89c2\u89d2\u5ea6\u770b\uff0c\u5b83\u4e3b\u8981\u901a\u8fc7\u4e0e\u76f8\u90bb\u8282\u70b9\u4e4b\u95f4\u8fb9\u8fde\u63a5\u7684\u7279\u5f81\u8fdb\u884c\u7ebf\u6027\u52a0\u548c\u3002\u8fd9\u4e9b\u6743\u91cd\u6765\u81ea\u4e8e\u8282\u70b9\u95f4\u81ea\u5e26\u7684\u6743\u91cd\u3002\u7531\u4e8e\u8fd9\u662f\u4e00\u4e2a\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\uff0c\u901a\u5e38\u9700\u8981\u53ef\u5b66\u4e60\u53c2\u6570\u6765\u9a71\u52a8\u5173\u7cfb\u548c\u7279\u5f81\u7684\u8fed\u4ee3\uff0c\u56e0\u6b64\u4f1a\u91c7\u7528\u5171\u4eab\u6743\u91cd\uff0c\u5373\u5404\u4e2a\u8282\u70b9\u4f7f\u7528\u540c\u4e00\u7cfb\u6570\u8868\u793a\u3002<\/span><\/section>\n

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\u8fd9\u4e2a\u77e9\u9635\u7684\u7ef4\u5ea6\u4e0e\u7279\u5f81\u7ef4\u5ea6\u4e00\u81f4\uff0c\u5176\u4f5c\u7528\u5728\u4e8e\u5b66\u4e60\u7279\u5f81\u4f20\u9012\u8fc7\u7a0b\u4e2d\u7684\u5171\u6027\uff0c\u540c\u65f6\u4e5f\u80fd\u4f53\u73b0\u6bcf\u4e2a\u8282\u70b9\u4e0a\u7684\u7ed3\u6784\u4fe1\u606f\u53ca\u5176\u7279\u5f81\u3002\u56e0\u6b64\uff0c\u8fd9\u6784\u6210\u4e86\u7ecf\u5178\u7684\u795e\u7ecf\u6d88\u606f\u4f20\u9012\u6a21\u578b<\/strong>\uff0c\u5e76\u5728\u8bb8\u591a\u6df1\u5ea6\u5b66\u4e60\u4efb\u52a1\u4e2d\uff0c\u5982\u8282\u70b9\u5206\u7c7b\u3001\u56de\u5f52\u4ee5\u53ca\u56fe\u5c42\u9762\u7684\u5206\u7c7b\u7b49\u95ee\u9898\u4e0a\u8868\u73b0\u51fa\u8272\u3002<\/span><\/section>\n

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\u8be5\u5b9e\u73b0\u5f62\u5f0f\u975e\u5e38\u7b80\u6d01\uff0c\u901a\u8fc7\u6d88\u606f\u4f20\u9012\u7684\u65b9\u5f0f\u8fdb\u884c\u8868\u8fbe\uff0c\u8fd9\u5728\u8ba1\u7b97\u673a\u5b9e\u73b0\u4e2d\uff0c\u5c24\u5176\u662f\u5728 GPU \u8fd0\u7b97\u548c\u5e95\u5c42\u5b9e\u73b0\u65f6\uff0c\u53ef\u4ee5\u663e\u8457\u52a0\u5feb\u8fd0\u7b97\u6548\u7387\u3002\u56e0\u6b64\uff0c\u76f4\u63a5\u91c7\u7528\u8fd9\u79cd\u6a21\u5f0f\u8fdb\u884c\u5b9e\u73b0\u662f\u9ad8\u6548\u7684\u3002<\/span><\/section>\n

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\u56fe\u795e\u7ecf\u7f51\u7edc Graph Neural Networks<\/span><\/strong><\/span><\/h2>\n
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3. \u7ecf\u5178\u56fe\u795e\u7ecf\u7f51\u7edc\u7684\u6a21\u578b\u6539\u8fdb\u53ca\u4f18\u5316<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u8c31\u56fe\u5377\u79ef Spectral Graph Convolution<\/span><\/strong><\/span><\/h2>\n

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\u5728\u6570\u5b66\u4e2d\uff0c<\/span>\u6d41\u5f62<\/strong>\uff08manifold\uff09\u662f\u53ef\u4ee5\u201c\u5c40\u90e8\u6b27\u51e0\u91cc\u5f97\u7a7a\u95f4\u5316\u201d\u7684\u4e00\u4e2a\u62d3\u6251\u7a7a\u95f4\uff0c\u5373\u5728\u6b64\u62d3\u6251\u7a7a\u95f4\u4e2d\uff0c\u6bcf\u4e2a\u70b9\u9644\u8fd1\u201c\u5c40\u90e8\u7c7b\u4f3c\u4e8e\u6b27\u6c0f\u7a7a\u95f4\u201d\u3002\u66f4\u7cbe\u786e\u5730\u8bf4\uff0c<\/span>n\u7ef4\u6d41\u5f62<\/strong>\uff08<\/span>n<\/em>-manifold\uff09\uff0c\u7b80\u79f0<\/span>n\u6d41\u5f62<\/strong>\uff0c\u662f\u4e00\u4e2a\u62d3\u6251\u7a7a\u95f4\uff0c\u5176\u6027\u8d28\u662f\u6bcf\u4e2a\u70b9\u90fd\u6709\u4e00\u4e2a\u90bb\u57df\uff0c\u8be5\u90bb\u57df\u540c\u80da\u4e8en\u7ef4\u6b27\u6c0f\u7a7a\u95f4\u7684\u4e00\u4e2a\u5f00\u96c6\u3002<\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


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\u8fd9\u91cc\u63d0\u5230\u7684<\/sub><\/span>\u662f\u62c9\u666e\u62c9\u65af\u77e9\u9635\u5bf9\u5e94\u7279\u5f81\u5411\u91cf\u5206\u89e3\u5f62\u6210\u7684\u77e9\u9635\u3002\u4ece\u53e6\u4e00\u4e2a\u89d2\u5ea6\u770b\uff0c\u8be5\u77e9\u9635\u4e0e\u56fe\u4fe1\u53f7<\/span>\uff08\u6574\u4e2a\u56fe\u4e0a\u7684\u7279\u5f81\uff09<\/span>\u76f8\u4e58\uff0c\u5373\u5bf9\u8be5\u4fe1\u53f7\u8fdb\u884c\u5085\u7acb\u53f6\u53d8\u6362\u3002\u5982\u679c\u6267\u884c\u9006\u53d8\u6362\uff0c\u5219\u4e3a\u5085\u7acb\u53f6\u9006\u53d8\u6362\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u90bb\u63a5\u77e9\u9635\u53ca\u5176\u5bf9\u5e94\u7279\u5f81\u5411\u91cf\u5b9a\u4e49\u6211\u4eec\u7684\u5085\u7acb\u53f6\u5377\u79ef\uff0c\u8fd9\u5b9e\u8d28\u4e0a\u5b8c\u5168\u9075\u5faa\u4e86\u5085\u7acb\u53f6\u5377\u79ef\u5b9a\u4e49\uff0c\u662f\u5bf9\u6bcf\u4e2a\u6570\u636e\u7279\u5f81\u548c\u6ee4\u6ce2\u5668\u7684\u5085\u7acb\u53f6\u53d8\u6362\u540e\u518d\u5355\u70b9\u76f8\u4e58\u5e76\u505a\u9006\u53d8\u6362\u6240\u5f97\u5230\u7684\u4e00\u79cd\u5377\u79ef\u3002<\/span><\/section>\n

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2013\u5e74\uff0cJoan Bruna \u548c Yann LeCun [1]\u63d0\u51fa\u4e86\u57fa\u4e8e\u5085\u7acb\u53f6\u53d8\u6362\u7684\u56fe\u5377\u79ef\u65b9\u6cd5<\/strong>\u3002\u65e9\u671f\uff0cLecun \u5bf9\u56fe\u795e\u7ecf\u7f51\u7edc\u7684\u53d1\u5c55\u6301\u652f\u6301\u6001\u5ea6\uff0c\u56e0\u4e3a\u5f53\u65f6\u5c1a\u672a\u660e\u786e\u5982\u4f55\u5b9a\u4e49\u975e\u89c4\u5219\u8282\u70b9\u4e0a\u7684\u6570\u636e\u3002\u5728\u5c0f\u89c4\u6a21\u56fe\u4e2d\uff0c\u8fd9\u79cd\u65b9\u6cd5\u7684\u51c6\u786e\u6027\u548c\u6548\u7387\u8f83\u9ad8\uff0c\u4f46\u5728\u5904\u7406\u5927\u578b\u56fe\uff08\u5982\u793e\u4ea4\u7f51\u7edc\u4e2d\u6570\u767e\u4e07\u6216\u6570\u4ebf\u4e2a\u8282\u70b9\uff09\u65f6\uff0c\u7531\u4e8e\u9700\u8981\u8fdb\u884c\u590d\u6742\u7684\u7279\u5f81\u5206\u89e3\uff0c\u8ba1\u7b97\u96be\u5ea6\u663e\u8457\u589e\u52a0\uff0c\u56e0\u6b64\u4e0d\u592a\u73b0\u5b9e\u3002<\/span><\/section>\n

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\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e00\u95ee\u9898\uff0c\u4ece 2013 \u5e74\u81f3 2017 \u5e74\u95f4\uff0c\u7814\u7a76\u8005\u4eec\u6301\u7eed\u63a2\u8ba8\u4f18\u5316\u65b9\u6848\u30022016 \u5e74\u51fa\u73b0\u4e86\u4e00\u79cd\u540d\u4e3aChebNet\u7684\u7f51\u7edc[2]\uff0c\u5b83\u901a\u8fc7\u5207\u6bd4\u96ea\u592b\u591a\u9879\u5f0f\u5c55\u5f00\u5bf9\u5085\u7acb\u53f6\u5377\u79ef\u8fdb\u884c\u4e86\u8fd1\u4f3c\uff0c\u4f7f\u5f97\u5728\u6ee4\u6ce2\u5668\u8bbe\u8ba1\u8fc7\u7a0b\u4e2d\u65e0\u9700\u76f4\u63a5\u8ba1\u7b97\u7279\u5f81\u5206\u89e3\uff0c\u4ece\u800c\u63d0\u9ad8\u4e86\u6548\u7387\u3002<\/span><\/section>\n

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Kipf \u548c Welling \u5728 2017 \u5e74[3]\u5bf9\u5377\u79ef\u7f51\u7edc\u8fdb\u884c\u4e86\u7b80\u5316\u3002\u4ed6\u4eec\u901a\u8fc7\u63d0\u53d6\u5207\u6bd4\u96ea\u592b\u5c55\u5f00\u7684\u524d\u4e24\u9879\uff0c\u5c06\u590d\u6742\u7684\u5377\u79ef\u5f62\u5f0f\u8f6c\u53d8\u4e3a\u66f4\u7b80\u5355\u7684\u683c\u5f0f\uff0c\u8fd9\u79cd\u7b80\u5316\u5728\u5b9e\u8df5\u4e2d\u8bc1\u660e\u975e\u5e38\u6709\u6548\uff0c\u56e0\u6b64\u88ab\u5e7f\u6cdb\u4f20\u64ad\u3002\u540c\u65f6\u4e3a\u4e86\u8fdb\u4e00\u6b65\u53d1\u5c55\u5377\u79ef\u5e76\u907f\u514d\u8ba1\u7b97\u590d\u6742\u6027\u7684\u6307\u6570\u589e\u957f\uff0c\u9700\u8981\u5bf9\u53d8\u6362\u8fdb\u884c\u4f18\u5316\u3002<\/span><\/section>\n

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\u65e9\u671f\u7814\u7a76\u8868\u660e\uff0c\u8c31\u56fe\u5377\u79ef\u4e0e\u76f8\u5e94\u7684\u4f18\u5316\u65b9\u7a0b\u6709\u76f4\u63a5\u5173\u7cfb\uff0c\u5b83\u5b9e\u9645\u4e0a\u662f\u62c9\u666e\u62c9\u65af\u6b63\u5219\u5316\u4f18\u5316\u89e3\u7684\u4e00\u79cd\u8fd1\u4f3c\u3002<\/strong>\u5728\u6b64\u8fc7\u7a0b\u4e2d\uff0c\u4f18\u5316\u76ee\u6807\u9664\u4e86\u539f\u672c\u7684\u5377\u79ef\uff0c\u8fd8\u5f15\u5165\u4e86\u4e0e\u62c9\u666e\u62c9\u65af\u9879\u76f8\u5173\u7684\u6b63\u5219\u9879\uff0c\u4ee5\u523b\u753b\u51e0\u4f55\u7279\u5f81\u3002<\/span><\/section>\n

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\u5c0f\u6ce2<\/sub>\u6b63\u5219\u63d0\u9ad8\u6297\u566a\u80fd\u529b Wavelet Regularization<\/span><\/strong><\/span><\/h2>\n
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\u6b64\u5916\uff0c\u53ef\u4ee5\u91c7\u7528\u5c0f\u6ce2\u53d8\u6362\u66ff\u4ee3\u5085\u7acb\u53f6\u53d8\u6362\uff0c\u901a\u8fc7\u975e\u5907\u964d\u5f0f\u7684\u5c0f\u6ce2\u5206\u89e3\u6765\u907f\u514d\u7ec6\u8282\u5904\u7406\uff0c\u4ece\u800c\u4f7f\u7528\u6574\u4f53\u62c9\u666e\u62c9\u65af\u591a\u9879\u5f0f\u7ec4\u5408\u8ba1\u7b97\u5c0f\u6ce2\u77e9\u9635\uff0c\u8fd9\u7c7b\u4f3c\u4e8e\u5207\u6bd4\u96ea\u592b\u591a\u9879\u5f0f\u7684\u4e00\u79cd\u8fd1\u4f3c\u3002\u8fd9\u79cd\u65b9\u6cd5\u80fd\u591f\u51cf\u5c11\u566a\u97f3\u4fe1\u53f7\u7684\u5f71\u54cd\u3002<\/span><\/section>\n

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\u611f\u5174\u8da3\u7684\u670b\u53cb\u53ef\u4ee5\u89c2\u770b\u76f8\u5173\u5206\u4eab\u2014\u2014AI+Science \u7b2c\u4e09\u5b63 \uff1a\u4eba\u5de5\u667a\u80fd\u4e0e\u6570\u5b66\uff1a7.\u5229\u7528\u5c0f\u6ce2\u5206\u6790\u589e\u5f3a\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\u7684\u9c81\u68d2\u6027\uff08https:\/\/pattern.swarma.org\/study_group_issue\/556\uff09\u3002<\/span><\/section>\n<\/section>\n<\/blockquote>\n

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\u8bbe\u8ba1\u5377\u79ef\u63d0\u9ad8\u9c81\u68d2\u6027 Enhance Robustness of GNNs<\/span><\/strong><\/h2>\n
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\u5c0f\u6ce2\u5377\u79ef\u53ef\u4ee5\u5b9a\u4e49\u4e3a\u5148\u8fdb\u884c\u5c0f\u6ce2\u5206\u89e3\u518d\u53cd\u53d8\u6362\u3002\u5176\u5728\u9891\u57df\u7a7a\u95f4\u4e2d\u7684\u64cd\u4f5c\uff0c\u53ef\u4ee5\u770b\u4f5c\u662f\u5728\u9891\u57df\u7a7a\u95f4\u4e2d\u7684\u5b66\u4e60\u8fc7\u7a0b\u3002<\/strong>\u6fc0\u6d3b\u51fd\u6570\u53ef\u4ee5\u7531\u5c0f\u6ce2\u5206\u89e3\u4e2d\u7684 Shrinkage \u6a21\u5f0f\u5b9a\u4e49\u3002\u4f20\u7edf\u6846\u67b6\u4e0b\u7684\u5c0f\u6ce2\u5377\u79ef\u5728\u566a\u97f3\u53bb\u9664\u548c\u591a\u5c3a\u5ea6\u6570\u636e\u8868\u793a\u65b9\u9762\u8868\u73b0\u51fa\u8272\u3002<\/span><\/section>\n


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Allen-Cahn Message Passing: Cucker-Smale model with Attractive and Repulsive Forces<\/span><\/strong><\/h2>\n
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\u5728\u56fe\u795e\u7ecf\u7f51\u7edc\u4e2d\uff0c\u4e00\u4e2a\u91cd\u8981\u7684\u95ee\u9898\u662f\u201c\u8fc7\u5149\u6ed1\u73b0\u8c61\u201d<\/strong>\u3002\u968f\u7740\u7f51\u7edc\u5c42\u6570\u7684\u52a0\u6df1\uff0c\u7279\u5f81\u8d8b\u540c\uff0c\u4f7f\u5f97\u8282\u70b9\u5206\u7c7b\u53d8\u5f97\u56f0\u96be\uff0c\u4ece\u800c\u964d\u4f4e\u4e86\u5b66\u4e60\u548c\u9884\u6d4b\u80fd\u529b\u3002\u8fd9\u79cd\u73b0\u8c61\u662f\u795e\u7ecf\u6d88\u606f\u4f20\u9012\u4e2d\u7684\u4e00\u4e2a\u4e0d\u53ef\u907f\u514d\u7684\u7ed3\u679c\u3002<\/span><\/section>\n

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\u7406\u8bba\u4e0a\u53ef\u4ee5\u8bc1\u660e\uff0c\u5982\u679c\u9075\u5faa\u7279\u5b9a\u7684\u6d88\u606f\u4f20\u9012\u6a21\u5f0f\u6784\u5efa\u795e\u7ecf\u7f51\u7edc\uff0c\u5b83\u5fc5\u7136\u4f1a\u51fa\u73b0\u7279\u5f81\u8d8b\u540c\u95ee\u9898\u3002\u8bb8\u591a\u5b66\u8005\u5bf9\u6b64\u8fdb\u884c\u4e86\u7814\u7a76\uff0c\u4f8b\u5982 Michael M. Bronstein \u63d0\u51fa\u4e86Gradient Flows[4]\u6765\u964d\u4f4e\u7279\u5f81\u8d8b\u540c\u9020\u6210\u7684\u5f71\u54cd\u3002<\/span><\/section>\n

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Cucker-Smale model to GNN: Allen-Cahn Energy<\/span><\/strong><\/h2>\n
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\u6211\u4eec\u53ef\u4ee5\u5c06\u6d88\u606f\u4f20\u9012\u89c6\u4f5c\u4e00\u4e2a\u52a8\u529b\u7cfb\u7edf\uff0c\u5e76\u7528\u7c92\u5b50\u65b9\u7a0b\u63cf\u8ff0\u5176\u6f14\u5316\u8fc7\u7a0b\uff0c\u8fd9\u5b9e\u9645\u4e0a\u5bf9\u5e94\u4e8e\u6269\u6563\u65b9\u7a0b\u3002<\/strong>\u7136\u800c\uff0c\u4f20\u7edf\u6269\u6563\u65b9\u7a0b\u53ea\u8003\u8651\u7c92\u5b50\u4e4b\u95f4\u7684\u5438\u5f15\u529b\uff0c\u800c\u5ffd\u7565\u4e86\u8ddd\u79bb\u51cf\u5c0f\u65f6\u53ef\u80fd\u4ea7\u751f\u7684\u6392\u65a5\u4f5c\u7528\u3002\u5982\u679c\u6ca1\u6709\u6392\u65a5\u6548\u5e94\uff0c\u6240\u6709\u7c92\u5b50\u6700\u7ec8\u4f1a\u805a\u96c6\u5230\u4e00\u70b9\uff0c\u8fd9\u662f\u4e0d\u7406\u60f3\u7684\u3002\u56e0\u6b64\uff0c\u53ef\u4ee5\u901a\u8fc7\u52a0\u5165\u6392\u65a5\u9879\u6765\u6539\u5584\u8fd9\u4e00\u70b9\u3002<\/span><\/section>\n

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\u7136\u800c\uff0c\u4ec5\u4ec5\u4f9d\u9760\u6392\u65a5\u529b\u53ef\u80fd\u5bfc\u81f4\u6781\u7aef\u60c5\u51b5\uff0c\u5373\u7279\u5f81\u65e0\u9650\u589e\u5927\u6216\u51cf\u5c0f\uff0c\u4ece\u800c\u5728\u6570\u636e\u8ba1\u7b97\u4e0a\u5e26\u6765\u95ee\u9898\u3002\u5f53\u7f51\u7edc\u52a0\u6df1\u65f6\uff0c\u4e5f\u53ef\u80fd\u51fa\u73b0\u8ba1\u7b97\u5931\u63a7\u7684\u95ee\u9898\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5c1d\u8bd5\u5f15\u5165\u4e00\u79cd\u5e73\u8861\u9879 Allen-Cahn \u9879\uff0c\u5b9e\u73b0\u5f15\u529b\u4e0e\u65a5\u529b\u4e4b\u95f4\u7684\u5e73\u8861\uff0c\u8fbe\u5230\u53cc\u4e95\u52bf\uff08double well potential\uff09\uff0c\u4f7f\u5f97\u7c92\u5b50\u80fd\u591f\u7a33\u5b9a\u5728\u591a\u4e2a\u5e73\u8861\u70b9\u4e0a\uff0c\u5b9e\u73b0\u6709\u6548\u5206\u7c7b\u3002<\/span><\/section>\n

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\u8fd9\u79cd\u65b9\u6cd5\u57fa\u4e8e\u591a\u4f53\u7cfb\u7edf\u7684\u4e00\u4e9b\u6570\u5b66\u7406\u8bba\uff0c\u5982 Cucker-Smale \u6a21\u578b\uff0c\u8be5\u6a21\u578b\u6d89\u53ca\u5f15\u529b\u4e0e\u65a5\u529b\u7cfb\u7edf\u3002\u5728\u8fd9\u4e2a\u6846\u67b6\u4e0b\uff0c\u53ef\u4ee5\u8bc1\u660e\u5373\u4f7f\u5f53\u7f51\u7edc\u5c42\u6570\u8fbe\u5230 50\u3001100 \u6216 500 \u65f6\uff0c\u4ecd\u7136\u5177\u6709\u826f\u597d\u7684\u53ef\u5206\u6027\uff0c\u4e0d\u4f1a\u51fa\u73b0\u8fc7\u5149\u6ed1\u95ee\u9898\u3002\u8fd9\u8868\u660e\uff0c\u901a\u8fc7\u6539\u8fdb\u548c\u4f18\u5316\u591a\u7c92\u5b50\u7cfb\u7edf\u53ca\u5176\u65b9\u7a0b\uff0c\u6211\u4eec\u80fd\u591f\u6709\u6548\u5730\u89e3\u51b3\u795e\u7ecf\u6d88\u606f\u4f20\u9012\u4e2d\u7684\u76f8\u5173\u6311\u6218\u3002<\/strong><\/span><\/section>\n

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4. \u6d88\u606f\u4f20\u9012\u5355\u7eaf\u590d\u5f62\u795e\u7ecf\u7f51\u7edc<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u8d85\u8d8a\u56fe\u795e\u7ecf\u7f51\u7edc\uff1a\u6d88\u606f\u4f20\u9012\u5355\u7eaf\u590d\u5f62\u7f51\u7edc Message Passing Simplicial Networks<\/span><\/strong><\/h2>\n
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\u53e6\u4e00\u4e2a\u6709\u8da3\u7684\u53d1\u5c55\u65b9\u5411\u662f\u5bf9\u590d\u6742\u6570\u636e\u6216\u51e0\u4f55\u7684\u523b\u753b\uff0c\u73b0\u79f0\u4e3a\u62d3\u6251\u6df1\u5ea6\u5b66\u4e60<\/strong>\uff0c\u8fd9\u662f\u4f20\u7edf\u62d3\u6251\u6570\u636e\u5206\u6790\u7684\u5ef6\u4f38\u3002\u8be5\u9886\u57df\u5173\u6ce8\u6570\u5b66\u4e0a\u4e25\u683c\u5b9a\u4e49\u7684\u7ed3\u6784\uff0c\u5982\u8d85\u56fe\u548c\u5355\u7eaf\u590d\u5f62\uff0c\u800c\u4e0d\u4ec5\u9650\u4e8e\u8ba1\u7b97\u673a\u79d1\u5b66\u4e2d\u5e38\u7528\u7684\u56fe\u3002<\/span><\/section>\n

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\u5355\u7eaf\u590d\u5f62\u8003\u8651\u7684\u4e0d\u4ec5\u662f\u4e24\u4e2a\u8282\u70b9\u4e4b\u95f4\u7684\u8fb9\u5173\u7cfb\uff0c\u8fd8\u5305\u62ec\u4e09\u4e2a\u8282\u70b9\u5f62\u6210\u9762\u7684\u5173\u7cfb\uff0c\u4ee5\u53ca\u56db\u4e2a\u8282\u70b9\u6784\u6210\u7acb\u65b9\u9525\u7b49\u591a\u9636\u62d3\u6251\u7279\u5f81\u3002\u8fd9\u4e9b\u9ad8\u9636\u62d3\u6251\u5173\u7cfb\u88ab\u79f0\u4e3a\u5355\u7eaf\u590d\u5f62\u7f51\u7edc\u3002<\/span><\/section>\n
\u6211\u4eec\u4e0e\u725b\u6d25\u5927\u5b66 Michael M. Bronstein \u6559\u6388\u56e2\u961f\u5408\u4f5c\u5f00\u53d1\u4e86\u4e00\u79cd\u65b0\u7684\u5355\u7eaf\u590d\u5f62\u7f51\u7edc<\/span>\uff08Message Passing Simplicial Networks, MPSN)<\/span>[5]\u3002\u9664\u4e86\u7814\u7a76\u51e0\u4f55\u4f53\u4e0d\u540c\u5c42\u6b21\u7684\u62d3\u6251\u7279\u5f81\u5916\uff0c\u6211\u4eec\u8fd8\u63a2\u8ba8\u5982\u4f55\u901a\u8fc7\u4f4e\u9636\u62d3\u6251\u6784\u9020\u9ad8\u9636\u62d3\u6251\uff0c\u4ece\u800c\u5efa\u7acb\u5b83\u4eec\u4e4b\u95f4\u7684\u8054\u7cfb\uff0c\u8fd9\u4e00\u8fc7\u7a0b\u5728\u6211\u4eec\u7684\u6d88\u606f\u4f20\u9012\u673a\u5236\u4e2d\u5f97\u4ee5\u4f53\u73b0\u3002<\/span><\/section>\n

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\u611f\u5174\u8da3\u7684\u670b\u53cb\u53ef\u4ee5\u89c2\u770b\u76f8\u5173\u5206\u4eab\u2014\u2014\u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60\uff1a1.AI\u5982\u4f55\u7406\u89e3\u9ad8\u9636\u7ed3\u6784\uff1f\u62d3\u6251\u6df1\u5ea6\u5b66\u4e60\u57fa\u7840\uff08https:\/\/pattern.swarma.org\/study_group_issue\/710\uff09\u3002<\/span><\/section>\n<\/section>\n<\/blockquote>\n

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GNNs \u7684\u4e09\u4e2a\u4e3b\u8981\u7f3a\u9677 Limitations<\/span><\/strong><\/h2>\n
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\u8fd9\u79cd\u5355\u7eaf\u590d\u5f62\u7f51\u7edc\u65e8\u5728\u514b\u670d\u4f20\u7edf\u56fe\u795e\u7ecf\u7f51\u7edc\u5b58\u5728\u7684\u4e00\u4e9b\u7f3a\u9677\uff0c\u5305\u62ec\u65e0\u6cd5\u6709\u6548\u63cf\u8ff0\u591a\u4e2a\u8282\u70b9\u95f4\u4ea4\u4e92\u3001\u96be\u4ee5\u68c0\u6d4b\u9ad8\u9636\u62d3\u6251\u5173\u7cfb\u4ee5\u53ca\u5904\u7406\u957f\u8def\u5f84\u4fe1\u53f7\u65f6\u6548\u679c\u4e0d\u4f73\u7b49\u95ee\u9898\u3002\u56e0\u6b64\uff0c\u6d88\u606f\u4f20\u9012\u7cfb\u7edf\u5728\u8fd9\u91cc\u8868\u73b0\u51fa\u8f83\u597d\u7684\u6027\u80fd\u3002<\/span><\/section>\n

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\u5355\u7eaf\u5f62WL Simplicial Weisfeiler-Lehman<\/span><\/strong><\/h2>\n
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\u8be5\u7cfb\u7edf\u6e90\u81ea Weisfeiler-Lehman \u6d4b\u8bd5\uff0c\u662f\u4e00\u79cd\u56fe\u540c\u6784\u68c0\u6d4b\u7b97\u6cd5\uff0c\u7528\u4e8e\u786e\u5b9a\u4e24\u4e2a\u56fe\u662f\u5426\u5177\u6709\u76f8\u540c\u7684\u7ed3\u6784\u3002<\/span><\/section>\n

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\u5177\u4f53\u800c\u8a00\uff0c\u8be5\u6d4b\u8bd5\u53ef\u7528\u4e8e\u8bc4\u4f30\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u6027\u80fd\uff0c\u4ee5\u786e\u5b9a\u5176\u662f\u5426\u6ee1\u8db3\u7279\u5b9a\u7684\u8ba1\u7b97\u590d\u6742\u5ea6\u8981\u6c42\u5e76\u80fd\u6709\u6548\u533a\u5206\u4e0d\u540c\u7ed3\u6784\u7684\u6570\u636e\u3002\u6b64\u5916\uff0c\u5355\u7eaf\u5f62\u4e0a\u8fd8\u5b58\u5728\u76f8\u5e94\u7684 WL \u6d4b\u8bd5\uff0c\u79f0\u4e3a\u5355\u7eaf\u5f62 WL<\/span>\uff08Simplicial WL\uff09<\/span> \u6d4b\u8bd5\u3002<\/span><\/section>\n

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\u8fd9\u79cd\u6d4b\u8bd5\u6e90\u81ea\u4f20\u7edf\u7740\u8272\u95ee\u9898\u7684\u8003\u8651\u3002\u7b80\u5355\u6765\u8bf4\uff0c\u6211\u4eec\u4f1a\u5206\u6790\u5355\u4e2a\u8282\u70b9\u3001\u8fb9\u4ee5\u53ca\u9762<\/span>\uff08\u5982\u4e8c\u9636\u6216\u4e09\u9636\u62d3\u6251\uff09<\/span>\u7684\u7279\u5f81\uff0c\u5c06\u5b83\u4eec\u6574\u5408\u540e\u8fdb\u884c HASH \u64cd\u4f5c\uff0c\u901a\u8fc7\u68c0\u67e5\u662f\u5426\u80fd\u591f\u6709\u6548\u533a\u5206\u4e0d\u540c\u7ed3\u6784\u7684\u6570\u636e\uff0c\u4ece\u800c\u5b9e\u73b0 WL \u6d4b\u8bd5\u3002\u6211\u4eec\u7684\u7814\u7a76\u53d1\u73b0\uff0c\u5355\u7eaf\u5f62 WL \u6d4b\u8bd5\u53ef\u4ee5\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u5b9a\u4e49\u6d88\u606f\u4f20\u9012\uff0c\u8fd9\u4f7f\u5f97\u5b83\u80fd\u591f\u8fc1\u79fb\u5230\u6d88\u606f\u4f20\u9012\u5e94\u7528\u4e2d\u3002<\/span><\/section>\n

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SWL \u5bf9\u5e94\u7684\u795e\u7ecf\u7f51\u7edc\u5c42\uff1a\u6d88\u606f\u4f20\u9012\u5355\u7eaf\u590d\u5f62\u7f51\u7edc MPSNs<\/span><\/strong><\/h2>\n
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\u9664\u4e86\u4e4b\u524d\u63d0\u5230\u7684\u8282\u70b9\u7279\u5f81\u5916\uff0c\u8fd8\u9700\u8003\u8651\u8fb9\u3001\u9762\u53ca\u9ad8\u9636\u62d3\u6251\u7279\u5f81\u7684\u6574\u5408\u3002\u8fd9\u4e9b\u6574\u5408\u57fa\u4e8e\u6d88\u606f\u4f20\u9012\u6a21\u5f0f\uff0c\u901a\u8fc7\u52a0\u548c\u6765\u5f62\u6210\u65b0\u7684\u4fe1\u606f\uff0c\u800c\u8fd9\u4e9b\u6a21\u5f0f\u9075\u5faa\u4e00\u5b9a\u89c4\u5219\uff0c\u4f8b\u5982\u8fde\u63a5\u65b9\u5f0f\u548c\u76f8\u5173\u6027\uff08\u5982\u540c\u5c5e\u4e8e\u67d0\u4e00\u9636\u62d3\u6251\uff09\u3002<\/span><\/section>\n

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\u76f8\u5173\u6027\u53ef\u80fd\u6d89\u53ca\u591a\u4e2a\u65b9\u9762\uff0c\u6bd4\u5982\u5171\u9762\u7684\u5173\u7cfb\uff0c\u4ee5\u53ca\u4e0d\u540c\u9636\u62d3\u6251\u4e4b\u95f4\u7684\u4ea4\u4e92\u3002\u4f8b\u5982\uff0c\u4e00\u9636\u4e0e\u4e8c\u9636\u6216\u4e09\u9636\u4e0e\u56db\u9636\u4e4b\u95f4\u5b58\u5728\u90bb\u63a5\u77e9\u9635\u5173\u7cfb\u3002\u4ece\u4f4e\u9636\u5230\u9ad8\u9636\u662f\u4e00\u79cd\u65b9\u5411\uff0c\u800c\u4ece\u9ad8\u9636\u5230\u4f4e\u9636\u5219\u662f\u53e6\u4e00\u79cd\u3002\u56e0\u6b64\uff0c\u9700\u8981\u8003\u8651\u4e0a\u4e0b\u90bb\u63a5\u7684\u95ee\u9898\u3002\u5c06\u6240\u6709\u8fd9\u4e9b\u4fe1\u606f\uff0c\u5305\u62ec\u5404\u4e2a\u62d3\u6251\u7684\u4fe1\u606f\u53ca\u5176\u76f8\u90bb\u9636\u95f4\u7684\u4fe1\u606f\uff0c\u901a\u8fc7\u7c7b\u4f3c\u4e8e\u56fe\u795e\u7ecf\u7f51\u7edc\u7684\u6d88\u606f\u4f20\u9012\u65b9\u5f0f\u8fdb\u884c\u6574\u5408\uff0c\u5c31\u80fd\u6784\u5efa\u51fa\u4e00\u79cd\u6709\u6548\u7684\u5355\u7eaf\u590d\u5f62\u7f51\u7edc\u3002<\/span><\/section>\n

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MPSNs = SWL  3-WL  GNNs<\/span><\/strong><\/span><\/h2>\n
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\u901a\u8fc7\u5bf9\u5176\u590d\u6742\u6027\u7684\u5206\u6790\u548c\u7ebf\u6027\u57df\u8ba1\u7b97\uff0c\u53ef\u4ee5\u6709\u6548\u5730\u8bc1\u660e\u8be5\u6d88\u606f\u4f20\u9012\u795e\u7ecf\u7f51\u7edc\u80fd\u529b\u8fdc\u8d85\u4f20\u7edf\u56fe\u795e\u7ecf\u7f51\u7edc\uff1a\u6587\u732e\u8868\u660e\u540e\u8005\u65e0\u6cd5\u8d85\u8fc7 3 \u9636 WL Test \u80fd\u529b\u3002\u800c\u4e00\u822c\u5355\u7eaf\u5f62\u6d88\u606f\u4f20\u9012\u7f51\u7edc\u5219\u80fd\u8d85\u8fc7 3 \u9636 WL Test\uff0c\u56e0\u6b64\u53ef\u4ee5\u8bc1\u5b9e\u8fd9\u4e00\u65b0\u578b\u7f51\u7edc\u5728\u5b66\u4e60\u548c\u9884\u6d4b\u80fd\u529b\u4e0a\u4f18\u4e8e\u4f20\u7edf\u56fe\u795e\u7ecf\u7f51\u7edc\u3002<\/span><\/section>\n

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MPSNS \u6bd4 GNNs \u7f51\u7edc\u590d\u6742\u6027\u66f4\u9ad8<\/span><\/strong><\/h2>\n
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\u8fd9\u4e2a\u7ed3\u679c\u8bf4\u660e\u4e86\u66f4\u9ad8\u9636\u7684\u4fe1\u606f\u548c\u62d3\u6251\u4fe1\u606f\u5bf9\u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\u7684\u91cd\u8981\u6027\u3002\u901a\u8fc7\u8ba1\u7b97\u67d0\u4e2a\u6848\u4f8b\u4e2d\u4e0d\u540c\u7f51\u7edc\u7684\u7ebf\u6027\u57df\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u89c2\u5730\u770b\u5230\u6a21\u578b\u7684\u590d\u6742\u5ea6\u3002\u4f7f\u7528 ReLU \u6fc0\u6d3b\u51fd\u6570\u65f6\uff0c\u7f51\u7edc\u4f1a\u8fdb\u884c\u7ebf\u6027\u7684\u5207\u5206\u6216\u4f7f\u7528\u8d85\u5e73\u9762\u8fdb\u884c\u9ad8\u7ef4\u7279\u5f81\u5207\u5206\uff0c\u8d85\u5e73\u9762\u7684\u6570\u91cf\u8d8a\u591a\uff0c\u8868\u660e\u7f51\u7edc\u5185\u90e8\u590d\u6742\u6027\u8d8a\u5f3a\uff0c\u4ece\u800c\u63d0\u5347\u5176\u8868\u793a\u80fd\u529b\u548c\u5b66\u4e60\u80fd\u529b\u3002<\/span><\/section>\n

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\u8def\u5f84\u5206\u7c7b Trajectory classification<\/span><\/strong><\/span><\/h2>\n
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Graph Representation of Protein Tertiary Structure<\/span><\/strong><\/h2>\n

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\u4e00\u4e2a\u6709\u8da3\u7684\u53d1\u5c55\u65b9\u5411\u662f\u5728\u751f\u7269\u9886\u57df\u7684\u4ea4\u53c9\uff0c\u7279\u522b\u662f\u5728\u86cb\u767d\u8bbe\u8ba1\u65b9\u9762\u3002\u6211\u4eec\u76ee\u524d\u7684\u7814\u7a76\u53d7\u5230 DeepMind \u7684 AlphaFold \u542f\u53d1\uff0c\u8be5\u6a21\u578b\u4e0d\u4ec5\u4f7f\u7528\u4e86\u591a\u5c42 Transformer\uff0c\u8fd8\u5f15\u5165\u4e86\u7ed3\u6784\u6df1\u5ea6\u5b66\u4e60\u6a21\u5757\uff0c\u8fd9\u5b9e\u9645\u4e0a\u662f\u4e00\u79cd\u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60\u3002<\/span><\/section>\n

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\u611f\u5174\u8da3\u7684\u670b\u53cb\u53ef\u4ee5\u89c2\u770b\u76f8\u5173\u5206\u4eab\u2014\u2014\u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60\uff1a4.\u89e3\u8bfb\u751f\u547d\u5bc6\u7801 | \u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60\u5728\u751f\u7269\u79d1\u5b66\u4e2d\u7684\u5e94\u7528\uff08https:\/\/pattern.swarma.org\/study_group_issue\/699\uff09\u3002<\/span><\/section>\n<\/section>\n<\/blockquote>\n

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Diffusion Process in Discrete Space<\/span><\/strong><\/h2>\n
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\u5c06\u6269\u6563\u6a21\u578b\u4e0e\u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60\u7ed3\u5408\uff0c\u53ef\u4ee5\u5b9e\u73b0\u751f\u6210\u5f0f AI \u7684\u6548\u679c\u3002\u901a\u8fc7\u5c06\u86cb\u767d\u8d28\u7684\u6c28\u57fa\u9178\u7a81\u53d8\u77e9\u9635\u4e0e\u6269\u6563\u6a21\u578b\u76f8\u7ed3\u5408\uff0c\u53ef\u4ee5\u5f62\u6210\u8fc1\u79fb\u6a21\u5f0f\uff0c\u4ece\u800c\u8fdb\u884c\u6709\u6548\u7684\u7edf\u8ba1\u63a8\u65ad\u3002<\/span><\/section>\n

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Generative Al: Structural Deep Learning-Based Diffusion Models for Novel Sequence Generation<\/span><\/strong><\/h2>\n
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\u4e0b\u9762\u662f\u4e00\u4e2a\u4f8b\u5b50\uff0c\u6211\u4eec\u53ef\u4ee5\u5229\u7528\u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60\u6784\u5efa\u4e00\u4e2a\u6269\u6563\u6a21\u578b\uff0c\u8fdb\u800c\u5f00\u53d1\u51fa\u4e00\u79cd\u751f\u6210\u5f0f AI \u7684\u65b9\u6cd5\uff0c\u7528\u4e8e\u9884\u6d4b\u65b0\u7684\u9ec4\u8272\u86cb\u767d\u7ed3\u6784\u3002\u8fd9\u79cd\u9ec4\u8272\u86cb\u767d\u548c\u7d2b\u8272\u86cb\u767d\u5728\u7ed3\u6784\u548c\u529f\u80fd\u4e0a\u975e\u5e38\u76f8\u4f3c\uff0c\u751a\u81f3\u53ef\u80fd\u5728\u67d0\u4e9b\u529f\u80fd\u4e0a\u6709\u6240\u63d0\u5347\uff0c\u4f46\u5b83\u4eec\u4e4b\u95f4\u7684\u5e8f\u5217\u76f8\u4f3c\u5ea6\u5374\u5f88\u4f4e\u3002\u56e0\u6b64\uff0c\u8fd9\u6837\u7684\u65b9\u6cd5\u80fd\u591f\u5e2e\u52a9\u6211\u4eec\u8bbe\u8ba1\u51fa\u4e00\u4e9b\u65b0\u578b\u86cb\u767d\u8d28\uff0c\u5e76\u521b\u9020\u51fa\u65b0\u7684\u4ea7\u54c1\u3002<\/span><\/section>\n

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\u53cc\u66f2\u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60 Hyperbolic geometric deep learning<\/span><\/strong><\/h2>\n
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\u53cc\u66f2\u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60\u7279\u70b9 Hyperbolic geometric deep learning<\/span><\/strong><\/h2>\n
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\u53cc\u66f2\u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60 Hyperbolic geometric deep learning<\/span><\/strong><\/span><\/h2>\n
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\u5728\u5904\u7406\u65f6\uff0c\u53cc\u66f2\u51e0\u4f55\u9700\u8981\u8003\u8651\u5c42\u6b21\u8868\u793a\uff0c\u5176\u7279\u5f81\u4f7f\u5f97\u5b83\u66f4\u9002\u5408\u6709\u6548\u8868\u8fbe\u6570\u636e\u5206\u5c42\u3002\u4f8b\u5982\uff0c\u5728\u793e\u4ea4\u7f51\u7edc\u4e2d\uff0c\u6709\u5f71\u54cd\u529b\u7684\u4e2d\u5fc3\u8282\u70b9\u4e0e\u8fb9\u7f18\u8282\u70b9\u4e4b\u95f4\u5b58\u5728\u660e\u663e\u533a\u522b\uff0c\u5982 Elon Musk \u5728 Twitter \u4e0a\u7684\u5f71\u54cd\u529b\u8fdc\u5927\u4e8e\u666e\u901a\u7528\u6237\uff0c\u8fd9\u79cd\u5c42\u6b21\u533a\u5206\u5bf9\u7406\u89e3\u7f51\u7edc\u5173\u952e\u7279\u5f81\u975e\u5e38\u6709\u5e2e\u52a9\u3002<\/span><\/section>\n

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\u6b64\u5916\uff0c\u53cc\u66f2\u51e0\u4f55\u80fd\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u4fdd\u6301\u539f\u59cb\u6570\u636e\u7684\u7ed3\u6784\u5173\u7cfb\uff0c\u4ece\u800c\u51cf\u5c11\u63a8\u65ad\u8fc7\u7a0b\u4e2d\u4e22\u5931\u7684\u91cd\u8981\u51e0\u4f55\u4fe1\u606f\u3002<\/strong>\u8fd9\u4e00\u70b9\u5bf9\u4e8e\u4ece\u9ad8\u7ef4\u6570\u636e\u5230\u4f4e\u7ef4\u62d3\u6251\u8868\u793a\u81f3\u5173\u91cd\u8981\uff0c\u5982\u4f55\u5b9e\u73b0\u9ad8\u6548\u5d4c\u5165\u4e5f\u662f\u8be5\u9886\u57df\u5173\u6ce8\u7684\u91cd\u70b9\u3002\u76f8\u8f83\u4e8e\u6b27\u5f0f\u7a7a\u95f4\uff0c\u53cc\u66f2\u7a7a\u95f4\u80fd\u591f\u4ee5\u66f4\u4f4e\u7ef4\u5ea6\u8868\u793a\u76f8\u540c\u7ed3\u6784\u7684\u4fe1\u606f\uff0c\u56e0\u6b64\u5728\u6355\u6349\u5404\u8282\u70b9\u95f4\u76f8\u4f3c\u5ea6\u65b9\u9762\u8868\u73b0\u51fa\u8272\u3002\u4f8b\u5982\uff0c\u5bf9\u4e8e\u5f02\u6784\u56fe<\/span>\uff08Heterogeneous Graph\uff09<\/span>\uff0c\u76f8\u4f3c\u7c7b\u8282\u70b9\u5373\u4fbf\u8ddd\u79bb\u8f83\u8fdc\uff0c\u901a\u8fc7\u53cc\u66f2\u53d8\u6362\u4e5f\u80fd\u4f7f\u5176\u5728\u7a7a\u95f4\u4e0a\u63a5\u8fd1\uff0c\u8fd9\u6709\u5229\u4e8e\u540e\u7eed\u795e\u7ecf\u7f51\u7edc\u63a8\u65ad\u3002<\/span><\/section>\n

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\u53cc\u66f2\u56fe\u5377\u79ef\u795e\u7ecf\u7f51\u7edc Hyperbolic GCN<\/span><\/strong><\/span><\/h2>\n
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\u73b0\u6709\u7684\u53cc\u66f2\u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60\u4e2d\uff0c\u6709\u4e24\u79cd\u7ecf\u5178\u7684\u65b9\u6cd5\u3002<\/strong>\u9996\u5148\u662f\u7531\u65af\u5766\u798f\u5927\u5b66\u7684 Leskovec \u56e2\u961f\u63d0\u51fa\u7684\u57fa\u4e8e\u53cc\u66f2\u51e0\u4f55\u7684\u56fe\u5377\u79ef\u7f51\u7edc\uff0c\u79f0\u4e3a\u53cc\u66f2\u56fe\u5377\u79ef\u7f51\u7edc[6]\u3002\u4ed6\u4eec\u4f7f\u7528\u5e9e\u52a0\u83b1\u7403\u6a21\u578b\u8fdb\u884c\u8282\u70b9\u5d4c\u5165\u548c\u5377\u79ef\u64cd\u4f5c\u3002<\/span><\/section>\n

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\u6b64\u5916\uff0c\u56fe\u795e\u7ecf\u7f51\u7edc\u4e5f\u53ef\u4ee5\u901a\u8fc7\u6ce8\u610f\u529b\u673a\u5236\u6765\u5b9e\u73b0\uff0c\u56e0\u6b64\u8fd8\u6709\u4e00\u79cd\u53eb\u505a\u53cc\u66f2\u6ce8\u610f\u529b\u673a\u5236\u7f51\u7edc<\/strong>\u7684\u65b9\u6cd5\u3002\u8fd9\u79cd\u65b9\u6cd5\u5141\u8bb8\u5728\u53cc\u66f2\u7a7a\u95f4\u4e2d\u5f15\u5165\u4e00\u5b9a\u7a0b\u5ea6\u7684\u6ce8\u610f\u529b\u673a\u5236\uff0c\u4ee5\u63d0\u5347\u7f51\u7edc\u8868\u793a\u80fd\u529b\u3002\u6ce8\u610f\u529b\u673a\u5236\u4f7f\u5f97\u5728\u8fed\u4ee3\u6216\u6d88\u606f\u4f20\u9012\u8fc7\u7a0b\u4e2d\uff0c\u4e0d\u540c\u8282\u70b9\u7279\u5f81\u5bf9\u7ed3\u679c\u4ea7\u751f\u663e\u8457\u5f71\u54cd\uff0c\u8fd9\u4e00\u70b9\u81f3\u5173\u91cd\u8981\u3002<\/span><\/section>\n

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\u5173\u4e8e\u53cc\u66f2\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\uff0c\u5b83\u9700\u8981\u5c06\u539f\u59cb\u6570\u636e\u7279\u5f81\u4e2d\u7684\u957f\u7279\u5f81\u5d4c\u5165\u5230\u4f4e\u7ef4\u7684\u53cc\u66f2\u6d41\u5f62\u4e2d\uff0c\u901a\u5e38\u91c7\u7528\u5e9e\u52a0\u83b1\u7403\u6a21\u578b\u6765\u5b9e\u73b0\u70b9\u5d4c\u5165\u3002\u5728\u6b64\u8fc7\u7a0b\u4e2d\uff0c\u9700\u8981\u8003\u8651\u4e0e\u4f20\u7edf\u6b27\u5f0f\u8ddd\u79bb\u6216\u7403\u9762\u8ddd\u79bb\u4e0d\u540c\u7684\u53cc\u66f2\u8ddd\u79bb\uff0c\u8be5\u8ddd\u79bb\u7531 arcosh \u51fd\u6570\u5b9a\u4e49\u3002<\/span><\/section>\n

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\u53cc\u66f2\u56fe\u5377\u79ef\u795e\u7ecf\u7f51\u7edc Hyperbolic GCN<\/span><\/strong><\/span><\/h2>\n
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\u5b8c\u6210\u8fd9\u4e9b\u51c6\u5907\u540e\uff0c\u53ef\u4ee5\u5bf9\u6570\u636e\u7279\u5f81\u8fdb\u884c\u53cc\u66f2\u5d4c\u5165\u3002\u5728\u5904\u7406\u65f6\uff0c\u53cc\u66f2\u56fe\u795e\u7ecf\u7f51\u7edc\u4f1a\u5229\u7528\u9ea6\u6bd4\u4e4c\u65af\u7ebf\u6027\u53d8\u6362\u6765\u5b9e\u73b0\u7279\u5f81\u52a0\u548c\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u7279\u5f81\uff0c\u5176\u9ea6\u6bd4\u4e4c\u65af\u7ebf\u6027\u5c42\u53ef\u5b9a\u4e49\u4e3a W \u548c x \u4e4b\u95f4\u7684\u53c9\u79ef\uff0c\u901a\u8fc7 x \u5728 W \u4e0a\u7684\u6295\u5f71\u4ee5\u53ca Wx \u5355\u4f4d\u5316\u76f8\u7ed3\u5408\u6765\u5b8c\u6210\u8fd9\u79cd\u53d8\u6362\u3002\u5176\u4e2d\uff0cW \u662f\u53ef\u5b66\u4e60\u53c2\u6570\u77e9\u9635\uff0c\u800c x \u5219\u662f\u539f\u59cb\u6570\u636e\u4e2d\u7279\u5f81\u5411\u91cf\u6784\u6210\u7684\u77e9\u9635\u3002\u6b64\u5916\uff0c\u8d1f\u66f2\u7387\u4f5c\u4e3a\u4e00\u79cd\u7279\u6b8a\u5c5e\u6027\uff0c\u4f1a\u88ab\u7528\u6765\u89c4\u8303\u5316\u8ba1\u7b97\uff0c\u4ece\u800c\u5b9a\u4e49\u9ea6\u6bd4\u4e4c\u65af\u7ebf\u6027\u53d8\u6362\u5c42\u3002<\/span><\/section>\n

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\u901a\u8fc7\u6709\u6548\u5730\u7ec4\u5408\u8fd9\u4e9b\u7ebf\u6027\u53d8\u6362\u5c42\uff0c\u5c31\u80fd\u5b9e\u73b0\u6570\u636e\u5d4c\u5165\u548c\u5377\u79ef\u64cd\u4f5c\uff0c\u5e76\u5c06\u8fd9\u4e9b\u5377\u79ef\u5c42\u6574\u5408\u8fdb\u4f20\u7edf\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784\u4e2d\uff0c\u4ece\u800c\u5f62\u6210\u5b8c\u6574\u7684\u53cc\u66f2\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u3002<\/span><\/section>\n

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7. \u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60\u7684\u53d1\u5c55\u8d8b\u52bf<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u51e0\u4f55\u8d8a\u53d1\u91cd\u8981 Geometry becomes increasingly important in ML<\/span><\/strong><\/span><\/h2>\n
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\u672a\u6765\u5728\u4eba\u5de5\u667a\u80fd\u9886\u57df\u6709\u51e0\u4e2a\u53ef\u80fd\u7684\u53d1\u5c55\u8d8b\u52bf\u3002\u5c3d\u7ba1\u5927\u6a21\u578b\u5907\u53d7\u5173\u6ce8\uff0c\u4f46\u51e0\u4f55\u5b66\u4ecd\u7136\u53d1\u6325\u7740\u81f3\u5173\u91cd\u8981\u7684\u4f5c\u7528<\/strong>\uff0c\u7279\u522b\u662f\u5fae\u5206\u51e0\u4f55\u7684\u91cd\u8981\u6027\u65e5\u76ca\u51f8\u663e\u3002\u5fae\u5206\u51e0\u4f55\u53ca\u5176\u76f8\u5173\u9886\u57df\u5c06\u4e3a\u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60\u5e26\u6765\u65b0\u7684\u601d\u8def\uff0c\u4f8b\u5982\u7b49\u53d8\u56fe\u795e\u7ecf\u7f51\u7edc<\/span>\uff08Equivariant Graph Neural Networks, EGNN\uff09<\/span>\u67b6\u6784\uff0c\u8fd9\u4e00\u91cd\u70b9\u5728\u4e8e\u8003\u8651\u51e0\u4f55\u63a8\u65ad\u548c\u795e\u7ecf\u6d88\u606f\u4f20\u9012\u8fc7\u7a0b\u4e2d\u7684\u4e0d\u53d8\u7279\u6027\u3002<\/span><\/section>\n

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\u5728\u6570\u5b66\u4e0a\uff0c\u201c\u7b49\u53d8\u201d\u6307\u7684\u662f\u7cfb\u7edf\u5bf9\u4e8e\u67d0\u4e9b\u64cd\u4f5c\u5177\u6709\u4e00\u81f4\u6027\u7684\u54cd\u5e94\uff0c\u5373\u5982\u679c\u8f93\u5165\u53d1\u751f\u4e86\u53d8\u5316\uff0c\u8f93\u51fa\u4e5f\u4f1a\u4ee5\u53ef\u9884\u6d4b\u7684\u65b9\u5f0f\u53d8\u5316\u3002\u8fd9\u4e00\u6027\u8d28\u7279\u522b\u9002\u7528\u4e8e\u5904\u7406\u7269\u7406\u7cfb\u7edf\u3001\u5206\u5b50\u7ed3\u6784\u7b49\u9886\u57df\uff0c\u56e0\u4e3a\u8fd9\u4e9b\u5bf9\u8c61\u901a\u5e38\u5177\u6709\u56fa\u6709\u7684\u5bf9\u79f0\u6027\u3002<\/span><\/span><\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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\u5229\u7528\u5bf9\u79f0\u6027\u548c\u66f2\u7387\u7b49\u56fe\u5f62\u7ed3\u6784\uff0c\u53ef\u4ee5\u66f4\u597d\u5730\u7406\u89e3\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\u4e2d\u7684\u4e0d\u786e\u5b9a\u6027\u3002<\/strong>\u4f8b\u5982\uff0c\u901a\u8fc7\u6700\u4f18\u4f20\u8f93\u7406\u8bba\u6216\u8868\u793a\u5b66\u4e60\u4e2d\u5fae\u5206\u51e0\u4f55\u7684\u66f2\u7387\u5173\u7cfb\uff0c\u6211\u4eec\u53ef\u4ee5\u53d1\u5c55\u51fa\u53cc\u66f2\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\u3002\u79bb\u6563\u5fae\u5206\u51e0\u4f55\u76f8\u8f83\u4e8e\u4f20\u7edf\u6574\u4f53\u548c\u8fde\u7eed\u5fae\u5206\u51e0\u4f55\u66f4\u5177\u6311\u6218\u6027\uff0c\u76ee\u524d\u4e5f\u53d7\u5230\u6570\u5b66\u5927\u5e08\u5982\u4e18\u6210\u6850\u7684\u5173\u6ce8\u3002<\/span><\/section>\n

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\u79bb\u6563\u5fae\u5206\u51e0\u4f55\u4f5c\u4e3a\u4e00\u79cd\u81ea\u7136\u5de5\u5177\uff0c\u5c06\u6709\u6548\u5e94\u7528\u4e8e\u56fe\u795e\u7ecf\u7f51\u7edc\uff0c\u56e0\u4e3a\u6570\u636e\u672c\u8eab\u662f\u79bb\u6563\u7684\u3002\u6b64\u5916\uff0c\u524d\u4e24\u5e74ICLR\u6700\u4f73\u63d0\u540d\u5956\u9881\u53d1\u7ed9\u4e86\u501f\u52a9\u91cc\u5947\u6d41\u548c\u91cc\u5947\u66f2\u7387\u7406\u8bba\uff0c\u89e3\u51b3\u56fe\u795e\u7ecf\u7f51\u7edc\u4e2d\u7684\u8fc7\u5ea6\u6324\u538b\u95ee\u9898\uff0c\u5e76\u51cf\u8f7b\u8d1f\u9762\u6548\u5e94\u7684\u5de5\u4f5c[7]\u3002\u672a\u6765\uff0c\u79bb\u6563\u66f2\u7387\u6709\u671b\u4e0e\u5176\u4ed6\u7ed3\u6784\u548c\u62d3\u6251\u95ee\u9898\u76f8\u7ed3\u5408\uff0c\u4ece\u800c\u8bbe\u8ba1\u51fa\u5168\u65b0\u7684\u795e\u7ecf\u7f51\u7edc\u3002<\/span><\/section>\n

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\u6d88\u606f\u4f20\u9012\u4ecd\u662f\u4e3b\u8981\u8303\u4f8b Message passing is still the dominant paradigm<\/span><\/strong><\/span><\/h2>\n
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\u6b64\u5916\uff0c\u6d88\u606f\u4f20\u9012\u673a\u5236\u5728\u6df1\u5ea6\u5b66\u4e60\u4e2d\u4f9d\u65e7\u662f\u4e00\u4e2a\u91cd\u8981\u8d8b\u52bf\uff0c\u81ea 2016 \u5e74\u8c37\u6b4c\u56e2\u961f\u63d0\u51fa\u4ee5\u6765\uff0c\u5b83\u5df2\u88ab\u5e7f\u6cdb\u5e94\u7528\uff0c\u5e76\u63ed\u793a\u4e86\u7279\u5f81\u4f20\u9012\u8fc7\u7a0b\u4e2d\u7684\u7ec6\u8282\u3002\u8fd9\u79cd\u673a\u5236\u672a\u6765\u53ef\u80fd\u4e0e\u4e0d\u540c\u7c7b\u578b\u7684\u51e0\u4f55\u7ed3\u5408\uff0c\u4ee5\u514b\u670d\u73b0\u6709\u74f6\u9888\u95ee\u9898\uff0c\u5982\u8fc7\u5149\u6ed1\u6216\u8fc7\u5ea6\u6324\u538b\u73b0\u8c61\u3002\u6211\u8ba4\u4e3a\u672a\u6765\u5728\u4e0e\u4e0d\u540c\u7c7b\u578b\u7684\u51e0\u4f55\u7ed3\u5408\u65f6\uff0c\u5c06\u4f1a\u6709\u5f88\u5927\u7684\u5e2e\u52a9\u3002\u521a\u624d\u6211\u4eec\u63d0\u5230\u8fc7\u56fe\u5f62\u6216\u795e\u7ecf\u6d88\u606f\u4f20\u9012\uff0c\u751a\u81f3\u66f4\u5e7f\u6cdb\u7684\u6982\u5ff5\u3002<\/span><\/section>\n

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\u5fae\u5206\u65b9\u7a0b\u4ea7\u751f\u65b0\u7684\u56fe\u795e\u7ecf\u7f51\u7edc\u67b6\u6784 Differential equations<\/span><\/strong><\/span><\/h2>\n
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\u53ef\u4ee5\u5c06\u5355\u7eaf\u590d\u5f62\u795e\u7ecf\u6d88\u606f\u4f20\u9012\u673a\u5236\u89c6\u4e3a\u4e00\u4e2a\u65b9\u7a0b\u3002<\/strong>\u5f53\u8fd9\u4e2a\u65b9\u7a0b\u4e0e\u5176\u4ed6\u5143\u7d20\u7ed3\u5408\u65f6\uff0c\u4f1a\u4ea7\u751f\u591a\u79cd\u7c7b\u578b\u7684\u6d88\u606f\u4f20\u9012\uff0c\u4ee5\u514b\u670d\u539f\u6709\u6d88\u606f\u4f20\u9012\u4e2d\u7684\u4e00\u4e9b\u74f6\u9888\u95ee\u9898\uff0c\u4f8b\u5982\u8fc7\u4e8e\u5149\u6ed1\u6216\u8fc7\u5ea6\u6324\u538b\u7684\u95ee\u9898\u3002<\/span><\/section>\n

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\u76f8\u4fe1\u672a\u6765\u8fd9\u4e00\u9886\u57df\u8fd8\u4f1a\u8fdb\u4e00\u6b65\u53d1\u5c55\uff0c\u7279\u522b\u662f\u5b83\u53ef\u80fd\u4e0e\u795e\u7ecf\u5e38\u5fae\u5206\u65b9\u7a0b<\/span>\uff08ODE\uff09<\/span>\u6c42\u89e3\u5668\u76f8\u7ed3\u5408\uff0c\u4ece\u800c\u5b9e\u73b0\u5feb\u901f\u548c\u9ad8\u6548\u7684\u56fe\u795e\u7ecf\u7f51\u7edc\u63a8\u65ad\uff0c\u5e76\u4e14\u80fd\u591f\u4f7f\u7f51\u7edc\u53d8\u5f97\u66f4\u52a0\u6df1\u5c42\u6b21\u3002<\/span><\/section>\n

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\u4fe1\u53f7\u5904\u7406\u3001\u795e\u7ecf\u79d1\u5b66\u3001\u7269\u7406\u5b66\u601d\u60f3\u83b7\u65b0\u751f Signal Processing\uff0cNeuroscience, and Physics get a new life<\/span><\/strong><\/span><\/h2>\n
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\u590d\u6742\u7cfb\u7edf\u5efa\u6a21\u9700\u8d85\u8d8a\u56fe Complex systems<\/span><\/strong><\/span><\/h2>\n
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\u63a8\u7406\u3001\u516c\u7406\u5316\u548c\u6cdb\u5316 Reasoning, axiomatisation, and generalisation<\/span><\/strong><\/span><\/h2>\n
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\u5f3a\u5316\u5b66\u4e60\u4e0e\u56fe\u7ed3\u5408 Graphs become popular in RL<\/span><\/strong><\/span><\/h2>\n
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\u6b64\u5916\uff0c\u8fd1\u4e24\u5e74\u4e5f\u6709\u4e00\u4e9b\u4e0e\u5f3a\u5316\u5b66\u4e60\u7ed3\u5408\u7684\u65b0\u5de5\u5177\uff0c\u4f8b\u5982\u5982\u4f55\u5c06\u56fe\u4e0e\u5f3a\u5316\u5b66\u4e60\u4e2d\u7684\u5168\u5c40\u53d8\u5316\u548c\u5c40\u90e8\u53d8\u5316\u673a\u5236\u76f8\u7ed3\u5408\uff0c\u8fd9\u53ef\u4ee5\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u589e\u5f3a\u6d88\u606f\u4f20\u9012\u548c\u6df1\u5ea6\u5b66\u4e60\u7684\u6548\u679c\uff0c\u4ece\u800c\u4fc3\u8fdb\u51e0\u4f55\u5728\u5f3a\u5316\u5b66\u4e60\u4e2d\u7684\u5e94\u7528\u3002<\/span><\/section>\n

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\u611f\u5174\u8da3\u7684\u670b\u53cb\u53ef\u4ee5\u89c2\u770b\u76f8\u5173\u5206\u4eab\u2014\u2014\u56fe\u795e\u7ecf\u7f51\u7edc\u4e0e\u7ec4\u5408\u4f18\u5316\uff1a1.\u7ec4\u5408\u4f18\u5316\u95ee\u9898\u7684\u673a\u5668\u5b66\u4e60\u6c42\u89e3\uff08https:\/\/pattern.swarma.org\/study_group_issue\/483\uff09\u3002\u5e76\u4e14\uff0c\u793e\u533a\u6210\u5458\u6574\u7406\u6210\u7b14\u8bb0\uff0c\u4f9b\u5927\u5bb6\u5b66\u4e60\u4eba\u5de5\u667a\u80fd\u524d\u6cbf\uff1a\u7ec4\u5408\u4f18\u5316\u95ee\u9898\u7684\u673a\u5668\u5b66\u4e60\u6c42\u89e3 | \u8303\u957f\u4fca\u5206\u4eab\u6574\u7406<\/a><\/span><\/section>\n<\/section>\n<\/blockquote>\n

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\u51e0\u4f55\u4e0e\u56fe\u673a\u5668\u5b66\u4e60\u52a9\u529b\u836f\u7269\u53d1\u73b0\u548c\u8bbe\u8ba1 Drug Discovery<\/span><\/strong><\/span><\/h2>\n
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\u81ea 2021 \u5e74\u4ee5\u6765\uff0c\u56fe\u795e\u7ecf\u7f51\u7edc\u4e0e\u86cb\u767d\u8d28\u5de5\u7a0b\u4e4b\u95f4\u7684\u8054\u7cfb\u65e5\u76ca\u7d27\u5bc6\uff0c\u5c24\u5176\u662f\u5728 AlphaFold 2 \u95ee\u4e16\u540e\uff0c\u5f15\u53d1\u4e86\u5927\u5bb6\u5bf9\u8fd9\u4e00\u9886\u57df\u7684\u5e7f\u6cdb\u5173\u6ce8\uff0c\u5e76\u8ba4\u4e3a\u5176\u80fd\u591f\u5728\u836f\u7269\u8bbe\u8ba1\u9886\u57df\u505a\u51fa\u91cd\u5927\u8d21\u732e\u3002\u901a\u8fc7\u56fe\u795e\u7ecf\u7f51\u7edc\u65b9\u6cd5\uff0c\u53ef\u4ee5\u6709\u6548\u5730\u4e3a\u5927\u5206\u5b50\u6216\u5c0f\u5206\u5b50\u7684\u8bbe\u8ba1\u63d0\u4f9b\u652f\u6301\u3002\u8fd9\u79cd\u56fe\u795e\u7ecf\u7f51\u7edc\u80fd\u591f\u5c06\u751f\u5316\u4fe1\u606f\u548c\u7279\u5f81\u6574\u5408\u8fdb\u63a8\u65ad\u673a\u5236\u4e2d\u3002<\/span><\/section>\n

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\u5728\u8fc7\u53bb\u51e0\u5e74\u91cc\uff0c\u8fd9\u4e00\u9886\u57df\u5f97\u5230\u4e86\u5e7f\u6cdb\u63a2\u7d22\uff0c\u4e0d\u4ec5\u6d89\u53ca\u4eba\u5de5\u667a\u80fd\uff0c\u8fd8\u5305\u62ec\u751f\u7269\u533b\u836f\u7b49\u79d1\u5b66\u9886\u57df\uff0c\u76f8\u5173\u6587\u732e\u5c42\u51fa\u4e0d\u7a77\u3002\u4f8b\u5982\uff0c\u9ec4\u8001\u5e08\u5728\u8fd9\u4e00\u65b9\u9762\u4e5f\u6709\u7a81\u51fa\u8d21\u732e\uff0c\u4ed6\u4eec\u5229\u7528\u56fe\u795e\u7ecf\u7f51\u7edc\u8fdb\u884c\u6297\u4f53\u8bbe\u8ba1[8]\uff0c\u5e76\u83b7\u5f97\u4e86\u524d\u51e0\u5e74\u7684 ICLR \u6700\u4f73\u8bba\u6587\u5956\u3002\u5728\u56fd\u5185\uff0c\u8be5\u9886\u57df\u5df2\u6709\u4e0d\u5c11\u4f18\u79c0\u7814\u7a76\u6210\u679c\u3002<\/span><\/section>\n

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\u91cf\u5b50\u673a\u5668\u5b66\u4e60 Quantum ML<\/span><\/strong><\/span><\/h2>\n
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\u6b64\u5916\uff0c\u8fd8\u6709\u4e00\u4e9b\u524d\u6cbf\u65b9\u5411\uff0c\u5982\u91cf\u5b50\u673a\u5668\u5b66\u4e60\u7684\u6574\u5408\uff0c\u76ee\u524d\u5c1a\u672a\u5b8c\u5168\u5b9e\u73b0\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u5c31\u662f\u5982\u4f55\u5c06\u56fe\u673a\u5668\u5b66\u4e60\u7684\u601d\u60f3\u878d\u5165\u91cf\u5b50\u673a\u5668\u5b66\u4e60\uff0c\u4ee5\u52a0\u901f\u5176\u63a8\u65ad\u8fc7\u7a0b\uff0c\u4ee5\u53ca\u5982\u4f55\u5728\u91cf\u5b50\u8ba1\u7b97\u673a\u4e0a\u5b9e\u73b0\u8fd9\u4e9b\u7f51\u7edc\u3002\u8fd9\u4e9b\u95ee\u9898\u90fd\u503c\u5f97\u6df1\u5165\u63a2\u8ba8\uff0c\u76ee\u524d\u76f8\u5173\u7814\u7a76\u4ecd\u8f83\u5c11\uff0c\u4f46\u672a\u6765\u51e0\u5e74\u53ef\u80fd\u4f1a\u51fa\u73b0\u7a81\u7834\u3002<\/span><\/section>\n

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\u53c2\u8003\u6587\u732e<\/span><\/strong><\/span><\/h1>\n

1. BRUNA J, SZLAM A, LECUN Y. Learning stable group invariant representations with convolutional networks[M. arXiv, 2013. http:\/\/arxiv.org\/abs\/1301.3537. DOI:10.48550\/arXiv.1301.3537.<\/span><\/p>\n

2. DEFFERRARD M, BRESSON X, VANDERGHEYNST P. Convolutional neural networks on graphs with fast localized spectral filtering[C\/\/Advances in Neural Information Processing Systems: \u5377 29. Curran Associates, Inc., 2016. https:\/\/proceedings.neurips.cc\/paper_files\/paper\/2016\/hash\/04df4d434d481c5bb723be1b6df1ee65-Abstract.html.<\/span><\/p>\n

3. BERG R van den, KIPF T N, WELLING M. Graph convolutional matrix completion[M. arXiv, 2017. http:\/\/arxiv.org\/abs\/1706.02263. DOI:10.48550\/arXiv.1706.02263.<\/span><\/p>\n

4. GIOVANNI F D, ROWBOTTOM J, CHAMBERLAIN B P, et al. Graph neural networks as gradient flows[J. 2022. https:\/\/openreview.net\/forum?id=0IywQ8uxJx.<\/span><\/p>\n

5. BODNAR C, FRASCA F, WANG Y, et al. Weisfeiler and lehman go topological: Message passing simplicial networks[C\/\/Proceedings of the 38th International Conference on Machine Learning. PMLR, 2021: 1026-1037. https:\/\/proceedings.mlr.press\/v139\/bodnar21a.html.<\/span><\/p>\n

6. CHAMI I, YING R, R\u00c9 C, et al. Hyperbolic graph convolutional neural networks[M. arXiv, 2019. http:\/\/arxiv.org\/abs\/1910.12933. DOI:10.48550\/arXiv.1910.12933.<\/span><\/p>\n

7. J, DI GIOVANNI F, CHAMBERLAIN B P, et al. Understanding over-squashing and bottlenecks on graphs via curvature[M. arXiv, 2022 http:\/\/arxiv.org\/abs\/2111.14522. DOI:10.48550\/arXiv.2111.14522.<\/span><\/p>\n

8. KONG X, HUANG W, LIU Y. Conditional antibody design as 3D equivariant graph translation[C\/\/The Eleventh International Conference on Learning Representations. 2022. https:\/\/openreview.net\/forum?id=LFHFQbjxIiP.<\/span><\/p>\n


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<\/span><\/section>\n
\u8be6\u60c5\u8bf7\u89c1\uff1a<\/span><\/section>\n
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<\/section>\n
\u63a8\u8350\u9605\u8bfb<\/span><\/strong><\/strong><\/strong><\/section>\n
1. <\/strong>\u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60\uff1a\u8ba9\u7269\u7406\u4e16\u754c\u62e5\u6709AI | \u9ec4\u6587\u70b3\u5206\u4eab\u6574\u7406<\/a><\/strong><\/span><\/section>\n
2. <\/strong>\u62d3\u6251\u6df1\u5ea6\u5b66\u4e60\u6355\u6349\u6570\u636e\u7684\u9ad8\u9636\u5173\u7cfb\uff1a\u4fe1\u606f\u4f20\u9012\u62d3\u6251\u795e\u7ecf\u7f51\u7edc\u6982\u8ff0<\/a><\/strong><\/span><\/section>\n
3. <\/strong>\u524d\u6cbf\u63a2\u8ba8\uff1a\u56fe\u795e\u7ecf\u7f51\u7edc\u3001\u7ec4\u5408\u4f18\u5316\u3001\u5927\u6a21\u578b\u4e0eAI4Science\u5982\u4f55\u76f8\u4e92\u4fc3\u8fdb\uff1f<\/a> <\/strong><\/span><\/section>\n
4. <\/strong><\/span>\u5f20\u6c5f\uff1a\u7b2c\u4e09\u4ee3\u4eba\u5de5\u667a\u80fd\u6280\u672f\u57fa\u7840\u2014\u2014\u4ece\u53ef\u5fae\u5206\u7f16\u7a0b\u5230\u56e0\u679c\u63a8\u7406 | \u96c6\u667a\u5b66\u56ed\u5168\u65b0\u8bfe\u7a0b<\/a><\/strong><\/strong><\/span><\/section>\n
<\/strong>5.<\/strong> \u9f99\u5e74\u5927\u8fd0\u8d77\uff0c\u5b66\u4e60\u6b63\u5f53\u65f6\uff01\u89e3\u9501\u96c6\u667a\u5168\u7ad9\u5185\u5bb9\uff0c\u5f00\u542f\u65b0\u5e74\u5b66\u4e60\u8ba1\u5212<\/a><\/strong><\/strong><\/strong><\/strong><\/span><\/strong><\/strong><\/section>\n

6. <\/strong>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/strong><\/span><\/a><\/p>\n


<\/p>\n


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

\u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u62a5\u540d\u8bfb\u4e66\u4f1a<\/span><\/section>\n

<\/mp-style-type><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

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