{"id":2347,"date":"2024-10-22T11:24:17","date_gmt":"2024-10-22T03:24:17","guid":{"rendered":"https:\/\/www.gnn.club\/?p=2347"},"modified":"2024-10-29T19:38:14","modified_gmt":"2024-10-29T11:38:14","slug":"gemnet","status":"publish","type":"post","link":"http:\/\/www.gnn.club\/?p=2347","title":{"rendered":"Gemnet"},"content":{"rendered":"\n

GemNet\u4e13\u95e8\u8bbe\u8ba1\u7528\u4e8e\u7cbe\u51c6\u9884\u6d4b\u5206\u5b50\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\uff0c\u76f8\u6bd4\u4e4b\u524d\u5e7f\u6cdb\u4f7f\u7528\u7684DimeNet\uff0cGemNet\u901a\u8fc7\u5f15\u5165\u51e0\u4f55\u4e8c\u9762\u89d2\u4fe1\u606f\uff0c\u4f7f\u5176\u80fd\u591f\u66f4\u597d\u7684\u6355\u6349\u539f\u5b50\u4e4b\u95f4\u590d\u6742\u7684\u7a7a\u95f4\u5173\u7cfb\uff0c\u8003\u8651\u5b83\u4eec\u7684\u4f4d\u7f6e\u548c\u7c7b\u578b\u3002<\/p>\n\n\n\n

1.1 \u5f15\u5165\u4e8c\u9762\u89d2\u4fe1\u606f<\/h4>\n\n\n\n

\u5bf9\u6bd4DimeNet\u7684\u6d88\u606f\u4f20\u9012\u673a\u5236\uff0cGemNet \u7684\u601d\u8def\u6bd4\u8f83\u597d\u7406\u89e3\uff0c\u65e2\u7136\u5728DimeNet\u4e2d\uff0c\u5f15\u5165\u65b9\u5411\u6027\u7684\u5939\u89d2\u6d88\u606f\u4f20\u9012\u80fd\u591f\u63d0\u5347\u7cbe\u5ea6\uff0c\u90a3\u4e48\u5f15\u5165\u66f4\u9ad8\u7ef4\u7684\u4e8c\u9762\u89d2\u4fe1\u606f\u7406\u8bba\u4e0a\u5e94\u8be5\u80fd\u66f4\u8fdb\u4e00\u6b65\uff0c\u5982\u56fe1\u6240\u793a\u3002<\/p>\n\n\n

\n
\"\"
\u56fe1 \u4e8c\u9762\u89d2\u4fe1\u606f<\/figcaption><\/figure><\/div>\n\n\n

\uff081\uff09\u89d2\u5ea6\u8868\u793a\uff1a\u56fe1\u4e2d\u5c55\u793a\u4e86\u4e09\u79cd\u89d2\u5ea6\u7c7b\u578b\uff1a\\(\\phi_{\\mathrm{cab}},\\phi_{\\mathrm{abd}}\\)\u548c\u4e8c\u9762\u89d2\\(\\theta_{\\mathrm{cabd}}\\)\u3002\u8fd9\u4e9b\u89d2\u5ea6\u88ab\u7528\u6765\u66f4\u65b0\u539f\u5b50a<\/em>\u548cb<\/em>\u4e4b\u95f4\u7684\u5d4c\u5165\\(m_{\\mathrm{ca}}\\)\u548c\\(m_{\\mathrm{db}}\\)\u3002<\/p>\n\n\n\n

\uff082\uff09\u4e8c\u9762\u89d2\u7684\u53ef\u89c6\u5316\uff1a\u5f53\u5206\u5b50\u88ab\u65cb\u8f6c\u4f7f\u5f97\u539f\u5b50a<\/em>\u548cb<\/em>\u91cd\u5408\u65f6\uff0c\u4e8c\u9762\u89d2\\(\\theta_{\\mathrm{cabd}}\\)\u53d8\u5f97\u53ef\u89c1\u3002\u4e8c\u9762\u89d2\u662f\u7531\u56db\u4e2a\u539f\u5b50a,b,c<\/em>\u548cd<\/em>\u5f62\u6210\u7684\uff0c\u5b83\u5173\u4e4e\u4e24\u4e2a\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\uff0c\u8fd9\u5728\u5316\u5b66\u7ed3\u6784\u4e2d\u975e\u5e38\u91cd\u8981\uff0c\u56e0\u4e3a\u5b83\u5f71\u54cd\u4e86\u5206\u5b50\u7684\u5f62\u72b6\u548c\u529f\u80fd\u3002<\/p>\n\n\n\n

GemNet\u4e2d\uff0c\u4e0a\u8ff0\u89d2\u5ea6\u4fe1\u606f\u7684\u516c\u5f0f\u5316\u8868\u8ff0\u5982\u516c\u5f0f1\u30012\u30013\u6240\u793a\uff0c\u6bcf\u4e2a\u516c\u5f0f\u90fd\u5b9a\u4e49\u4e86\u7279\u5b9a\u7684\u6570\u5b66\u51fd\u6570\uff0c\u7528\u4e8e\u8ba1\u7b97\u539f\u5b50\u95f4\u76f8\u4e92\u4f5c\u7528\u7684\u51e0\u4f55\u7279\u5f81\u3002<\/p>\n\n\n

\\(\\boldsymbol{e}_{{_{{\\mathrm{RBF},n}}}}(x_{{_{{\\mathrm{db}}}}})=\\sqrt{\\frac{2}{c_{{_{{\\mathrm{emb}}}}}}}\\frac{\\sin(\\frac{n\\pi}{c_{{_{{\\mathrm{emb}}}}}}x_{{_{{\\mathrm{db}}}}})}{x_{{_{{\\mathrm{db}}}}}}\\)<\/p>\n

\\(e_{\\mathrm{CBF,ln}}(x_{\\mathrm{ba}},\\varphi_{\\mathrm{abd}})=\\sqrt{\\frac2{c_{\\mathrm{int}}^3j_{l+1}^2(z_{\\mathrm{ln}})}}j_l(\\frac{z_{\\mathrm{ln}}}{c_{\\mathrm{int}}}x_{\\mathrm{ba}})Y_{\\mathrm{l0}}(\\varphi_{\\mathrm{abd}})\\)<\/p>\n

\\(e_{\\mathrm{SBF,lnm}}(x_{\\mathrm{ca}},\\varphi_{\\mathrm{cab}},\\theta_{\\mathrm{cabd}})=\\sqrt{\\frac2{c_{\\mathrm{emb}}^3j_{l+1}^2(z_{\\mathrm{ln}})}}j_l(\\frac{z_{\\mathrm{ln}}}{c_{\\mathrm{emb}}}x_{\\mathrm{ca}})Y_{\\mathrm{lm}}(\\varphi_{\\mathrm{cab}},\\theta_{\\mathrm{cabd}})\\)<\/p>\n\n\n

\u516c\u5f0f1\u79f0\u4e3a\u5f84\u5411\u57fa\u51fd\u6570\uff0c\u5176\u4e2d\\(e_{\\mathrm{RBF},n}(x_{\\mathrm{db}})\\)\u662f\u7b2cn<\/em>\u4e2a\u5f84\u5411\u57fa\u51fd\u6570\uff0c\u7528\u4e8e\u7f16\u7801\u4e24\u4e2a\u539f\u5b50d<\/em>\u548cb<\/em>\u4e4b\u95f4\u7684\u8ddd\u79bb\\(x_{\\mathrm{db}}\\)\u3002\\(c_{\\mathrm{emb}}\\)\u662f\u5f52\u4e00\u5316\u5e38\u6570\uff0c\u7528\u4e8e\u8c03\u6574\u51fd\u6570\u7684\u5468\u671f\u6027\u3002\u516c\u5f0f1\u7684\u4f5c\u7528\u662f\u6355\u6349\u539f\u5b50\u5bf9\u4e4b\u95f4\u7684\u8ddd\u79bb\u4fe1\u606f\uff0c\u5b83\u901a\u8fc7\u6b63\u5f26\u51fd\u6570\u5f62\u5f0f\u7684\u5f84\u5411\u57fa\u51fd\u6570\u6765\u8868\u793a\u539f\u5b50\u95f4\u8ddd\u7684\u4fe1\u606f\uff0c\u5e76\u5c06\u8be5\u4fe1\u606f\u7f16\u7801\u4e3a\u795e\u7ecf\u7f51\u7edc\u53ef\u4ee5\u5904\u7406\u7684\u5f62\u5f0f\uff0c\u8fd9\u79cd\u7f16\u7801\u5bf9\u4e8e\u7406\u89e3\u539f\u5b50\u5bf9\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u662f\u91cd\u8981\u7684\u3002<\/p>\n\n\n\n

\u516c\u5f0f2\u79f0\u4e3a\u590d\u5408\u57fa\u51fd\u6570\uff08Continuous Filter\uff0cCBF\uff09\uff0c\u8fd9\u4e2a\u8868\u8fbe\u5f0f\u7ed3\u5408\u4e86\u7403\u8d1d\u585e\u5c14\u51fd\u6570\\(j_{l}\\)\u548c\u7b2cl<\/em>\u9636\u7684\u7403\u8c10\u51fd\u6570\\(Y_{_{l 0}}\\)\uff0c\u4ee5\u7f16\u7801\u539f\u5b50b<\/em>\u548ca<\/em>\u4e4b\u95f4\u7684\u8ddd\u79bb\\(x_{\\mathrm{ba}}\\)\uff0c\u4ee5\u53ca\u5b83\u4eec\u4e0e\u7b2c\u4e09\u4e2a\u539f\u5b50d<\/em>\u5f62\u6210\u7684\u89d2\u5ea6\\(\\varphi_{\\mathrm{abd}}\\)\u3002\\(c_{\\mathrm{int}}\\)\u662f\u53e6\u4e00\u4e2a\u5f52\u4e00\u5316\u5e38\u6570\uff0c\u800c\\(z_{ln}\\)\u8868\u793al<\/em>\u9636\u7403\u8d1d\u585e\u5c14\u51fd\u6570\u7684\u7b2cn<\/em>\u4e2a\u96f6\u70b9\u3002\u516c\u5f0f2\u7ed3\u5408\u4e86\u7403\u8d1d\u585e\u5c14\u51fd\u6570\u548c\u7403\u8c10\u51fd\u6570\uff0c\u5b83\u7684\u4f5c\u7528\u662f\u6355\u6349\u539f\u5b50\u4e09\u5143\u7ec4\u4e4b\u95f4\u7684\u89d2\u5ea6\u5173\u7cfb\uff0c\u7528\u4e8e\u8868\u5f81\u7531\u4e09\u4e2a\u539f\u5b50\u6784\u6210\u7684\u89d2\u5ea6\u7279\u5f81\uff0c\u8fd9\u4e9b\u4fe1\u606f\u5bf9\u4e8e\u5b9a\u4e49\u5206\u5b50\u7ed3\u6784\u4e2d\u7684\u89d2\u5ea6\u4f9d\u8d56\u6027\u7279\u5f81\u81f3\u5173\u91cd\u8981\u3002<\/p>\n\n\n\n

\u516c\u5f0f3\u79f0\u4e3a\u7ed3\u6784\u57fa\u51fd\u6570\uff08Structural Basis Function\uff0cSBF\uff09\uff0c\u8fd9\u4e2a\u516c\u5f0f\u7528\u4e8e\u7f16\u7801\u539f\u5b50c<\/em>\u548ca<\/em>\u4e4b\u95f4\u7684\u8ddd\u79bb\\(x_{\\mathrm{ca}}\\)\uff0c\u4ee5\u53ca\u5b83\u4eec\u4e0e\u5176\u4ed6\u4e24\u4e2a\u539f\u5b50b<\/em>\u548cd<\/em>\u5f62\u6210\u7684\u89d2\u5ea6\\(\\varphi_{\\mathrm{cab}}\\)\u548c\u4e8c\u9762\u89d2\\(\\theta_{\\mathrm{cabd}}\\)\u3002\u8fd9\u91cc\u4f7f\u7528\u4e86l<\/em>\u9636\u7403\u8d1d\u585e\u5c14\u51fd\u6570\u548cl<\/em>\u9636m<\/em>\u6b21\u7403\u8c10\u51fd\u6570\\(Y_{\\mathrm{lm}}\\)\u3002\u7c7b\u4f3c\u4e8eCBF\uff0cSBF\u7684\u4f5c\u7528\u662f\u901a\u8fc7\u8003\u8651\u66f4\u591a\u7684\u89d2\u5ea6\u4fe1\u606f\uff08\u5982\u4e8c\u9762\u89d2\uff09\u6765\u7f16\u7801\u539f\u5b50\u56db\u5143\u7ec4\u95f4\u7684\u7a7a\u95f4\u5173\u7cfb\uff0c\u8fd9\u79cd\u590d\u5408\u7684\u57fa\u51fd\u6570\u5141\u8bb8\u6a21\u578b\u6355\u6349\u5206\u5b50\u7ed3\u6784\u7684\u66f4\u590d\u6742\u51e0\u4f55\u7279\u5f81\uff0c\u5982\u626d\u66f2\u548c\u7acb\u4f53\u6392\u5217\u3002<\/p>\n\n\n\n

\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u5728\u516c\u5f0f3\u4e2d\uff0c\u7403\u8c10\u51fd\u6570\u7684\u53c2\u6570m<\/em>\uff0c\u5f53m<\/em>=0\u65f6\uff0c\u7403\u8c10\u51fd\u6570\\(Y_{l}^{m}\\left(\\theta,\\varphi\\right)\\)\u53ea\u4f9d\u8d56\u4e8e\u6781\u89d2\\(\\theta \\)\uff0c\u4e0e\u65b9\u4f4d\u89d2\\(\\varphi \\)\u65e0\u5173\u3002\u8fd9\u610f\u5473\u7740\u51fd\u6570\u5728\u65b9\u4f4d\u89d2\\(\\varphi \\)\u65b9\u5411\u4e0a\u662f\u5bf9\u79f0\u7684\uff0c\u5373\u5728\u7ed5z<\/em>\u8f74\u65cb\u8f6c\u65f6\u4fdd\u6301\u4e0d\u53d8\u3002\u800c\u4e14\uff0c\u516c\u5f0f2\u7684\u4e3b\u8981\u4f5c\u7528\u662f\u8861\u91cf\u89d2\u5ea6\u4fe1\u606f\uff0c\u5bf9\u4e8e\u8fd9\u79cd\u7b80\u5355\u7684\u89d2\u5ea6\u4fe1\u606f\u63cf\u8ff0\uff0c\u4e00\u4e2a\u57fa\u672c\u7684\u5bf9\u79f0\u6027\u5206\u91cf\u5c31\u8db3\u591f\u63cf\u8ff0\u4e86\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5728\u516c\u5f0f3\u4e2d\uff0c\u5176\u4e3b\u8981\u76ee\u7684\u662f\u8861\u91cf\u4e8c\u9762\u89d2\u4fe1\u606f\uff0c\u4e8c\u9762\u89d2\u66f4\u4e3a\u590d\u6742\uff0c\u56e0\u4e3a\u5b83\u6d89\u53ca\u4e09\u4e2a\u5e73\u9762\u4e4b\u95f4\u7684\u89d2\u5ea6\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u9700\u8981\u6355\u6349\u66f4\u591a\u7684\u89d2\u5ea6\u4fe1\u606f\uff0c\u8fd9\u9700\u8981\u7403\u8c10\u51fd\u6570\u7684\u591a\u4e2a\u5206\u91cf\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u7403\u8c10\u51fd\u6570\\(Y_{l}^{m}\\left(\\theta,\\varphi\\right)\\)\u4e2d\u7684m<\/em>\u53d6\u503c\u8303\u56f4\u4e3a -l<\/em>\u5230l <\/em>\uff0c\u4ee5\u6355\u6349\u5230\u6240\u6709\u53ef\u80fd\u7684\u5bf9\u79f0\u6027\u548c\u89d2\u5ea6\u53d8\u5316\u3002<\/p>\n\n\n\n

1.2 GemNet\u6d88\u606f\u4f20\u9012\u673a\u5236<\/h4>\n\n\n\n

GemNet\u7684\u6d88\u606f\u4f20\u9012\u673a\u5236\u662f\u901a\u8fc7\u52a0\u6743\u548c\u7ec4\u5408\u524d\u9762\u63d0\u5230\u7684\u57fa\u51fd\u6570\u6765\u6784\u9020\u7684\uff0c\u8fd9\u4e9b\u6d88\u606f\u5c06\u5728\u56fe\u795e\u7ecf\u7f51\u7edc\u4e2d\u6d41\u52a8\u3002\u6d88\u606f\u4f20\u9012\u65b9\u6848\u8d1f\u8d23\u805a\u5408\u548c\u66f4\u65b0\u8282\u70b9\uff08\u539f\u5b50\uff09\u7684\u7279\u5f81\u4fe1\u606f\uff0c\u4ece\u800c\u5141\u8bb8\u6a21\u578b\u5b66\u4e60\u548c\u9884\u6d4b\u590d\u6742\u7684\u5206\u5b50\u6027\u8d28\uff0c\u51e0\u4f55\u6d88\u606f\u4f20\u9012\u7684\u65b9\u6848\u5982\u4e0b\u516c\u5f0f\uff1a<\/p>\n\n\n\n

1.3 \u6a21\u578b\u7ed3\u6784<\/h4>\n\n\n\n

GemNet\u7684\u6a21\u578b\u6574\u4f53\u7ed3\u6784\u5982\u56fe2(a)\u6240\u793a\uff0cDimeNet\u7684\u6a21\u578b\u6574\u4f53\u7ed3\u6784\u5982\u56fe2 (b)\u6240\u793a\u3002<\/p>\n\n\n

\n
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\u56fe2 \u6a21\u578b\u6574\u4f53\u7ed3\u6784\u56fe<\/figcaption><\/figure><\/div>\n\n\n

\u4ece\u56fe2\u53ef\u4ee5\u770b\u51fa\uff0c\u4e24\u4e2a\u6a21\u578b\u6574\u4f53\u7684\u7ed3\u6784\u5f88\u76f8\u4f3c\uff0c\u90fd\u662f\u4e00\u4e2a\u5d4c\u5165\u5c42\uff08Embedding\uff09\u540e\u8ddf\u4e86\u56db\u4e2a\u4fe1\u606f\u4ea4\u4e92\u5c42\uff08Interaction\uff09\u505a\u8fdb\u4e00\u6b65\u7684\u4fe1\u606f\u5904\u7406\uff0c\u7136\u540e\u628a\u6bcf\u4e2a\u4ea4\u4e92\u5c42\u5904\u7406\u540e\u7684\u7ed3\u6784\u6c42\u548c\u4f5c\u4e3a\u6a21\u578b\u6700\u7ec8\u7684\u8f93\u51fa\u7ed3\u679c\u3002<\/p>\n\n\n\n

\u4e0d\u540c\u7684\u662f\uff0cGemNet\u901a\u8fc7\u5f15\u5165\u4e8c\u9762\u89d2\\(\\theta_{\\mathrm{cabd}}\\)\u7684\u4fe1\u606f\uff0c\u8fdb\u4e00\u6b65\u589e\u5f3a\u4e86\u6a21\u578b\u5904\u7406\u590d\u6742\u5206\u5b50\u7ed3\u6784\u7684\u80fd\u529b\u3002\u4e8c\u9762\u89d2\u662f\u5206\u5b50\u7ed3\u6784\u4e2d\u56db\u4e2a\u539f\u5b50\u5f62\u6210\u7684\u4e24\u4e2a\u5e73\u9762\u4e4b\u95f4\u7684\u5939\u89d2\uff0c\u662f\u63cf\u8ff0\u5206\u5b50\u7a7a\u95f4\u5f62\u72b6\u7684\u91cd\u8981\u53c2\u6570\u4e4b\u4e00\u3002\u5728\u5206\u5b50\u52a8\u529b\u5b66\u548c\u7ed3\u6784\u751f\u7269\u5b66\u4e2d\uff0c\u4e8c\u9762\u89d2\u5bf9\u4e8e\u7406\u89e3\u5206\u5b50\u5982\u4f55\u6298\u53e0\u548c\u76f8\u4e92\u4f5c\u7528\u81f3\u5173\u91cd\u8981\u3002GemNet\u7684\u5d4c\u5165\u5c42\uff08Embedding\uff09\u5982\u56fe3(a)\u6240\u793a\uff0cDimeNet\u7684\u5d4c\u5165\u5c42\uff08Embedding\uff09\u5982\u56fe3(b)\u6240\u793a\u3002<\/p>\n\n\n

\n
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\u56fe3 \u5d4c\u5165\u5c42\u6a21\u578b\u7ed3\u6784<\/figcaption><\/figure><\/div>\n\n\n

\u4ece\u56fe3\u53ef\u4ee5\u770b\u51fa\uff0c\u4e24\u4e2a\u6a21\u578b\u63a5\u53d7\u7684\u8f93\u5165\u6570\u636e\u7684\u4e00\u6837\u7684\uff0c\u90fd\u662f\u57fa\u4e8e\u5f84\u5411\u51fd\u6570\u7684\u8ddd\u79bb\u4fe1\u606f\u548c\u4e24\u70b9\u81ea\u8eab\u7684\u7279\u5f81\u5411\u91cf\u3002\u5bf9\u6bd4DimeNet\uff0cGemNet\u5728\u63a5\u4e0b\u6765\u7684\u64cd\u4f5c\u4e2d\uff0c\\(e_{\\mathrm{RBF}}\\)\u6ca1\u6709\u7ecf\u8fc7\u7ebf\u6027\u53d8\u6362\uff0c\u800c\u662f\u76f4\u63a5\u4e0e\u8282\u70b9\u5411\u91cf\\(\\boldsymbol{h}_{c}\\)\u548c\\(\\boldsymbol{h}_{a}\\)\u8fdb\u884c\u62fc\u63a5\uff0c\u8282\u70b9\u5411\u91cf\\(\\boldsymbol{h}_{a}\\)\u9664\u4e86\u53c2\u4e0e\u62fc\u63a5\u64cd\u4f5c\u5916\uff0c\u6b64\u65f6\u4e5f\u4f1a\u590d\u5236\u4e00\u4efd\u76f4\u63a5\u4f5c\u4e3aEmbedding\u5c42\u7684\u8f93\u51fa\u3002\u800c\u62fc\u63a5\u540e\u7684\u4fe1\u606f\u5219\u7ecf\u8fc7\u4e00\u4e2a\u795e\u7ecf\u7f51\u7edc\u505a\u8fdb\u4e00\u6b65\u7684\u5b66\u4e60\u6620\u5c04\uff0c\u5f97\u5230\u7684\u7ed3\u679c\\(m_{\\mathrm{ca}}^{(1)}\\) \u4f5c\u4e3a\u8be5\u5d4c\u5165\u6a21\u5757\u9001\u5165\u540e\u7eed\u4ea4\u4e92\u6a21\u578b\u7684\u4fe1\u606f\u3002\u8fd9\u4e00\u6b65\u4e0eDimeNet\u76f8\u540c\uff0c\u4e0d\u540c\u7684\u662f\uff0c\u8be5\u5d4c\u5165\u6a21\u5757\u7684\u8f93\u51fa\u7ed3\u679ct<\/em><\/strong>\u4e0d\u662fm<\/strong><\/em>\u7ecf\u8fc7Output\u5c42\u5f97\u5230\u7684\uff0c\u800c\u662f\u7ecf\u8fc7Atom emb\u5c42\u8ba1\u7b97\u5f97\u5230\u7684\uff0cOutput\u5c42\u548cAtom emb\u5c42\u5982\u56fe4\u6240\u793a\u3002<\/p>\n\n\n

\n
\"\"
\u56fe4 \u7ed3\u679c\u5bf9\u6bd4\u56fe<\/figcaption><\/figure><\/div>\n\n\n

\u53ef\u4ee5\u770b\u51fa\uff0c\u53ea\u662fGemNet\u7684\u5d4c\u5165\u6a21\u5757\u6bd4DimeNet\u7684\u5d4c\u5165\u6a21\u5757\u591a\u4e86\u4e00\u4e9b\u7ebf\u6027\u5c42\u4e0e\u6b8b\u5dee\u7ed3\u6784\u800c\u5df2\u3002<\/p>\n\n\n\n

GemNet\u7684\u4ea4\u4e92\u6a21\u5757\u5982\u56fe5\u6240\u793a\u3002<\/p>\n\n\n

\n
\"\"
\u56fe5 GemNet\u4ea4\u4e92\u6a21\u5757<\/figcaption><\/figure><\/div>\n\n\n

\u5728\u4ea4\u4e92\u6a21\u578b\u7684\u4e0a\u5c42\uff0c\u53ef\u4ee5\u53d1\u73b0\\(m_{ca}^{(l-1)}h_{a}^{(l-1)}\\)\u7684\u8f93\u5165\uff0c\u5b83\u4eec\u5206\u522b\u4ee3\u8868\u4e0a\u4e00\u5c42\u4f20\u9012\u4e0b\u6765\u7684\u6d88\u606f\u548c\u539f\u5b50\u7684\u7279\u5f81\u5411\u91cf\u3002\u6d88\u606f\u4f20\u9012\uff08MP\uff09\u6a21\u5757\u5229\u7528\u57fa\u4e8e\u4e0d\u540c\u9636\u7684\u7403\u8c10\u57fa\u51fd\u6570\\(e_{\\mathrm{CBF}}\\)\u548c\\(e_{\\mathrm{SBF}}\\)\uff0c\u4ee5\u53ca\u57fa\u4e8e\u5f84\u5411\u57fa\u51fd\u6570\u7684\\(e_{\\mathrm{RBF}}\\)\u6765\u5904\u7406\u8fd9\u4e9b\u6d88\u606f\uff0c\u4ee5\u4fbf\u6355\u83b7\u539f\u5b50\u95f4\u7684\u89d2\u5ea6\u548c\u8ddd\u79bb\u4fe1\u606f\u3002\u7ecf\u8fc7MP\u6a21\u5757\u548c\u6b8b\u5dee\u8fde\u63a5\uff08Residual\uff09\u540e\uff0c\u6d88\u606f\\(m_{ca}\\)\u88ab\u66f4\u65b0\u3002<\/p>\n\n\n\n

MP\u6a21\u5757\uff08Message passing\uff09\u7684\u7ed3\u6784\u5982\u56fe5\u7684\u4e2d\u95f4\u90e8\u5206\uff0c\u8f93\u5165\u4fe1\u606f\\(m_{ca}^{(l-1)}\\)\u4ece\u4e0a\u4e00\u5c42\u4f20\u6765\u7684\u6d88\u606f\uff0c\u662f\u539f\u5b50c<\/em>\u5230\u539f\u5b50a<\/em>\u7684\u6d88\u606f\u5d4c\u5165\u3002\u5b83\u5305\u542b\u4e86\u5148\u524d\u5c42\u4e2d\u4e24\u539f\u5b50\u4e4b\u95f4\u76f8\u4e92\u4f5c\u7528\u7684\u4fe1\u606f\u3002\u8be5\u4fe1\u606f\u5728\u88ab\u5904\u7406\u4e4b\u524d\u4f1a\u590d\u5236\u4e00\u4efd\u7528\u4e8eMP\u6a21\u5757\u5e95\u90e8\u7684\u6b8b\u5dee\u8fde\u63a5\uff0c\u9632\u6b62\u6df1\u5c42\u7f51\u7edc\u4e2d\u51fa\u73b0\u68af\u5ea6\u6d88\u5931\u6216\u68af\u5ea6\u7206\u70b8\u7684\u95ee\u9898\u3002<\/p>\n\n\n\n

T-MP\u548cQ-MP\u8fd9\u4e24\u4e2a\u6a21\u5757\u4ee3\u8868\u4e86\u4e0d\u540c\u7c7b\u578b\u7684\u6d88\u606f\u4f20\u9012\u65b9\u5f0f\u3002Q-MP\u4ee3\u8868\u201c\u56db\u5143\u7ec4\u201d\u6d88\u606f\u4f20\u9012\uff0c\u5904\u7406\u56db\u4e2a\u539f\u5b50\u95f4\uff08\u5373\u4e8c\u9762\u89d2\uff09\u7684\u76f8\u4e92\u4f5c\u7528\uff1b\u800cT-MP\u53ef\u4ee3\u8868\u201c\u4e09\u5143\u7ec4\u201d\u6d88\u606f\u4f20\u9012\uff0c\u5904\u7406\u4e09\u4e2a\u539f\u5b50\u95f4\uff08\u5373\u89d2\u5ea6\uff09\u7684\u76f8\u4e92\u4f5c\u7528\u3002\u8fd9\u4e9b\u6a21\u5757\u5747\u4f7f\u7528\u7403\u8c10\u57fa\u51fd\u6570\u548c\u5f84\u5411\u57fa\u51fd\u6570\u7684\u4fe1\u606f\u6765\u66f4\u65b0\u6d88\u606f\uff0cT-MP\u548cQ-MP\u8fd9\u4e24\u4e2a\u6a21\u5757\u8be6\u89c1\u56fe5\u7684\u53f3\u4fa7\u3002<\/p>\n\n\n\n

\u4ee5Q-MP\u4e3a\u4f8b\uff0c\u8f93\u5165\u7279\u5f81\u5305\u62ec\u539f\u5b50\u5bf9\u7279\u5f81\\(e_{\\mathrm{RBF}}\\)\uff0c\u539f\u5b50\u4e09\u5143\u7ec4\u5939\u89d2\u7279\u5f81\\(e_{\\mathrm{CBF}}\\)\uff0c\u539f\u5b50\u56db\u5143\u7ec4\u4e8c\u9762\u89d2\u7279\u5f81\\(e_{\\mathrm{SBF}}\\)\u4ee5\u53ca\u4e0a\u4e00\u5c42\u7684\u6d88\u606fm<\/em><\/strong>\u3002\u6d88\u606fm<\/em><\/strong>\u9996\u5148\u7ecf\u8fc7\u795e\u7ecf\u7f51\u7edc\u5c42\u7684\u5904\u7406\uff0c\u8fd9\u4e00\u6b65\u5c06\u8f93\u5165\u7279\u5f81m<\/em><\/strong>\u6620\u5c04\u5230\u4e00\u4e2a\u65b0\u7684\u8868\u793a\u7a7a\u95f4\u3002\u7136\u540e\u4e0e\u7ecf\u8fc7\u7ebf\u6027\u53d8\u5316\u540e\u7684\u539f\u5b50\u5bf9\u7279\u5f81\\(e_{\\mathrm{RBF}}\\)\u8fdb\u884c\u9010\u5143\u7d20\u4e58\uff0c\u76ee\u7684\u662f\u8ba9\u6d88\u606fm<\/em><\/strong>\u7684\u66f4\u65b0\u8003\u8651\u539f\u5b50\u5bf9\u7684\u8ddd\u79bb\u7279\u5f81\u3002\u63a5\u4e0b\u6765\uff0c\u518d\u6b21\u7ecf\u8fc7\u795e\u7ecf\u7f51\u7edc\u5c42\u7684\u5904\u7406\uff0c\u4e0e\u7ecf\u8fc7\u7ebf\u6027\u53d8\u5316\u540e\u7684\u4e09\u5143\u7ec4\u5939\u89d2\u7279\u5f81\\(e_{\\mathrm{CBF}}\\)\u8fdb\u884c\u9010\u5143\u7d20\u76f8\u4e58\uff0c\u8fd9\u4e00\u6b65\u7684\u76ee\u7684\u662f\u8ba9\u6d88\u606fm<\/em><\/strong>\u7684\u66f4\u65b0\u8fdb\u4e00\u6b65\u8003\u8651\u65b9\u5411\u5939\u89d2\u7684\u7279\u5f81\u3002\u4e0b\u4e00\u6b65\uff0c\u8ba1\u7b97\u540e\u7684\u7ed3\u679c\u4f1a\u4e0e\u56db\u5143\u7ec4\u4e8c\u9762\u89d2\u7279\u5f81\\(e_{\\mathrm{SBF}}\\)\u4e00\u8d77\u9001\u5165\u53cc\u7ebf\u6027\u5c42\u505a\u8fdb\u4e00\u6b65\u7684\u7279\u5f81\u878d\u5408\uff0c\u901a\u8fc7\u6c42\u548c\u805a\u5408\u6240\u6709\u76f8\u5173d<\/em>\u548cb<\/em>\u7684\u5904\u7406\u540e\u4fe1\u606f\u3002\u805a\u5408\u540e\u7684\u6d88\u606f\u88ab\u590d\u5236\u6210\u4e24\u4efd\u5206\u522b\u9001\u5165\u4e24\u4e2a\u795e\u7ecf\u7f51\u7edc\u5c42\u505a\u5904\u7406\uff0c\u6700\u540e\u76f8\u52a0\u7ed3\u679c\u5f97\u5230\u6700\u7ec8\u7684\u8f93\u51fa\uff0c\u5373\u66f4\u65b0\u540e\u7684\u6d88\u606fm<\/em><\/strong>\u3002<\/p>\n\n\n\n

\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\\(ca\\to ac\\)\u8fd9\u4e00\u6b65\u9aa4\u6307\u7684\u662f\u5c06\u539f\u5b50\u5bf9\u7684\u65b9\u5411\u5d4c\u5165\u4ece\u4e00\u4e2a\u65b9\u5411\u8f6c\u6362\u5230\u76f8\u53cd\u65b9\u5411\u7684\u8fc7\u7a0b\u3002\u8fd9\u662f\u56e0\u4e3a\u6d88\u606f\u4f20\u9012\u901a\u5e38\u662f\u65b9\u5411\u6027\u7684\uff0c\u8fd9\u610f\u5473\u7740\u4ece\u539f\u5b50c<\/em>\u5230\u539f\u5b50a<\/em>\u7684\u4fe1\u606f\u6d41\u662f\u4e0e\u4ece\u539f\u5b50a<\/em>\u5230\u539f\u5b50c<\/em>\u7684\u4fe1\u606f\u6d41\u4e0d\u540c\u7684\u3002\u7136\u800c\uff0c\u7531\u4e8e\u7269\u7406\u76f8\u4e92\u4f5c\u7528\u7684\u5bf9\u79f0\u6027\uff0c\u539f\u5b50c<\/em>\u5bf9a<\/em>\u7684\u5f71\u54cd\u5728\u672c\u8d28\u4e0a\u4e0e\u539f\u5b50a<\/em>\u5bf9c<\/em>\u7684\u5f71\u54cd\u662f\u76f8\u540c\u7684\uff0c\u53ea\u662f\u65b9\u5411\u76f8\u53cd\u3002GemNet\u5728\u66f4\u65b0\u65b9\u5411\u6027\u5d4c\u5165\\(m_{ca}\\)\u65f6\uff0c\u5b83\u4eec\u4e5f\u4f1a\u540c\u65f6\u8003\u8651\u5bf9\u79f0\u7684\u5d4c\u5165 \u3002\u4e3a\u4e86\u907f\u514d\u91cd\u590d\u8ba1\u7b97\uff0cGemNet \u901a\u8fc7\u7b80\u5355\u7684\u91cd\u7d22\u5f15\u64cd\u4f5c\u6765\u533a\u5206\u65b9\u5411\u3002\u8fd9\u6837\u505a\u53ef\u4ee5\u4fdd\u6301\u4e24\u4e2a\u65b9\u5411\u5d4c\u5165\u4e4b\u95f4\u7684\u533a\u522b\uff0c\u540c\u65f6\u907f\u514d\u4e0d\u5fc5\u8981\u7684\u8ba1\u7b97\u8d1f\u62c5\u3002\u56e0\u6b64\uff0c\\(ca\\to ac\\)\u7684\u4f5c\u7528\u662f\u5728\u6a21\u578b\u5185\u90e8\u6267\u884c\u4e00\u4e2a\u8f6c\u6362\uff0c\u786e\u4fdd\u5bf9\u4e8e\u6bcf\u5bf9\u539f\u5b50\uff0c\u4fe1\u606f\u5728\u4e24\u4e2a\u65b9\u5411\u4e0a\u90fd\u5f97\u5230\u66f4\u65b0\uff0c\u800c\u4e0d\u9700\u8981\u8fdb\u884c\u4e24\u6b21\u72ec\u7acb\u7684\u8ba1\u7b97\u3002\u8fd9\u4e0d\u4ec5\u63d0\u9ad8\u4e86\u8ba1\u7b97\u6548\u7387\uff0c\u8fd8\u4fdd\u6301\u4e86\u6a21\u578b\u5bf9\u5206\u5b50\u5185\u76f8\u4e92\u4f5c\u7528\u5bf9\u79f0\u6027\u7684\u8003\u8651\u3002<\/p>\n\n\n\n

\u5728MP\u6a21\u5757\u7684\u6700\u540e\uff0cT-MP\u3001Q-MP\u548c\u7ecf\u8fc7\u795e\u7ecf\u7f51\u7edc\u5c42\u5904\u7406\u7684\\(m_{ca}^{(l-1)}\\)\u5c06\u8fdb\u884c\u76f8\u52a0\uff0c\u9001\u5165\u6b8b\u5dee\u6a21\u578b\u505a\u8fdb\u4e00\u6b65\u7684\u8ba1\u7b97\u5904\u7406\u5f97\u5230MP\u6a21\u578b\u7684\u8ba1\u7b97\u7ed3\u679c\uff0c\u5373\u66f4\u65b0\u4fe1\u606f\u540e\u7684\\(m_{ca}^{(l)}\\)\u3002\u5728MP\u6a21\u5757\u8ba1\u7b97\u7ed3\u675f\u540e\uff0c\u8ba1\u7b97\u7ed3\u679c\u4f1a\u8fdb\u4e00\u6b65\u7684\u9001\u5165\u539f\u5b50\u81ea\u76f8\u4e92\u4f5c\u7528\u6a21\u5757\uff08Atom Self-interaction\uff09\uff0c\u5176\u7ed3\u6784\u5982\u56fe6\u6240\u793a\u3002<\/p>\n\n\n

\n
\"\"
\u56fe6 \u539f\u5b50\u81ea\u76f8\u4e92\u4f5c\u7528\u6a21\u5757\u7ed3\u6784\u56fe<\/figcaption><\/figure><\/div>\n\n\n

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\n
\"\"
\u56fe7 GimNet\u6a21\u578b\u67b6\u6784<\/figcaption><\/figure><\/div>\n\n\n

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