{"id":2516,"date":"2024-12-28T10:05:27","date_gmt":"2024-12-28T02:05:27","guid":{"rendered":"https:\/\/www.gnn.club\/?p=2516"},"modified":"2025-01-07T16:55:07","modified_gmt":"2025-01-07T08:55:07","slug":"leftnet","status":"publish","type":"post","link":"http:\/\/gnn.club\/?p=2516","title":{"rendered":"LEFTNet"},"content":{"rendered":"\n

1\u3001\u4e09\u79cd\u56fe\u540c\u6784\u95ee\u9898<\/h2>\n\n\n\n

\u56fe\u540c\u6784\u95ee\u9898\u662f\u56fe\u8bba\u4e2d\u7684\u4e00\u4e2a\u57fa\u672c\u95ee\u9898\uff0c\u5b83\u8981\u6c42\u786e\u5b9a\u4e24\u4e2a\u56fe\u662f\u5426\u5728\u7ed3\u6784\u4e0a\u5b8c\u5168\u76f8\u540c\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u8fd9\u610f\u5473\u7740\u5b58\u5728\u4e00\u79cd\u9876\u70b9\u95f4\u7684\u4e00\u5bf9\u4e00\u6620\u5c04\uff0c\u4f7f\u5f97\u4e24\u4e2a\u56fe\u4e2d\u7684\u9876\u70b9\u76f8\u4e92\u8fde\u63a5\u7684\u65b9\u5f0f\u5b8c\u5168\u4e00\u81f4\u3002\u5982\u679c\u8fd9\u6837\u7684\u6620\u5c04\u5b58\u5728\uff0c\u8fd9\u4e24\u4e2a\u56fe\u88ab\u8ba4\u4e3a\u662f\u540c\u6784\u7684\u3002\u56fe\u795e\u7ecf\u7f51\u7edc\u662f\u4e00\u79cd\u4e13\u4e3a\u5904\u7406\u56fe\u7ed3\u6784\u6570\u636e\u8bbe\u8ba1\u7684\u795e\u7ecf\u7f51\u7edc\u67b6\u6784\uff0c\u5b83\u80fd\u591f\u901a\u8fc7\u8282\u70b9\u7684\u7279\u5f81\u4fe1\u606f\u548c\u8fde\u63a5\u6a21\u5f0f\u6765\u5b66\u4e60\u56fe\u7684\u8868\u793a\u3002\u4e00\u4e2a\u4f18\u79c0\u7684\u51e0\u4f55GNN\u6a21\u578b\u53ef\u4ee5\u6709\u6548\u5730\u5b66\u4e60\u548c\u63d0\u53d6\u8282\u70b9\u548c\u8fb9\u7684\u7279\u5f81\u3002\u8fd9\u79cd\u5b66\u4e60\u65b9\u5f0f\u4f7f\u5f97GNN\u80fd\u591f\u6355\u6349\u5230\u56fe\u7684\u5c40\u90e8\u548c\u5168\u5c40\u7ed3\u6784\u7279\u5f81\uff0c\u8fd9\u662f\u5224\u65ad\u56fe\u540c\u6784\u95ee\u9898\u65f6\u7684\u5173\u952e\u3002\u7b80\u5355\u8bf4\uff0c\u5bf9\u4e8e\u56fe\u540c\u6784\u7684\u8bc6\u522b\u80fd\u529b\u662f\u8861\u91cfGNN\u6a21\u578b\u8868\u5f81\u80fd\u529b\u7684\u91cd\u8981\u65b9\u9762\u3002<\/p>\n\n\n\n

LEFTNet\u4e2d\uff0c\u5b9a\u4e49\u4e86\u4e09\u79cd\u56fe\u540c\u6784\u7ed3\u6784\uff1a<\/p>\n\n\n\n

\uff081\uff09\u6811\u540c\u6784\uff1a\u4efb\u610f\u90bb\u63a5\u7684\u4e24\u539f\u5b50\u95f4\u7684\u8ddd\u79bb\u4e00\u81f4\u3002<\/p>\n\n\n\n

\uff082\uff09\u4e09\u89d2\u540c\u6784\uff1a\u4efb\u610f\u90bb\u63a5\u7684\u4e09\u539f\u5b50\u6784\u6210\u7684\u4e09\u89d2\u5f62\u4e00\u81f4\u3002<\/p>\n\n\n\n

\uff083\uff09\u5b50\u56fe\u540c\u6784\uff1a\u4efb\u610f\u4e24\u4e2a\u4e09\u89d2\u5f62\u7684\u76f8\u5bf9\u4f4d\u7f6e\u4fdd\u6301\u4e00\u81f4\u3002<\/p>\n\n\n\n

\u5177\u4f53\u793a\u4f8b\u5982\u56fe1\u6240\u793a\uff1a<\/p>\n\n\n

\n
\"\"
\u56fe1 \u56fe\u540c\u6784\u7ed3\u6784<\/figcaption><\/figure><\/div>\n\n\n

\u5728\u56fe1(a)\u4e2d\uff0c\u5c55\u793a\u4e86\u4e00\u79cd\u6ee1\u8db3\u6811\u540c\u6784\uff0c\u4f46\u4e0d\u6ee1\u8db3\u4e09\u89d2\u540c\u6784\u7684\u60c5\u51b5\u3002\u4e09\u89d2\u540c\u6784\u4e0d\u4ec5\u4ec5\u662f\u8ddd\u79bb\u4e0a\u7684\u76f8\u4f3c\uff0c\u8fd8\u5305\u62ec\u4e86\u89d2\u5ea6\u548c\u65b9\u5411\u7684\u4e00\u81f4\u6027\u3002\u5728\u56fe1(b)\u4e2d\uff0c\u5c55\u793a\u4e86\u4e00\u79cd\u6ee1\u8db3\u4e09\u89d2\u540c\u6784\uff0c\u4f46\u4e0d\u6ee1\u8db3\u5b50\u56fe\u540c\u6784\u7684\u60c5\u51b5\uff0c\u800cLEFTNet\u7684\u6a21\u578b\u8bbe\u8ba1\u65b9\u5411\u662f\u8ba9\u6a21\u578b\u5bf9\u8fd9\u4e09\u79cd\u60c5\u51b5\u90fd\u6709\u8868\u5f81\u80fd\u529b\u3002<\/p>\n\n\n\n

\u9996\u5148\uff0c\u4e3a\u4e86\u6ee1\u8db3\u6811\u540c\u6784\u7684\u8981\u6c42\uff0c\u4f5c\u8005\u8ba4\u4e3a\uff1a\u53ea\u8981\u6b63\u786e\u62bd\u53d6\u539f\u5b50\u95f4\u8ddd\u79bb\u5373\u53ef\uff0c\u6240\u6709\u7684\u51e0\u4f55GNN\uff0c\u65e0\u8bba\u662f\u7b49\u53d8\u6027\u8d28\u7684\u8fd8\u662f\u4e0d\u53d8\u6027\u8d28\u7684\u51e0\u4e4e\u5747\u6ee1\u8db3\u3002<\/p>\n\n\n\n

\u5176\u6b21\uff0c\u4e3a\u4e86\u6ee1\u8db3\u4e09\u89d2\u540c\u6784\u7684\u8981\u6c42\uff0c\u4f5c\u8005\u8ba4\u4e3a\uff1a\u4e09\u89d2\u540c\u6784\u672c\u8d28\u4e0a\u662f\u5c40\u57df\u5b8c\u5907\u6027\u95ee\u9898\u3002\u901a\u8fc7\u8bbe\u8ba1\u4e00\u4e2a\u5408\u7406\u7684\u5c40\u57df\u6b63\u4ea4\u5750\u6807\u7cfb\uff0c\u8ba9\u6b64\u5c40\u57df\u5750\u6807\u6709\u80fd\u529b\u53ef\u4ee5\u8868\u5f81\u5c40\u90e8\u7a7a\u95f4\u8303\u56f4\u5185\u6240\u6709\u7684\u51e0\u4f55\u5411\u91cf\u3002\u540c\u65f6\u8fd8\u9700\u8981\u6ee1\u8db3\u7b49\u53d8\u8981\u6c42\uff0c\u901a\u8fc7\u5c06\u539f\u5750\u6807\u6620\u5c04\u5230\u5c40\u57df\u5750\u6807\uff0c\u5373\u53ef\u6ee1\u8db3\u5c40\u57df\u5b8c\u5907\u6027\u7684\u8981\u6c42\u3002\u8fd9\u91cc\uff0cLEFTNet\u7684\u6a21\u578b\u76f4\u63a5\u91c7\u7528ClofNet\u4e2d\u63d0\u51fa\u7684\u5c40\u57df\u5750\u6807\u7cfb\u3002<\/p>\n\n\n\n

\u6700\u540e\uff0c\u4e3a\u4e86\u6ee1\u8db3\u5b50\u56fe\u540c\u6784\u7684\u8981\u6c42\uff0c\u6a21\u578b\u9700\u8981\u5c06\u5c40\u57df\u5b8c\u5907\u6027\u6269\u5c55\u5230\u5168\u57df\u5b8c\u5907\u6027\uff0c\u4e14\u8fd9\u4e2a\u8fc7\u7a0b\u662f\u4fe1\u606f\u65e0\u635f\u7684\u3002\u4e0d\u5e78\u7684\u662f\uff0c\u56fe\u7ed3\u6784\u4e2d\u4e0d\u540c\u7684\u8282\u70b9\u5efa\u7acb\u7684\u5c40\u57df\u5750\u6807\u7cfb\u662f\u4e0d\u540c\u7684\u3002\u4e0d\u540c\u5c40\u57df\u5750\u6807\u7cfb\u76f8\u5bf9\u4f4d\u7f6e\u4e0d\u4e00\u6837\uff0c\u6362\u53e5\u8bdd\u8bf4\uff0c\u5bf9\u4e0d\u540c\u5c40\u57df\u5750\u6807\u7cfb\u5bf9\u5c40\u90e8\u8303\u56f4\u5185\u70b9\u4f4d\u7f6e\u4fe1\u606f\u7684\u5efa\u6a21\u89d2\u5ea6\u4e0d\u540c\uff0c\u8fd9\u5bfc\u81f4\u5c40\u57df\u4fe1\u606f\u6c47\u805a\u8fc7\u7a0b\u4e2d\u906d\u53d7\u4fe1\u606f\u635f\u5931\uff0c\u5982\u56fe2\u6240\u793a\u3002<\/p>\n\n\n

\n
\"\"
\u56fe2 \u4e0d\u540c\u5c40\u57df\u5750\u6807\u7cfb<\/figcaption><\/figure><\/div>\n\n\n

\u5982\u56fe2\u6240\u793a\uff0c\u70b9b\u548c\u70b9c\u5206\u522b\u5efa\u7acb\u4e86\u5c40\u57df\u5750\u6807\u7cfb\uff0c\u5728\u8fd9\u4e24\u4e2a\u5c40\u57df\u5750\u6807\u7cfb\u4e0b\uff0ccluster\uff08\u56e2\u7c07\uff09b\u548ccluster c\u8fdb\u884c\u4e86\u6709\u6548\u6620\u5c04\u3002\u4f46\u7531\u4e8e\u5c40\u57df\u5750\u6807\u4e0b\u7684\u4e0d\u540c\uff0cb\u5904\u7684\u5c40\u57df\u4fe1\u606f\u548cc\u5904\u7684\u5c40\u57df\u4fe1\u606f\u878d\u5408\u65f6\u4f1a\u5b58\u5728\u95ee\u9898\u3002\u7c7b\u6bd4\u7406\u89e3\u53ef\u4ee5\u5c06cluster b\u548ccluster c\u770b\u4f5c\u559c\u7ed3\u8fde\u7406\u7684\u4e00\u5bf9\u592b\u59bb\u7684\u539f\u751f\u5bb6\u5ead\uff0c\u7531\u4e8e\u4e24\u4e2a\u539f\u751f\u5bb6\u5ead\u6240\u5728\u7684\u751f\u6d3b\u73af\u5883\u4e0d\u540c\uff0c\u76f4\u63a5\u4ea4\u6d41\u8d77\u6765\u96be\u514d\u5b58\u5728\u77db\u76fe\u3002\u8fd9\u65f6\u5019\u600e\u4e48\u529e\u5462\uff1f\u5f53\u7136\u662f\u627e\u592b\u59bb\u7684\u5bb6\u4eba\u6216\u670b\u53cb\u505a\u4e2d\u95f4\u8c03\u7406\u4eba\u5440\uff01\u540c\u7406\uff0c\u53ef\u4ee5\u901a\u8fc7\u8282\u70b9b\u548cc\u4e8c\u8005\u5171\u540c\u7684\u90bb\u5c45\u4eec a\uff08\u53ef\u80fd\u4e0d\u6b62\u4e00\u4e2a\uff09\uff0c\u4e24\u4e2a\u5c40\u57df\u5750\u6807\u7cfb\u7684\u4fe1\u606f\u4ea4\u4e92\u4e0e\u878d\u5408\u4fbf\u4f1a\u66f4\u52a0\u7684\u6709\u6548\u3002\u4e0b\u9762\u7ed9\u51fa\u76f8\u5173\u6982\u5ff5\u7684\u5177\u4f53\u5b9a\u4e49\uff1a<\/p>\n\n\n\n

\u4ee4\\(S_{i}\\)\u8868\u793a\u4e0e\u4e0a\u56fe\u8282\u70b9\\(\\mathrm{b}\\)\u5173\u8054\u7684\u5c40\u57df\\(\\text{clusterb}\\)\uff0c\u8fd9\u4e2a\u5c40\u57df\u5305\u542b\u8282\u70b9\\(\\mathrm{b}\\)\u7684\u6240\u6709\u4e00\u8df3\u90bb\u5c45\uff081-hop neighbors\uff09\u3002\u7c7b\u4f3c\u7684\uff0c\u5b9a\u4e49\u4ee4\\(S_{j}\\)\u8868\u793a\u4e0e\u4e0a\u56fe\u8282\u70b9\\(\\mathrm{c}\\)\u5173\u8054\u7684\u5c40\u57df\\(\\text{clusterc}\\)\u3002\u8fd9\u4e2a\u5c40\u57df\u5305\u542b\u8282\u70b9\\(\\mathrm{c}\\)\u7684\u6240\u6709\u4e00\u8df3\u90bb\u5c45\uff081-hop neighbors\uff09\u3002\u6b64\u65f6\u53ef\u4ee5\u5b9a\u4e49\\(S_{i-j}\\)\uff0c\u8868\u793a\u8282\u70b9\\(\\mathrm{b}\\)\u548c\u8282\u70b9\\(\\mathrm{c}\\)\u4e4b\u95f4\u7684\u5171\u4eab\u6216\u76f8\u4e92\u76843D\u5b50\u7ed3\u6784\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u662f\u901a\u8fc7\u53d6\u4e24\u4e2a\u5c40\u57df\\(\\text{clusterb}\\)\u548c\\(\\text{clusterc}\\)\u7684\u4ea4\u96c6\u6765\u5b9a\u4e49\u7684\uff0c\u8fd9\u610f\u5473\u7740\\(S_{i-j}\\)\u5305\u62ec\u4e86\u6240\u6709\u540c\u65f6\u662f\u8282\u70b9\\(\\mathrm{b}\\)\u548c\u8282\u70b9\\(\\mathrm{c}\\)\u7684\u4e00\u8df3\u90bb\u5c45\u7684\u8282\u70b9\uff0c\u4ee5\u53ca\u8fde\u63a5\u8fd9\u4e9b\u8282\u70b9\u7684\u8fb9\u3002<\/p>\n\n\n\n

2\u3001LSE\u6a21\u5757\u63d0\u53d6\u5c40\u57df\u4fe1\u606f<\/h2>\n\n\n\n

\u5b9a\u4e49LEFNet\u7684\u8f93\u5165\u6570\u636e\u4e3a\u51e0\u4f55\u56fe\u6570\u636e\uff0c\u5176\u5177\u6709\u7b49\u53d8\u4f4d\u7f6e\u4fe1\u606f\\(X=\\left(x_{1},\\ldots,x_{n}\\right)\\in\\mathbb{R}^{n\\times3}\\)\u3001\u4e0d\u53d8\u8282\u70b9\u7279\u5f81\\(h_i\\in\\mathbb{R}^d\\)\u3001\u4e0d\u53d8\u76f8\u5bf9\u8ddd\u79bb\\(d_{ij}\\in R^{1}\\)\u3001\u7b49\u53d8\u8fb9\u7279\u5f81\\(e_{ij}\\in\\mathbb{R}^c\\)\u3002LEFNet\u6a21\u578b\u4e2d\u4f7f\u7528LSE\u6a21\u5757\u63d0\u53d6\u5c40\u57df\u4fe1\u606f\u7684\u6b65\u9aa4\u5982\u4e0b\uff1a<\/p>\n\n\n\n

\u6b65\u9aa41\uff1a\u4e0eClofNet\u7c7b\u4f3c\uff0c\u5c06\u4f4d\u7f6e\u4fe1\u606f\u4e2d\u5fc3\u5316\uff1a\\(X\\leftarrow X-\\mathrm{CoM}(X)\\)\u3002\u8fd9\u901a\u5e38\u610f\u5473\u7740\u4f1a\u4ece\u6bcf\u4e2a\u4f4d\u7f6e\u5411\u91cf\u4e2d\u51cf\u53bb\u6240\u6709\u4f4d\u7f6e\u5411\u91cf\u7684\u5e73\u5747\u503c\uff0c\u4ee5\u786e\u4fdd\u6a21\u578b\u5bf9\u5e73\u79fb\u4fdd\u6301\u4e0d\u53d8\u3002<\/p>\n\n\n\n

\u6b65\u9aa42\uff1a\u901a\u8fc7ClofNet\u4e2d\u63d0\u51fa\u7684\u5c40\u57df\u6b63\u5219\u5750\u6807\u7cfb\uff0c\u8ba1\u7b97\u56fe\u4e2d\u6bcf\u4e2a\u8282\u70b9\\(\\mathrm{i}\\)\u4e0e\u5176\u5bf9\u5e94\u7684\u6bcf\u4e2a\u90bb\u5c45\u8282\u70b9\\(\\mathrm{j}\\)\u4e4b\u95f4\u5f62\u6210\u7684\u7b49\u53d8\u5c40\u57df\u6b63\u4ea4\u8868\u793a\\(\\mathcal{F}_{ij}\\)\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u8003\u8651\u8282\u70b9\\(\\mathrm{i}\\)\u548c\u5b83\u7684\u4e00\u4e2a\u90bb\u5c45\u8282\u70b9\\(\\mathrm{j}\\)\uff0c\u5b83\u4eec\u7684\u4f4d\u7f6e\u5206\u522b\u662f\\(x_{i}\\)\u548c\\(x_{j}\\)\u3002\u5b9a\u4e49\u4e0e\\(x_{i}\\)\u548c\\(x_{j}\\)\u76f8\u5173\u7684\u6b63\u4ea4\u7b49\u53d8\u6846\u67b6\\(F_{ij}\\)\u5982\u4e0b\uff1a<\/p>\n\n\n

\\(F_{ij}:=\\left(\\frac{x_i-x_j}{\\left\\|x_i-x_j\\right\\|},\\frac{x_i\\times x_j}{\\left\\|x_i\\times x_j\\right\\|},\\frac{\\left(x_i-x_j\\right)\\times\\left(x_i\\times x_j\\right)}{\\left\\|\\left(x_i-x_j\\right)\\times\\left(x_i\\times x_j\\right)\\right\\|}\\right)\\)<\/p>\n\n\n

\u7c7b\u4f3c\u7684\uff0c\u8ba1\u7b97\u56fe\u4e2d\u6bcf\u4e2a\u8282\u70b9\\(\\mathrm{i}\\)\u7684\u7b49\u53d8\u5c40\u57df\u6b63\u4ea4\u8868\u793a\\(\\mathcal{F}_{i}\\)\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u8003\u8651\u5177\u6709\u4e09\u7ef4\u4f4d\u7f6e\\(x_{i}\\)\u7684\u8282\u70b9\\(\\mathrm{i}\\)\uff0c\u5e76\u4ee4\\(\\overline{x}i:=\\frac{1}{N}\\sum<\/em>{x_j\\in N(x_i)}x_j\\)\u4e3a\\(x_{i}\\)\u76841\u8df3\u90bb\u57df\u5185\u6240\u6709\u8282\u70b9\u7684\u8d28\u5fc3\u3002\u5b9a\u4e49\u4e0e\\(x_{i}\\)\u76f8\u5173\u7684\u6b63\u4ea4\u7b49\u53d8\u6846\u67b6\\(\\mathcal{F}_{i}\\)\u5982\u4e0b\uff1a<\/p>\n\n\n

\\(F_i:=\\left(\\frac{x_i-\\overline{x}_i}{\\left\\|x_i-\\overline{x}_i\\right\\|},\\frac{\\overline{x}_i\\times x_i}{\\left\\|\\overline{x}_i\\times x_i\\right\\|},\\frac{\\left(x_i-\\overline{x}_i\\right)\\times\\left(\\overline{x}_i\\times x_i\\right)}{\\left\\|\\left(x_i-\\overline{x}_i\\right)\\times\\left(\\overline{x}_i\\times x_i\\right)\\right\\|}\\right)\\)<\/p>\n\n\n

\u6b65\u9aa43\uff1a\u83b7\u53d6\u8282\u70b9\\(\\mathrm{i}\\)\u76841-hop\u90bb\u57df\u548c\u8282\u70b9 \u76841-hop\u7684\u5171\u4eab3D\u533a\u57df\\(S_{i-j}\\)\uff0c\u5e76\u901a\u8fc7\\(\\mathcal{F}_{ij}\\)\u8fdb\u884c\\(S_{i-j}\\)\u5c40\u90e8\u4fe1\u606f\u7684\u6807\u91cf\u5316\uff1a<\/p>\n\n\n

\\(t_{ij}=\\left\\{\\mathrm{Scalarize}\\left(S_{i-j},F_{ij}\\right)\\right\\}\\)<\/p>\n\n\n

\u6807\u91cf\u5316\u7684\u5177\u4f53\u65b9\u5f0f\u4e0eclofNet\u4e2d\u63d0\u51fa\u7684\u4e00\u6837\uff0c\u5c06\u4ee3\u8868\\(S_{i-j}\\)\u5c40\u90e8\u4fe1\u606f\u7684\u51e0\u4f55\u5411\u91cf\u6295\u5f71\u5230\\(\\mathcal{F}_{ij}\\)\u7684\u57fa\u7ec4\u4e0a\uff0c\u901a\u8fc7\u5185\u79ef\u83b7\u5f97\u76f8\u5e94\u7684\u7cfb\u6570\u5373\u53ef\u5f97\u5230\u7ed3\u679c\\(t_{ij}\\)\uff0c\\(t_{ij}\\)\u662f\u7528\u6807\u91cf\u5f62\u5f0f\u5b58\u50a8\u7684\u51e0\u4f55\u5411\u91cf\u4fe1\u606f\u3002<\/p>\n\n\n\n

\u6b65\u9aa44\uff1a\u5bf9\\(t_{ij}\\)\u8fdb\u884c\u6700\u540e\u7684\u7279\u5f81\u7f16\u7801\u5f97\u5230\u533a\u57df\\(S_{i-j}\\)\u7684\u51e0\u4f55\u7a7a\u95f4\u7279\u5f81\u8868\u793a\uff0c\u5177\u4f53\u6765\u8bf4\uff0c\\(S_{i-j}\\)\u4f1a\u5148\u7ecf\u8fc7\u5f84\u5411\u6a21\u578bRBF\u7684\u5904\u7406\uff0c\u5f97\u5230\u76f8\u5bf9\u8ddd\u79bb\u4fe1\u606f\uff0c\u5c06\u6b64\u4fe1\u606f\u4e0e\u51e0\u4f55\u5411\u91cf\u4fe1\u606f\\(t_{ij}\\)\u70b9\u4e58\u8fdb\u884c\u6807\u91cf\u4fe1\u606f\u548c\u5411\u91cf\u4fe1\u606f\u7684\u4ea4\u4e92\u3002\u5176\u7ed3\u679c\u5c06\u4f7f\u7528\u795e\u7ecf\u7f51\u7edc\u5c42MLP\u8fdb\u884c\u6700\u540e\u7684\u5b66\u4e60\uff0c\u8ba1\u7b97\u51fa\\(S_{i-j}\\)\u6700\u540e\u7684\u51e0\u4f55\u7a7a\u95f4\u7279\u5f81\u8868\u793a\\(A_{ij}\\)\u3002\u4e0a\u8ff0LSE\u6a21\u5757\u63d0\u53d6\u5c40\u57df\u4fe1\u606f\u7684\u8ba1\u7b97\u6d41\u7a0b\u53ef\u7528\u56fe3\u8fdb\u884c\u8868\u793a\u3002<\/p>\n\n\n

\n
\"\"
\u56fe3 LSE\u6a21\u5757\u63d0\u53d6\u5c40\u57df\u4fe1\u606f<\/figcaption><\/figure><\/div>\n\n\n

3\u3001EMP\u6a21\u5757\u8fdb\u884c\u56fe\u7684\u6d88\u606f\u4f20\u9012<\/h2>\n\n\n\n

EMP\u88ab\u5b9a\u4e49\u4e3aEquivariant Massage Passin\uff0c\u5f53\u901a\u8fc7LSE\u6a21\u5757\u5f97\u5230\\(S_{i-j}\\)\u7684\u51e0\u4f55\u7a7a\u95f4\u7279\u5f81\u8868\u793a\\(A_{ij}\\)\u4e4b\u540e\uff0c\u5c31\u53ef\u4ee5\u8fdb\u884c\u8282\u70b9\\(\\mathrm{i}\\)\u548c\u5176\u90bb\u5c45\\(\\mathrm{j}\\)\u4e4b\u95f4\u7684\u7b49\u53d8\u6027\u6d88\u606f\u4f20\u9012\u4e86\uff0c\u5176\u516c\u5f0f\u8868\u793a\u4e3a\uff1a<\/p>\n\n\n

\\(\\boldsymbol{m}_{ij}=\\phi_m^1\\left(h_i,A_{ij}\\odot h_j,d_{ij}\\right)+\\phi_m^2\\left(h_i,A_{ij}\\odot h_j,d_{ij}\\right)\\cdotp\\boldsymbol{e}_{ij}+\\phi_m^3\\left(h_i,A_{ij}\\odot h_j,d_{ij}\\right)\\cdotp\\mathcal{F}_{ij}\\)<\/p>\n\n\n

\u5176\u4e2d\uff1a<\/p>\n\n\n\n

\uff081\uff09\\(m_{ij}\\)\u662f\u4ece\u8282\u70b9\\(\\mathrm{j}\\)\u5230\u8282\u70b9\\(\\mathrm{i}\\)\u7684\u6d88\u606f\u3002<\/p>\n\n\n\n

\uff082\uff09\\(h_{i}\\)\u548c\\(h_{j}\\)\u5206\u522b\u662f\u8282\u70b9\\(\\mathrm{i}\\)\u548c\u8282\u70b9\\(\\mathrm{j}\\)\u7684\u7279\u5f81\u5411\u91cf\u3002<\/p>\n\n\n\n

\uff083\uff09\\(A_{ij}\\)\u662f\u901a\u8fc7LSE\u6a21\u5757\u83b7\u5f97\u7684\uff0c\u8868\u793a\u8282\u70b9\\(\\mathrm{i}\\)\u548c\u8282\u70b9\\(\\mathrm{j}\\)\u4e4b\u95f4\u7684\u5c40\u90e8\u51e0\u4f55\u7a7a\u95f4\u7279\u5f81\u3002<\/p>\n\n\n\n

\uff084\uff09\\(\\odot\\)\u8868\u793a\u54c8\u8fbe\u739b\u79ef\uff08\u5143\u7d20\u7ea7\u7684\u4e58\u6cd5\uff09\uff0c\u5728\u8fd9\u91cc\u7528\u4e8e\u5c06\u7a7a\u95f4\u5173\u7cfb\\(A_{ij}\\)\u76f4\u63a5\u4e0e\u8282\u70b9\\(\\mathrm{j}\\)\u7684\u7279\u5f81\\(h_{j}\\)\u7ed3\u5408\u8d77\u6765\uff0c\u4ee5\u83b7\u5f97\u8282\u70b9\\(\\mathrm{j}\\)\u4e0e\u51e0\u4f55\u7a7a\u95f4\u76f8\u5173\u7684\u7279\u5f81\u3002<\/p>\n\n\n\n

\uff085\uff09\\(d_{ij}\\)\u662f\u8282\u70b9\\(\\mathrm{i}\\)\u548c\\(\\mathrm{j}\\)\u4e4b\u95f4\u7684\u4e0d\u53d8\u8ddd\u79bb\uff0c\u5b83\u63d0\u4f9b\u4e86\u4e24\u4e2a\u8282\u70b9\u4e4b\u95f4\u8ddd\u79bb\u5173\u7cfb\u7684\u9644\u52a0\u4fe1\u606f\u3002<\/p>\n\n\n\n

\uff086\uff09\\(e_{ij}\\)\u662f\u8fde\u63a5\u8282\u70b9\\(\\mathrm{i}\\)\u548c\\(\\mathrm{j}\\)\u7684\u8fb9\u7684\u5411\u91cf\u7279\u5f81\u3002<\/p>\n\n\n\n

\uff087\uff09\\(\\mathcal{F}_{ij}\\)\u662f\u8fb9\\((i,j)\\)\u7684\u7b49\u53d8\u6846\u67b6\u3002<\/p>\n\n\n\n

\uff088\uff09\\(\\phi_m^1,\\phi_m^2,\\phi_m^3\\)\u662f\u53ef\u5b66\u4e60\u7684\u51fd\u6570\uff0c\u5b83\u4eec\u901a\u8fc7\u53c2\u6570\u5316\u7684\u65b9\u5f0f\u5904\u7406\u8f93\u5165\u7684\u7279\u5f81\uff0c\u751f\u6210\u6700\u7ec8\u6d88\u606f\u3002\u8fd9\u4e9b\u51fd\u6570\u662f\u7531\u795e\u7ecf\u7f51\u7edc\u5c42\u5982\u5168\u8fde\u63a5\u5c42\u5b9e\u73b0\u7684\u3002<\/p>\n\n\n\n

\u4e0a\u8ff0\u516c\u5f0f\u7684\u7406\u89e3\u53ef\u4ee5\u5206\u6210\u4e09\u4e2a\u90e8\u5206\u6765\u89e3\u91ca\uff1a<\/p>\n\n\n\n

1\u3001\u7279\u5f81\u7ec4\u5408\uff1a<\/p>\n\n\n\n

\u5c06\u8282\u70b9\\(\\mathrm{i}\\)\u548c\u8282\u70b9\\(\\mathrm{j}\\)\u7684\u7279\u5f81\\(h_{i}\\)\u548c\\(h_{j}\\)\u4e0e\u5c40\u90e8\u7ed3\u6784\u8868\u793a\\(A_{ij}\\)\u8fdb\u884c\u7ec4\u5408\u3002\u7b26\u53f7\\(\\odot\\)\u8868\u793a\u7279\u5f81\u4e4b\u95f4\u7684\u9010\u5143\u7d20\u4e58\u79ef\u64cd\u4f5c\uff0c\u7528\u4e8e\u7ed3\u5408\u8282\u70b9\u7279\u5f81\u548c\u5c40\u90e8\u7ed3\u6784\u4fe1\u606f\uff1a<\/p>\n\n\n

\\(\\phi_m^1(h_i,A_{ij}\\odot h_j,d_{ij})\\)<\/p>\n\n\n

\u5176\u4e2d\\(\\phi_m^1\\)\u662f\u4e00\u4e2a\u795e\u7ecf\u7f51\u7edc\uff0c\u7528\u4e8e\u5904\u7406\u7ed3\u5408\u540e\u7684\u7279\u5f81\u3002\\(d_{ij}\\)\u662f\u8282\u70b9\\(\\mathrm{i}\\)\u548c\u8282\u70b9\\(\\mathrm{j}\\)\u4e4b\u95f4\u7684\u8ddd\u79bb\u4fe1\u606f\uff0c\u4f5c\u4e3a\u989d\u5916\u7684\u8f93\u5165\u7279\u5f81\u3002<\/p>\n\n\n\n

2\u3001\u65b9\u5411\u4fe1\u606f\u5904\u7406\uff1a<\/p>\n\n\n\n

\u4f7f\u7528\u8fb9\u7684\u65b9\u5411\u4fe1\u606f\\(\\boldsymbol{e}_{ij}\\)\u6765\u589e\u5f3a\u7279\u5f81\u8868\u793a\uff0c\u901a\u8fc7\u51fd\u6570\\(\\phi_{m}^{2}\\)\u5bf9\u7ec4\u5408\u7279\u5f81\u548c\u65b9\u5411\u4fe1\u606f\u8fdb\u884c\u5904\u7406\uff1a<\/p>\n\n\n

\\(\\phi_{m}^{2}(h_{i},A_{ij}\\odot h_{j},d_{ij})\\cdot\\boldsymbol{e}_{ij}\\)<\/p>\n\n\n

\u65b9\u5411\u4fe1\u606f\\(\\boldsymbol{e}_{ij}\\)\u4e0e\u7279\u5f81\u7684\u70b9\u79ef\u64cd\u4f5c\u6355\u6349\u4e86\u8282\u70b9\u4e4b\u95f4\u7684\u76f8\u5bf9\u65b9\u5411\u4fe1\u606f\u3002<\/p>\n\n\n\n

3\u3001\u6846\u67b6\u4fe1\u606f\u5904\u7406\uff1a<\/p>\n\n\n\n

\u5904\u7406\u8282\u70b9\\(\\mathrm{i}\\)\u7684\u6846\u67b6\u4fe1\u606f\\(\\mathcal{F}_i\\)\uff0c\u5e76\u7ed3\u5408\u5230\u7279\u5f81\u8868\u793a\u4e2d\uff0c\u901a\u8fc7\u51fd\u6570\\(\\phi_m^3\\)\u5bf9\u7ec4\u5408\u7279\u5f81\u548c\u6846\u67b6\u4fe1\u606f\u8fdb\u884c\u5904\u7406\uff1a<\/p>\n\n\n

\\(\\phi_m^3(h_i,A_{ij}\\odot h_j,d_{ij})\\cdot\\mathcal{F}_i\\)<\/p>\n\n\n

\u8fd9\u4e00\u6b65\u786e\u4fdd\u4e86\u8282\u70b9\u7279\u5f81\u4e2d\u5305\u542b\u6846\u67b6\u8f6c\u79fb\u4fe1\u606f\uff0c\u4f7f\u5f97\u8868\u793a\u66f4\u4e30\u5bcc\u3002<\/p>\n\n\n\n

\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u8fd9\u4e2a\u6d88\u606f\u4f20\u9012\u673a\u5236\u662f\u7b49\u53d8\u7684\uff0c\u56e0\u4e3a\u5b83\u5c06\u7a7a\u95f4\u7ed3\u6784\u4fe1\u606f\\(A_{ij}\\)\u548c\u7b49\u53d8\u6846\u67b6\\(\\mathcal{F}_{ij}\\)\u7ed3\u5408\u5230\u6d88\u606f\u4f20\u9012\u8fc7\u7a0b\u4e2d\u3002\u7b49\u53d8\u6846\u67b6\\(\\mathcal{F}_{ij}\\)\u4fdd\u8bc1\u4e86\u6d88\u606f\u7684\u65b9\u5411\u4e0e\u56fe\u5f62\u7684\u51e0\u4f55\u65b9\u5411\u4e00\u81f4\uff0c\u800c\\(A_{ij}\\)\u4fdd\u6301\u4e86\u8282\u70b9\u95f4\u5173\u7cfb\u7684\u51e0\u4f55\u4e00\u81f4\u6027\u3002<\/p>\n\n\n\n

4\u3001FTE\u6a21\u578b\u8fdb\u884c\u56fe\u7684\u6d88\u606f\u66f4\u65b0<\/h2>\n\n\n\n

\u5728\u4f7f\u7528EMP\u6a21\u5757\u8fdb\u884c\u56fe\u7684\u6d88\u606f\u4f20\u9012\u4e4b\u540e\uff0c\u63a5\u4e0b\u6765\u4f7f\u7528FTE\u6a21\u5757\u8fdb\u884c\u56fe\u6d88\u606f\u7684\u66f4\u65b0\uff0c\u6574\u4e2a\u6d88\u606f\u4ea4\u4e92\u6a21\u5757\u5982\u56fe4\u6240\u793a\u3002<\/p>\n\n\n

\n
\"\"
\u56fe4 FTE\u56fe\u6d88\u606f\u66f4\u65b0<\/figcaption><\/figure><\/div>\n\n\n

\u5728FTE\u6a21\u5757\u4e2d\uff0c\u9996\u5148\u8fdb\u884c\u6d88\u606f\u805a\u5408\uff1a\\(m_i=\\sum_{j\\in N(i)}m_{ij}\\)\uff0c\u8fd9\u4e2a\u64cd\u4f5c\u8868\u660e\u6bcf\u4e2a\u8282\u70b9\\(\\mathrm{i}\\)\u7684\u6d88\u606f\\(m_{i}\\)\u662f\u5176\u6240\u6709\u90bb\u5c45\\(\\mathrm{j}\\)\u7684\u6d88\u606f\\(m_{ij}\\)\u7684\u603b\u548c\uff0c\u63a5\u4e0b\u6765\u7684\u64cd\u4f5c\u5982\u56fe5\u6240\u793a\u3002<\/p>\n\n\n

\n
\"\"
\u56fe5 \u56fe\u6d88\u606f\u66f4\u65b0\u6d41\u7a0b<\/figcaption><\/figure><\/div>\n\n\n

\u901a\u8fc7\u5c40\u57df\u5750\u6807\u7cfb\\(\\mathcal{F}_{i}\\)\u5c06\u8282\u70b9\u7279\u5f81\u4e2d\u7684\u4f4d\u7f6e\u4fe1\u606f\u8fdb\u884c\u6807\u91cf\u5316\uff1a\\(t_i=Scalarize(m_i,\\mathcal{F}_i)\\)\uff0c\u6807\u91cf\u5316\u662f\u5c06\u5411\u91cf\u4fe1\u606f\uff08\u5728\u8fd9\u91cc\u662f\u6d88\u606f\\(m_{i}\\)\uff09\u6295\u5f71\u5230\u4e00\u7ec4\u57fa\\(\\begin{pmatrix}\\mathcal{F}_i\\end{pmatrix}\\)\u4e0a\uff0c\u4ea7\u751f\u4e00\u7ec4\u6807\u91cf\u503c\u3002\u6807\u91cf\u5316\u7684\u7ed3\u679c\u4e0e\u8282\u70b9\\(\\mathrm{i}\\)\u7684\u7279\u5f81\u8fdb\u884c\u62fc\u63a5\uff0c\u9001\u5165MLP\u4e2d\u8fdb\u884c\u5b66\u4e60\uff0c\u6620\u5c04\u5f97\u5230\u66f4\u65b0\u540e\u7684\u8282\u70b9\\(\\mathrm{i}\\)\u7684\u7279\u5f81\\(h_{i}^{l+1}\\)\uff0c\\(h_{i}^{l+1}\\)\u4e0d\u4ec5\u4ec5\u53cd\u6620\u4e86\u8282\u70b9\\(\\mathrm{i}\\)\u81ea\u5df1\u7684\u4fe1\u606f\uff0c\u56e0\u4e3a\u6807\u91cf\u5316\u7684\u53c2\u4e0e\uff0c\u8fd8\u53ef\u4ee5\u5305\u542b\u5176\u90bb\u5c45\u8282\u70b9\u76f8\u5bf9\u4e8e\\(\\mathrm{i}\\)\u7684\u51e0\u4f55\u5173\u7cfb\u3002<\/p>\n\n\n\n

\u63a5\u4e0b\u6765\u66f4\u65b0\u7b49\u53d8\u5411\u91cf\u7279\u5f81\\(\\boldsymbol{h}_{i}^{l+1}\\)\uff0c\\(\\boldsymbol{h}_i^{l+1}=\\mathrm{Tensorize}\\left(h_i^{l+1},\\mathcal{F}_i\\right)\\)\uff0c\u901a\u8fc7\u6807\u91cf\u5316\u7684\u9006\u64cd\u4f5c Tensorize\uff0c\u5c06\u66f4\u65b0\u7684\u8282\u70b9\u7279\u5f81\\(h_{i}\\)\u8f6c\u6362\u56de\u5411\u91cf\u5f62\u5f0f\u3002\u51fd\u6570Tensorize \u5229\u7528\u8282\u70b9\\(\\mathrm{i}\\)\u7684\u5c40\u90e8\u53c2\u7167\u6846\u67b6\\(\\mathcal{F}_{i}\\)\uff0c\u5c06\u6807\u91cf\u7279\u5f81\\(h_{i}\\)\u8f6c\u6362\u56de\u4e00\u4e2a\u5411\u91cf\u6216\u8005\u5f20\u91cf\uff0c\u8fd9\u4e2a\u5411\u91cf\u6216\u8005\u5f20\u91cf\u80fd\u591f\u53cd\u6620\u51fa\u56fe\u6570\u636e\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u7684\u65b9\u5411\u6027\u548c\u4f4d\u7f6e\u3002<\/p>\n\n\n\n

\u901a\u8fc7\u4e0a\u8ff0\u64cd\u4f5c\uff0cLEFTNet\u7684\u6d88\u606f\u4f20\u9012\u6a21\u5757\u6700\u7ec8\u83b7\u5f97\u4e86\u4e00\u4e2a\u8282\u70b9\u7279\u5f81\u8868\u793a\\(h_i^{l+1}\\)\uff0c\u4ee5\u53ca\u4e00\u4e2a\u5411\u91cf\u8868\u793a\\(\\boldsymbol{h}_{i}^{l+1}\\)\u3002\u5b83\u4eec\u65e2\u8574\u542b\u4e86\u8282\u70b9\u5728\u5176\u90bb\u57df\u5185\u7684\u4e30\u5bcc\u4fe1\u606f\uff0c\u53c8\u80fd\u591f\u54cd\u5e94\u5916\u90e8\u7684\u7a7a\u95f4\u53d8\u6362\uff0c\u786e\u4fdd\u7f51\u7edc\u8f93\u51fa\u7684\u4e00\u81f4\u6027\u548c\u9002\u7528\u6027\uff0c\u8fd9\u5bf9\u4e8e\u5efa\u7acb\u9c81\u68d2\u7684\u56fe\u5904\u7406\u6a21\u578b\u81f3\u5173\u91cd\u8981\uff0cLEFTNet\u6574\u4f53\u7684\u6a21\u578b\u7ed3\u6784\u5982\u56fe6\u6240\u793a\u3002<\/p>\n\n\n

\n
\"\"
\u56fe6 LEFTNet\u6574\u4f53\u6a21\u578b\u7ed3\u6784<\/figcaption><\/figure><\/div>\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

1\u3001\u4e09\u79cd\u56fe\u540c\u6784\u95ee\u9898 \u56fe\u540c\u6784\u95ee\u9898\u662f\u56fe\u8bba\u4e2d\u7684\u4e00\u4e2a\u57fa\u672c\u95ee\u9898\uff0c\u5b83\u8981\u6c42\u786e\u5b9a\u4e24\u4e2a\u56fe\u662f\u5426\u5728\u7ed3\u6784\u4e0a\u5b8c\u5168\u76f8\u540c\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u8fd9\u610f\u5473\u7740 […]<\/p>\n","protected":false},"author":1,"featured_media":2518,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[27,23],"tags":[],"class_list":["post-2516","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-27","category-23"],"_links":{"self":[{"href":"http:\/\/gnn.club\/index.php?rest_route=\/wp\/v2\/posts\/2516","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/gnn.club\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/gnn.club\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/gnn.club\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/gnn.club\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2516"}],"version-history":[{"count":2,"href":"http:\/\/gnn.club\/index.php?rest_route=\/wp\/v2\/posts\/2516\/revisions"}],"predecessor-version":[{"id":2524,"href":"http:\/\/gnn.club\/index.php?rest_route=\/wp\/v2\/posts\/2516\/revisions\/2524"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/gnn.club\/index.php?rest_route=\/wp\/v2\/media\/2518"}],"wp:attachment":[{"href":"http:\/\/gnn.club\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2516"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/gnn.club\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2516"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/gnn.club\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2516"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}