{"id":2292,"date":"2024-10-14T09:26:07","date_gmt":"2024-10-14T01:26:07","guid":{"rendered":"https:\/\/www.gnn.club\/?p=2292"},"modified":"2024-10-14T10:40:46","modified_gmt":"2024-10-14T02:40:46","slug":"schnet","status":"publish","type":"post","link":"http:\/\/gnn.club\/?p=2292","title":{"rendered":"SchNet"},"content":{"rendered":"\n

SchNet\u662f\u4e00\u79cd\u7528\u4e8e\u5206\u5b50\u548c\u6750\u6599\u7684\u91cf\u5b50\u5316\u5b66\u8ba1\u7b97\u7684\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\uff0c\u6700\u521d\u7531\u5fb7\u56fd\u7684\u7814\u7a76\u4eba\u5458\u57282017\u5e74\u5f00\u53d1\u3002\u5b83\u662f\u4e00\u79cd\u57fa\u4e8e\u56fe\u7684\u795e\u7ecf\u7f51\u7edc\uff0c\u4e13\u95e8\u8bbe\u8ba1\u6765\u5904\u7406\u4e09\u7ef4\u5206\u5b50\u7ed3\u6784\u4e2d\u7684\u539f\u5b50\u95f4\u76f8\u4e92\u4f5c\u7528\u3002SchNet\u7684\u72ec\u7279\u4e4b\u5904\u5728\u4e8e\u5b83\u4f7f\u7528\u4e86\u8fde\u7eed\u5377\u79ef\u64cd\u4f5c\uff0c\u53ef\u4ee5\u6355\u6349\u5230\u539f\u5b50\u4e4b\u95f4\u590d\u6742\u7684\u8ddd\u79bb\u4f9d\u8d56\u5173\u7cfb\uff0c\u4ece\u800c\u80fd\u591f\u9884\u6d4b\u5206\u5b50\u7684\u80fd\u91cf\u3001\u529b\u4ee5\u53ca\u5176\u4ed6\u91cd\u8981\u7684\u5316\u5b66\u6027\u8d28\u3002\u8fd9\u79cd\u6a21\u578b\u901a\u8fc7\u5b66\u4e60\u539f\u5b50\u73af\u5883\u7684\u8868\u793a\u6765\u5b9e\u73b0\u9ad8\u7cbe\u5ea6\u7684\u9884\u6d4b\uff0c\u800c\u4e0d\u4f9d\u8d56\u4e8e\u4efb\u4f55\u4eba\u5de5\u5b9a\u4e49\u7684\u7279\u5f81\u6216\u5148\u9a8c\u7684\u7269\u7406\u77e5\u8bc6\u3002SchNet\u5df2\u7ecf\u5728\u591a\u79cd\u5316\u5b66\u548c\u6750\u6599\u79d1\u5b66\u4efb\u52a1\u4e2d\u5c55\u73b0\u51fa\u4e86\u5353\u8d8a\u7684\u6027\u80fd\uff0c\u6210\u4e3a\u4e86\u5206\u5b50\u6a21\u62df\u9886\u57df\u7684\u4e00\u79cd\u91cd\u8981\u5de5\u5177\u3002<\/p>\n\n\n\n

1.1 SchNet\u6a21\u578b\u7ed3\u6784<\/h3>\n\n\n\n

SchNet\u7684\u67b6\u6784\u5982\u56fe1\u6240\u793a\uff0c\u8fd9\u662f\u4e00\u4e2a\u9488\u5bf9\u5206\u5b50\u548c\u6750\u6599\u5efa\u6a21\u800c\u8bbe\u8ba1\u7684\u6df1\u5ea6\u5b66\u4e60\u7f51\u7edc\u3002\u56fe\u4e2d\u5206\u4e3a\u4e09\u4e2a\u4e3b\u8981\u90e8\u5206\uff1a\u67b6\u6784\u603b\u89c8\u3001\u4ea4\u4e92\u6a21\u5757\u548c\u6ee4\u6ce2\u5668\u751f\u6210\u7f51\u7edc\u3002<\/p>\n\n\n\n

\n
\"\"
\u56fe1 SchNet\u7f51\u7edc\u67b6\u6784<\/figcaption><\/figure>\n<\/figure>\n\n\n\n

1.\u67b6\u6784\u603b\u89c8<\/h4>\n\n\n\n

\u5982\u56fe1\u5de6\u56fe\u6240\u793a\uff0c\u8f93\u5165\u8868\u793a\u4e3a\\((Z_1,\\cdots,Z_n)\\)\u548c\\((r_1,\\cdots,r_n)\\)\uff0c\u5176\u4e2d\\(\\mathbf{z}_{i}\\)\u662f\u539f\u5b50\u7c7b\u578b\uff08\u4f8b\u5982\u6c22\u3001\u6c27\u3001\u78b3\u7b49\uff09\u88ab\u7f16\u7801\u6210\u7684\u4e00\u4e2aone-hot\u7f16\u7801\u7684\u5411\u91cf\u3002\u8fd9\u662f\u57fa\u672c\u7684\u5316\u5b66\u4fe1\u606f\uff0c\u5bf9\u4e8e\u8bc6\u522b\u4e0d\u540c\u539f\u5b50\u7684\u6027\u8d28\u975e\u5e38\u91cd\u8981\u3002\\(r_{i}\\)\u662f\u6bcf\u4e2a\u539f\u5b50\u5728\u5206\u5b50\u4e2d\u7684\u4e09\u7ef4\u5750\u6807\uff0c\u8fd9\u4e9b\u4f4d\u7f6e\u4fe1\u606f\u5bf9\u4e8e\u6a21\u578b\u6765\u8bf4\u81f3\u5173\u91cd\u8981\uff0c\u56e0\u4e3a\u5b83\u4eec\u76f4\u63a5\u51b3\u5b9a\u4e86\u539f\u5b50\u4e4b\u95f4\u7684\u8ddd\u79bb\u548c\u76f8\u4e92\u4f5c\u7528\uff0c\u8fd9\u4e9b\u90fd\u662f\u51b3\u5b9a\u5206\u5b50\u6027\u8d28\u7684\u5173\u952e\u56e0\u7d20\u3002<\/p>\n\n\n\n

\u8f93\u5165\u6570\u636e\u9996\u5148\u7ecf\u8fc7\u5d4c\u5165\u5c42\uff08embedding\uff09\uff0c\u8fd9\u662f\u4e00\u4e2a\u5e38\u89c1\u7684\u6df1\u5ea6\u5b66\u4e60\u6280\u672f\uff0c\u4e00\u822c\u4f7f\u7528\u795e\u7ecf\u7f51\u7edc\u5c42\u5c06\u6bcf\u4e2a\u539f\u5b50\u7684one-hot\u8282\u70b9\u7279\u5f81\u5411\u91cf\u8f6c\u6362\u6210\u4e00\u4e2a\u56fa\u5b9a\u5927\u5c0f\u7684\u8fde\u7eed\u7279\u5f81\u5411\u91cf\u3002\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6bcf\u4e2a\u539f\u5b50\u7ecf\u8fc7\u795e\u7ecf\u7f51\u7edc\u5c42\u6620\u5c04\u6210\u7684\u65b0\u7279\u5f81\u5411\u91cf\u7684\u7ef4\u5ea6\u662f64\uff0c\u5373\u6bcf\u4e2a\u539f\u5b50\u88ab\u6620\u5c04\u4e3a\u4e00\u4e2a\u5305\u542b64\u4e2a\u5143\u7d20\u7684\u5411\u91cf\u3002\u8fd9\u4e2a\u5411\u91cf\u7f16\u7801\u4e86\u539f\u5b50\u7684\u67d0\u4e9b\u5c5e\u6027\uff0c\u53ef\u4ee5\u5728\u7f51\u7edc\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u8fdb\u884c\u5b66\u4e60\u548c\u4f18\u5316\u3002\u63a5\u4e0b\u6765\u662f\u591a\u4e2a\u4ea4\u4e92\u5c42\uff0c\u6bcf\u4e2a\u5c42\u90fd\u65e8\u5728\u6355\u6349\u548c\u66f4\u65b0\u539f\u5b50\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u4fe1\u606f\uff0c\u5f97\u5230\u66f4\u6709\u6548\u7684\u539f\u5b50\u7279\u5f81\u5411\u91cf\u8868\u793a\u3002\u4e4b\u540e\uff0c\u4e00\u4e2a\u539f\u5b50\u7ea7\u522b\u7684\u64cd\u4f5c\uff08atom-wise\uff09\u5bf9\u6bcf\u4e2a\u539f\u5b50\u7684\u7279\u5f81\u8fdb\u884c\u8f6c\u6362\u3002\u539f\u5b50\u7ea7\u522b\u64cd\u4f5c\u5c06\u5bf9\u6bcf\u4e2a\u539f\u5b50\u7684\u7279\u5f81\u5411\u91cf\u72ec\u7acb\u5730\u8fdb\u884c\u5b66\u4e60\u53d8\u6362\u3002\u8fd9\u610f\u5473\u7740\u7f51\u7edc\u5728\u8fdb\u884c\u8fd9\u4e9b\u64cd\u4f5c\u65f6\uff0c\u4e0d\u4f1a\u8003\u8651\u539f\u5b50\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u6216\u539f\u5b50\u7684\u90bb\u5c45\uff0c\u800c\u662f\u5c06\u6ce8\u610f\u529b\u96c6\u4e2d\u5728\u5355\u4e2a\u539f\u5b50\u7684\u7279\u5f81\u5411\u91cf\u4e0a\u3002\u5728\u5b9e\u8df5\u4e2d\uff0c\u8fd9\u901a\u5e38\u901a\u8fc7\u5e94\u7528\u4e00\u4e2a\u5168\u8fde\u63a5\u5c42\u6765\u5b9e\u73b0\u3002<\/p>\n\n\n\n

Shifted softplus\u662f\u4e00\u79cd\u6fc0\u6d3b\u51fd\u6570\uff0c\u7528\u4e8e\u5f15\u5165\u975e\u7ebf\u6027\uff0c\u8be5\u6fc0\u6d3b\u51fd\u6570\u5b9a\u4e49\u4e3a\uff1a\\(\\text{Shifted softplus}(x)=\\ln(0.5e^x+0.5)\\)<\/p>\n\n\n\n

\u5176\u51fd\u6570\u56fe\u50cf\u5982\u56fe2\u6240\u793a\u3002<\/p>\n\n\n

\n
\"\"
\u56fe2 shifted softplus\u6fc0\u6d3b\u51fd\u6570\u66f2\u7ebf<\/figcaption><\/figure><\/div>\n\n\n

\u5b83\u662f\u4e00\u4e2a\u5e73\u6ed1\u7684\u975e\u7ebf\u6027\u51fd\u6570\uff0c\u53ef\u4ee5\u5c06\u975e\u7ebf\u6027\u5f15\u5165\u795e\u7ecf\u7f51\u7edc\u3002Shifted Softplus\u7c7b\u4f3c\u4e8e\u6fc0\u6d3b\u51fd\u6570ReLU\uff0c\u4f46\u5bf9\u4e8e\u8d1f\u8f93\u5165\u503c\u5177\u6709\u975e\u96f6\u68af\u5ea6\u3002\u5373\u4f7f\u8f93\u5165\u5177\u6709\u8d1f\u503c\uff0c\u4e5f\u53ef\u4ee5\u5e2e\u52a9\u7f51\u7edc\u7ee7\u7eed\u5b66\u4e60\uff0c\u4e14\u5728x=0\u7684\u4f4d\u7f6e\u8fc7\u5ea6\u7684\u66f4\u52a0\u5e73\u6ed1\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0cShifted Softplus \u5728\u5904\u7406\u51e0\u4f55\u6570\u636e\u65f6\u5f80\u5f80\u6bd4ReLU\u66f4\u53d7\u6b22\u8fce\uff0c\u4e3b\u8981\u539f\u56e0\u6709\u4e0b\u9762\u51e0\u4e2a\uff1a<\/p>\n\n\n\n

\uff081\uff09\u5e73\u6ed1\u7684\u68af\u5ea6\uff1aShifted Softplus \u51fd\u6570\u5728\u6574\u4e2a\u5b9a\u4e49\u57df\u4e2d\u90fd\u6709\u4e00\u4e2a\u5e73\u6ed1\u7684\u5bfc\u6570\u3002\u8fd9\u610f\u5473\u7740\u68af\u5ea6\u4e0d\u4f1a\u7a81\u7136\u53d8\u4e3a\u96f6\uff08\u5982ReLU\u5728\u8d1f\u8f93\u5165\u65f6\u7684\u8868\u73b0\uff09\uff0c\u4ece\u800c\u907f\u514d\u4e86\u795e\u7ecf\u7f51\u7edc\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u7684\u68af\u5ea6\u6d88\u5931\u95ee\u9898\u3002\u5728\u51e0\u4f55\u7ed3\u6784\u7684\u6570\u636e\u4e2d\uff0c\u539f\u5b50\u6216\u8282\u70b9\u7684\u7279\u5f81\u53ef\u80fd\u6d89\u53ca\u590d\u6742\u7684\u76f8\u4e92\u4f5c\u7528\u548c\u7ec6\u5fae\u7684\u53d8\u5316\uff0c\u5e73\u6ed1\u7684\u68af\u5ea6\u5141\u8bb8\u6a21\u578b\u66f4\u7ec6\u81f4\u5730\u8c03\u6574\u5176\u53c2\u6570\u4ee5\u6355\u83b7\u8fd9\u4e9b\u7279\u5f81\u3002<\/p>\n\n\n\n

\uff082\uff09\u975e\u9971\u548c\u6027\uff1aShifted Softplus\u662f\u4e00\u4e2a\u975e\u9971\u548c\u6fc0\u6d3b\u51fd\u6570\uff0c\u8fd9\u610f\u5473\u7740\u5b83\u7684\u8f93\u51fa\u4e0d\u4f1a\u5728\u8f83\u5927\u7684\u6b63\u8f93\u5165\u503c\u65f6\u9971\u548c\u5230\u4e00\u4e2a\u56fa\u5b9a\u503c\uff08\u4e0eSigmoid\u6216Tanh\u4e0d\u540c\uff09\u3002\u975e\u9971\u548c\u6027\u6709\u52a9\u4e8e\u51cf\u8f7b\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u7684\u68af\u5ea6\u9971\u548c\u95ee\u9898\uff0c\u63d0\u9ad8\u7f51\u7edc\u5728\u6df1\u5c42\u7ed3\u6784\u4e2d\u7684\u4fe1\u606f\u6d41\u52a8\u3002<\/p>\n\n\n\n

\uff083\uff09\u5904\u7406\u8d1f\u8f93\u5165\uff1a\u4e0eReLU\u76f8\u6bd4\uff0cShifted Softplus \u5373\u4f7f\u5728\u8d1f\u8f93\u5165\u4e0b\u4e5f\u80fd\u63d0\u4f9b\u5c0f\u7684\u4f46\u975e\u96f6\u7684\u68af\u5ea6\u3002\u8fd9\u79cd\u7279\u6027\u4f7f\u5f97\u7f51\u7edc\u80fd\u591f\u4ece\u6240\u6709\u6570\u636e\u4e2d\u5b66\u4e60\uff0c\u5373\u4f7f\u662f\u90a3\u4e9b\u5728\u51e0\u4f55\u7a7a\u95f4\u4e2d\u53ef\u80fd\u8868\u793a\u4e0d\u540c\u7c7b\u578b\u76f8\u4e92\u4f5c\u7528\uff08\u5982\u6392\u65a5\u529b\uff09\u7684\u8d1f\u8f93\u5165\u503c\u3002<\/p>\n\n\n\n

\uff084\uff09\u8fde\u7eed\u6027\uff1a\u51e0\u4f55\u6df1\u5ea6\u5b66\u4e60\u9886\u57df\u901a\u5e38\u9700\u8981\u5904\u7406\u8fde\u7eed\u6570\u636e\uff0c\u5982\u539f\u5b50\u4f4d\u7f6e\u6216\u7ed3\u6784\u52a8\u529b\u5b66\u3002Shifted Softplus \u7684\u5e73\u6ed1\u6027\u548c\u8fde\u7eed\u6027\u5bf9\u4e8e\u8fd9\u4e9b\u5e94\u7528\u6765\u8bf4\u662f\u6709\u5229\u7684\uff0c\u56e0\u4e3a\u5b83\u5141\u8bb8\u6a21\u578b\u751f\u6210\u8fde\u7eed\u7684\u8f93\u51fa\u548c\u68af\u5ea6\uff0c\u8fd9\u5bf9\u4e8e\u5b66\u4e60\u6570\u636e\u4e2d\u7684\u590d\u6742\u6a21\u5f0f\u81f3\u5173\u91cd\u8981\u3002<\/p>\n\n\n\n

\u00a0\u5728\u6a21\u578b\u67b6\u6784\u603b\u89c8\u7684\u6700\u540e\uff0c\u4f7f\u7528\u795e\u7ecf\u7f51\u7edc\u5c42\uff08atom-wise level\uff09\u5c06\u7279\u5f81\u8fdb\u884c\u7f29\u51cf\uff0c\u7136\u540e\u901a\u8fc7\u6c42\u548c\u6c60\u5316\uff08sum pooling\uff09\u8ba1\u7b97\u51fa\u4e00\u4e2a\u6807\u91cf\uff0c\u6765\u4ee3\u8868\u6574\u4e2a\u5206\u5b50\u7684\u80fd\u91cf\u4f30\u8ba1\\(\\hat{E}\\)\u3002<\/p>\n\n\n\n

2.\u4ea4\u4e92\u6a21\u5757<\/h4>\n\n\n\n

\u4ea4\u4e92\u6a21\u5757\u5982\u56fe1\u4e2d\u95f4\u90e8\u5206\u6240\u793a\uff0c\u5176\u76ee\u7684\u662f\u66f4\u65b0\u539f\u5b50\u7684\u7279\u5f81\uff0c\u5176\u7ec4\u6210\u7ed3\u6784\u901a\u5e38\u4f7f\u7528\u57fa\u4e8e\u8fde\u7eed\u6ee4\u6ce2\u5377\u79ef\u7684\u7f51\u7edc\uff0c\u8fd9\u5141\u8bb8\u6a21\u578b\u5b66\u4e60\u539f\u5b50\u4e4b\u95f4\u5728\u8fde\u7eed\u7a7a\u95f4\u4e2d\u7684\u590d\u6742\u76f8\u4e92\u4f5c\u7528\u3002\u4ea4\u4e92\u6a21\u5757\u7684\u8f93\u5165\u662f\u6bcf\u4e2a\u539f\u5b50\u7684\u7279\u5f81\u8868\u793a\uff0c\u5177\u4f53\u6765\u8bf4\u662f\u901a\u8fc7\u5d4c\u5165\u5c42\u5f97\u5230\u521d\u59cb\u7684\u7279\u5f81\u5411\u91cf\uff0c\u4e5f\u53ef\u4ee5\u662f\u81ea\u5b9a\u4e49\u7684\u539f\u5b50\u7279\u5f81\u8868\u793a\uff0c\u4f8b\u5982\u5176\u7c7b\u578b\u3001\u7535\u8377\u3001\u7535\u5b50\u6392\u5e03\u7b49\u7f16\u7801\u3002\u4ea4\u4e92\u6a21\u5757\u7684\u6838\u5fc3\u5904\u7406\u64cd\u4f5c\u662f\u8fde\u7eed\u6ee4\u6ce2\u5377\u79ef\uff08cfconv\uff09\uff0c\u5176\u5c06\u6839\u636e\u539f\u5b50\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\u52a8\u6001\u751f\u6210\u5377\u79ef\u6838\u7684\u5927\u5c0f\u548c\u6743\u91cd\uff0c\u8fd9\u6837\u7684\u8bbe\u8ba1\u975e\u5e38\u9002\u5408\u5904\u7406\u5206\u5b50\u52a8\u529b\u5b66\u548c\u5316\u5b66\u7ed3\u6784\u6570\u636e\u3002<\/p>\n\n\n\n

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3.\u8fde\u7eed\u6ee4\u6ce2\u5377\u79ef\u7f51\u7edc<\/h4>\n\n\n\n

\u5728\u6df1\u5ea6\u5b66\u4e60\u9886\u57df\uff0c\u4f20\u7edf\u7684\u5377\u79ef\u5c42\u662f\u4e3a\u5904\u7406\u89c4\u5219\u5316\u7684\u6570\u636e\u800c\u8bbe\u8ba1\u7684\u3002\u8fd9\u4e9b\u6570\u636e\u7c7b\u578b\u901a\u5e38\u5305\u62ec\u56fe\u50cf\u50cf\u7d20\u3001\u89c6\u9891\u5e27\u6216\u6570\u5b57\u97f3\u9891\u6570\u636e\uff0c\u5b83\u4eec\u5728\u672c\u8d28\u4e0a\u662f\u7ed3\u6784\u5316\u7684\uff0c\u56e0\u4e3a\u5b83\u4eec\u7684\u6570\u636e\u70b9\u88ab\u6574\u9f50\u5730\u6392\u5217\u5728\u4e00\u4e2a\u56fa\u5b9a\u7684\u7f51\u683c\u4e0a\u3002\u4f8b\u5982\uff0c\u5728\u56fe\u50cf\u5904\u7406\u4e2d\uff0c\u6bcf\u4e2a\u50cf\u7d20\u90fd\u6709\u56fa\u5b9a\u7684\u4f4d\u7f6e\uff0c\u5377\u79ef\u6838\u53ef\u4ee5\u5728\u8fd9\u4e9b\u4f4d\u7f6e\u4e0a\u6ed1\u52a8\uff0c\u4ee5\u68c0\u6d4b\u8fb9\u7f18\u3001\u7eb9\u7406\u7b49\u7279\u5f81\u3002\u5728\u5904\u7406\u50cf\u89c6\u9891\u5e27\u8fd9\u6837\u7684\u8fde\u7eed\u6570\u636e\u6d41\u65f6\uff0c\u5377\u79ef\u5c42\u53ef\u4ee5\u6355\u83b7\u65f6\u95f4\u4e0a\u7684\u53d8\u5316\u5e76\u5b66\u4e60\u52a8\u6001\u6a21\u5f0f\u3002<\/p>\n\n\n\n

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\n
\"\"
\u56fe3 \u539f\u5b50\u5206\u5e03<\/figcaption><\/figure><\/div>\n\n\n

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\u5728\u4e8c\u7ef4\u7a7a\u95f4\u4e2d\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u56fe\u50cfI<\/em>\u548c\u4e00\u4e2a3\u00d73\u7684\u5377\u79ef\u6838K<\/em>\uff0c\u5728\u4f4d\u7f6e(x,y)<\/em>\u5904\u7684\u79bb\u6563\u5377\u79efC<\/em>\u53ef\u4ee5\u5b9a\u4e49\u4e3a\uff1a<\/p>\n\n\n

\\(C(x,y)=\\sum_{i=-1}^1\\sum_{j=-1}^1I(x+i,y+j)\\cdot K(i,j)\\)<\/p>\n\n\n

\u5176\u4e2d\uff0c\u6bcf\u4e2aI(x+i,y+j)<\/em>\u662f\u56fe\u50cf\u4e0a\u7684\u4e00\u4e2a\u50cf\u7d20\uff0cK(i,j)<\/em>\u662f\u5377\u79ef\u6838\u4e0a\u5bf9\u5e94\u7684\u6743\u91cd\u3002\u5377\u79ef\u6838\u8986\u76d6\u7684\u50cf\u7d20\u662f\u5c40\u90e8\u90bb\u57df\uff0c\u800c\u5377\u79ef\u64cd\u4f5c\u672c\u8eab\u662f\u4e00\u4e2a\u5c40\u90e8\u7684\u7ebf\u6027\u64cd\u4f5c\uff0c\u56e0\u4e3a\u5b83\u4ec5\u8003\u8651\u56fe\u50cf\u4e2d(x,y)<\/em>\u70b9\u5468\u56f4\u7684\u4e00\u4e2a\u5c0f\u533a\u57df\uff08\u5373\u5c40\u90e8\u90bb\u57df\uff09\u3002<\/p>\n\n\n\n

\u8fde\u7eed\u6ee4\u6ce2\u5377\u79ef\u662f\u4e00\u79cd\u66f4\u4e3a\u6cdb\u5316\u7684\u64cd\u4f5c\uff0c\u5b83\u80fd\u591f\u5904\u7406\u975e\u89c4\u5219\u5206\u5e03\u7684\u6570\u636e\u70b9\uff0c\u5176\u64cd\u4f5c\u53ef\u4ee5\u7528\u4ee5\u4e0b\u516c\u5f0f\u8868\u793a\uff1a<\/p>\n\n\n

\\(x_i'=\\sum_{j\\in N(i)}x_j\\odot h_\\Theta(\\exp(-\\gamma(e_{j,i}-\\mu)))\\)<\/p>\n\n\n

\u4e0a\u5f0f\u7684\u5404\u4e2a\u7b26\u53f7\u548c\u64cd\u4f5c\u89e3\u91ca\u5982\u4e0b\uff1a<\/p>\n\n\n\n

\uff081\uff09\\(x_i^{\\prime}\\)\uff1a\u8868\u793a\u66f4\u65b0\u540e\u7684\u7279\u5f81\u5411\u91cf\uff0c\u662f\u8282\u70b9i<\/em>\u5728\u5e94\u7528\u5377\u79ef\u64cd\u4f5c\u540e\u7684\u7279\u5f81\u3002<\/p>\n\n\n\n

\uff082\uff09\\(\\sum_{j\\in N(i)}\\)\uff1a\u8868\u793a\u5bf9\u8282\u70b9i<\/em>\u7684\u90bb\u5c45\u8282\u70b9j<\/em>\u8fdb\u884c\u6c42\u548c\u64cd\u4f5c\uff0cN(i)<\/em>\u8868\u793a\u8282\u70b9i<\/em>\u7684\u90bb\u5c45\u8282\u70b9\u96c6\u5408\u3002<\/p>\n\n\n\n

\uff083\uff09\\(x_{j}\\)\uff1a\u8868\u793a\u90bb\u5c45\u8282\u70b9j<\/em>\u7684\u7279\u5f81\u5411\u91cf\u3002<\/p>\n\n\n\n

\uff084\uff09\\(\\odot\\)\uff1a\u8868\u793aHadamard\u4e58\u79ef\uff08\u5143\u7d20\u4e58\u79ef\uff09\uff0c\u5373\u5bf9\u4e24\u4e2a\u5411\u91cf\u5bf9\u5e94\u5143\u7d20\u76f8\u4e58\u3002<\/p>\n\n\n\n

\uff085\uff09\\(h_{\\Theta}\\)\uff1a\u8868\u793a\u8fde\u7eed\u5377\u79ef\u6838\u751f\u6210\u51fd\u6570\uff0c\u5728\u5177\u4f53\u5b9e\u73b0\u65f6\uff0c\u53ef\u4ee5\u9009\u62e9\u4e00\u4e9b\u56fa\u5b9a\u7684\u6570\u5b66\u51fd\u6570\uff0c\u4e5f\u53ef\u4ee5\u9009\u62e9\u4e00\u4e9b\u5e26\u53ef\u5b66\u4e60\u53c2\u6570\u53ef\u5b66\u4e60\u7684\u6a21\u578b\u3002<\/p>\n\n\n\n

\uff086\uff09\\(\\exp(-\\gamma(e_{j,i}-\\mu))\\)\uff1a\u8868\u793a\u4e00\u4e2a\u9ad8\u65af\u5f84\u5411\u57fa\u51fd\u6570\uff0c\u5176\u4e2d\\(\\text{r}\\)\u662f\u4e00\u4e2a\u8d85\u53c2\u6570\uff0c\u63a7\u5236\u9ad8\u65af\u51fd\u6570\u7684\u5bbd\u5ea6\uff1b\\(e_{j,i}\\)\u8868\u793a\u539f\u5b50i<\/em>\u548c\u539f\u5b50j<\/em>\u4e4b\u95f4\u7684\u8ddd\u79bb\uff1b\\(\\mu \\)\u662f\u4e00\u4e2a\u5747\u503c\uff0c\u8868\u793a\u9ad8\u65af\u57fa\u51fd\u6570\u7684\u4e2d\u5fc3\u4f4d\u7f6e\u3002<\/p>\n\n\n\n

\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u5728\u8ba1\u7b97\u76ee\u6807\u8282\u70b9\u4e0e\u5176\u90bb\u5c45\u76f8\u5bf9\u8ddd\u79bb\\((e_{j,i}-\\mu)\\)\u7684\u8fd9\u4e2a\u64cd\u4f5c\u4e2d\uff0c\u8fd8\u53ef\u4ee5\u901a\u8fc7\u589e\u52a0\u4e00\u4e2a\u622a\u65ad\u53d8\u91cfC\u6765\u9650\u5236\u8fde\u7eed\u5377\u79ef\u6838\u53ea\u8ba1\u7b97\u76ee\u6807\u8282\u70b9\u4e0e\u5b83\u4e00\u5b9a\u534a\u5f84\u5185\u7684\u90bb\u5c45\u4e4b\u95f4\u7684\u8ddd\u79bb\uff0c\u800c\u4e0d\u662f\u5168\u90e8\u90bb\u5c45\u7684\u8ddd\u79bb\uff0c\u5982\u56fe4\u6240\u793a\u3002<\/p>\n\n\n

\n
\"\"
\u56fe4 \u8ddd\u79bb\u8ba1\u7b97<\/figcaption><\/figure><\/div>\n\n\n

\u5728\u56fe4\u4e2d\uff0c\u76ee\u6807\u8282\u70b9\u4e3a\\(x_{i}\\)\uff0c\u5176\u4ed6\u8282\u70b9\u5168\u90e8\u4e3a\u76ee\u6807\u8282\u70b9\\(x_{i}\\)\u7684\u90bb\u5c45\u8282\u70b9\uff0c\u4f46\u662f\u7531\u4e8e\u622a\u65ad\u8ddd\u79bb\u7684\u9650\u5236\uff0c\u6709\u4e24\u4e2a\u622a\u65ad\u8ddd\u79bb\u5916\u7684\u8282\u70b9\u5e76\u6ca1\u6709\u53c2\u52a0\u76f8\u5bf9\u8ddd\u79bb\u7684\u8ba1\u7b97\u3002<\/p>\n\n\n\n

\u6700\u540e\uff0c\u9488\u5bf9\u8fde\u7eed\u6ee4\u6ce2\u5377\u79ef\u7684\u5173\u952e\uff1a\u8fde\u7eed\u5377\u79ef\u6838\u751f\u6210\u51fd\u6570\u8fdb\u884c\u5c55\u5f00\u63a2\u8ba8\u3002\u5728\u5177\u4f53\u5b9e\u73b0\u65f6\uff0c\u53ef\u4ee5\u9009\u62e9\u4e00\u4e9b\u5e38\u89c1\u7684\u6570\u5b66\u51fd\u6570\u6216\u7ed3\u6784\uff0c\u4f8b\u5982\uff1a<\/p>\n\n\n\n

\uff081\uff09\u4f59\u5f26\u51fd\u6570\uff1a<\/p>\n\n\n

\\(C=0.5\\times(\\cos(\\textbf{edge_weight}\\times\\pi\/\\text{cutoff })+1.0)\\)<\/p>\n\n\n

\u5176\u4e2d\uff0cedge_weight<\/strong>\u662f\u8fb9\u7684\u7279\u5f81\u5411\u91cf\uff0c\u4e00\u822c\u662f\u76ee\u6807\u8282\u70b9\u4e0e\u5176\u90bb\u5c45\u7684\u8ddd\u79bb\u4fe1\u606f\u7ecf\u8fc7\u9ad8\u65af\u57fa\u51fd\u6570\u6620\u5c04\u4ee5\u540e\u5f97\u5230\u7684\u7279\u5f81\u5411\u91cf\uff0ccutoff\u662f\u622a\u65ad\u53d8\u91cf\u3002\u4e3a\u4e86\u65b9\u4fbf\u7406\u89e3\uff0c\u4ee4edge_weight<\/strong>\u7684\u503c\u57df\u662f[0,5]\uff0c\u622a\u65ad\u53d8\u91cf\u5206\u522b\u4e3a1\u30013\u30015\u3002\u5bf9\u4f59\u5f26\u7ed3\u679cC<\/strong><\/em>\u7684\u53ef\u89c6\u5316\u5982\u56fe5\u6240\u793a\u3002<\/p>\n\n\n

\n
\"\"
\u56fe5 \u4f59\u5f26\u51fd\u6570\u4f5c\u4e3a\u8fde\u7eed\u5377\u79ef\u6838\u751f\u6210\u51fd\u6570<\/figcaption><\/figure><\/div>\n\n\n

\u53ef\u4ee5\u53d1\u73b0\uff0c\u5728\u622a\u65ad\u53d8\u91cf\u7684\u8303\u56f4\u5185\uff0cC<\/strong><\/em>\u7684\u53d8\u5316\u503c\u57df\u59cb\u7ec8\u4e3a[0,1]\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u5f53\u76ee\u6807\u8282\u70b9\u7684\u90bb\u5c45\u79bb\u76ee\u6807\u8282\u70b9\u65e0\u9650\u8fd1\u65f6\uff0cC<\/strong><\/em>\u63a5\u8fd11\uff1b\u5728\u76ee\u6807\u8282\u70b9\u7684\u90bb\u5c45\u79bb\u76ee\u6807\u8282\u70b9\u8f83\u8fdc\uff0c\u63a5\u8fd1\u622a\u65ad\u53d8\u91cf\u9650\u5236\u7684\u8fb9\u754c\u65f6\uff0cC<\/strong><\/em>\u63a5\u8fd10\u3002\u5b9e\u9645\u4e0a\uff0c\u8ba1\u7b97\u7ed3\u679cC<\/strong><\/em>\u53ef\u4ee5\u770b\u4f5c\u4e00\u79cd\u6743\u91cd\uff0c\u901a\u8fc7\u4e0e\u90bb\u5c45\u7279\u5f81\u76f8\u4e58\u7684\u65b9\u5f0f\u6839\u636e\u76f8\u5bf9\u8ddd\u79bb\u6765\u63a7\u5236\u90bb\u5c45\u8282\u70b9\u5bf9\u4e8e\u5f53\u524d\u76ee\u6807\u8282\u70b9\u7684\u5f71\u54cd\u3002<\/p>\n\n\n\n

\uff082\uff09\u591a\u9879\u5f0f\u6216\u5f84\u5411\u57fa\u51fd\u6570\uff08RBF\uff09\uff1a<\/p>\n\n\n

\\(W(r_i-r_j)=\\sum_k\\alpha_k\\phi_k(\\parallel r_i-r_j\\parallel)\\)<\/p>\n\n\n

\u5176\u4e2d\uff0c\\(\\phi_{k}\\)\u53ef\u4ee5\u662f\u9ad8\u65af\u6838\u3001\u591a\u9879\u5f0f\u6838\u6216\u5176\u4ed6\u4efb\u4f55\u5408\u9002\u7684\u5f84\u5411\u57fa\u51fd\u6570\uff0c\\(\\alpha_{k}\\)\u662f\u9700\u8981\u5b66\u4e60\u7684\u53c2\u6570\u3002<\/p>\n\n\n\n

\uff083\uff09\u795e\u7ecf\u7f51\u7edc\uff1a<\/p>\n\n\n\n

\u7531\u4e8eW<\/em>\u662f\u4ece\\(R^{D}\\)\u5230\\(R^{F}\\)\u7684\u6620\u5c04\uff0c\u53ef\u4ee5\u4f7f\u7528\u4e00\u4e2a\u5c0f\u578b\u7684\u524d\u9988\u795e\u7ecf\u7f51\u7edc\u6765\u5b9e\u73b0\uff1a<\/p>\n\n\n

\\(W(r_i-r_j)=\\mathrm{NN}(\\parallel r_i-r_j\\parallel)\\)<\/p>\n\n\n

\u5176\u4e2dNN \u8868\u793a\u795e\u7ecf\u7f51\u7edc\uff0c\u5b83\u63a5\u53d7\u4f4d\u7f6e\u5dee\u7684\u67d0\u79cd\u8868\u793a\uff08\u4f8b\u5982\uff0c\u5411\u91cf\u7684\u6a21\u957f\u6216\u8005\u7ecf\u8fc7\u67d0\u79cd\u5904\u7406\u7684\u5411\u91cf\uff09\u4f5c\u4e3a\u8f93\u5165\uff0c\u5e76\u8f93\u51fa\u5377\u79ef\u6838\u7684\u6743\u91cd\u3002<\/p>\n\n\n\n

\uff084\uff09\u6ce8\u610f\u529b\u673a\u5236\uff1a<\/p>\n\n\n\n

\u7c7b\u4f3c\u4e8eTransformer\u6a21\u578b\u4e2d\u7684\u6ce8\u610f\u529b\u673a\u5236\uff0cW<\/em>\u53ef\u4ee5\u8bbe\u8ba1\u4e3a\u8003\u8651\u8f93\u5165\u7279\u5f81\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a<\/p>\n\n\n

\\(W(r_i,r_j,x_i,x_j)=\\mathrm{softmax}\\Bigg(\\frac{Q(r_i,x_i)K(r_j,x_j)^T}{\\sqrt{d_k}}\\Bigg)V(r_j,x_j)\\)<\/p>\n\n\n

\u5176\u4e2dQ,K,V<\/em>\u662f\u67e5\u8be2\uff08Query\uff09\u3001\u952e\uff08Key\uff09\u3001\u503c\uff08Value\uff09\u7684\u51fd\u6570\uff0c\u901a\u5e38\u662f\u7531\u4f4d\u7f6e\u548c\u7279\u5f81\u7684\u8054\u5408\u8868\u793a\u7ecf\u8fc7\u7ebf\u6027\u53d8\u6362\u5f97\u5230\u7684\uff0c\\(d_{k}\\)\u662f\u7f29\u653e\u56e0\u5b50\u3002<\/p>\n\n\n\n

\uff085\uff09\u8ddd\u79bb\u52a0\u6743\uff1a<\/p>\n\n\n\n

\u53ef\u4ee5\u7b80\u5355\u5730\u5c06\u6743\u91cd\u8bbe\u7f6e\u4e3a\u8ddd\u79bb\u7684\u51fd\u6570\uff0c\u4f8b\u5982\uff1a<\/p>\n\n\n

\\(W(r_i-r_j)=\\frac{1}{\\|r_i-r_j\\|^p+\\epsilon}\\)<\/p>\n\n\n

\u5176\u4e2dp<\/em>\u662f\u4e00\u4e2a\u8d85\u53c2\u6570\uff0c\\(\\epsilon \\)\u662f\u4e00\u4e2a\u5c0f\u7684\u5e38\u6570\uff0c\u4ee5\u907f\u514d\u9664\u4ee5\u96f6\u3002<\/p>\n\n\n\n

\u79bb\u6563\u5377\u79ef\u548c\u8fde\u7eed\u5377\u79ef\u7684\u4e3b\u8981\u533a\u522b\u5728\u4e8e\u5b83\u4eec\u5904\u7406\u7684\u6570\u636e\u7ed3\u6784\u548c\u64cd\u4f5c\u65b9\u5f0f\u3002\u5728\u6570\u636e\u7ed3\u6784\u4e0a\uff0c\u79bb\u6563\u5377\u79ef\u5904\u7406\u7684\u662f\u6392\u5217\u5728\u56fa\u5b9a\u7f51\u683c\u4e0a\u7684\u70b9\uff0c\u4f8b\u5982\u56fe\u50cf\u50cf\u7d20\u3002\u800c\u8fde\u7eed\u5377\u79ef\u5904\u7406\u7684\u662f\u4e0d\u4f9d\u8d56\u4e8e\u56fa\u5b9a\u7f51\u683c\u7684\u6570\u636e\u3002\u5b83\u53ef\u4ee5\u5e94\u7528\u4e8e\u4efb\u610f\u5206\u5e03\u7684\u70b9\uff0c\u4f8b\u5982\u4e0d\u89c4\u5219\u6392\u5217\u7684\u539f\u5b50\u6216\u5176\u4ed6\u4efb\u610f\u7a7a\u95f4\u5206\u5e03\u7684\u6570\u636e\u70b9\u3002<\/p>\n\n\n\n

\u5728\u64cd\u4f5c\u65b9\u5f0f\u4e0a\uff0c\u79bb\u6563\u5377\u79ef\u7684\u5c40\u90e8\u6027\u662f\u7531\u5377\u79ef\u6838\u7684\u5c3a\u5bf8\u5f3a\u5236\u5b9a\u4e49\u7684\uff0c\u5e76\u5728\u56fe\u50cf\u6570\u636e\u4e0a\u5c40\u90e8\u5730\u5e94\u7528\u5377\u79ef\u6838\uff0c\u901a\u5e38\u8fd9\u4e2a\u5377\u79ef\u6838\u662f\u4e00\u4e2a\u5c0f\u578b\u7684\u77e9\u9635\uff0c\u6bd4\u59823\u00d73\u3002\u8fd9\u4e2a\u5927\u5c0f\u7684\u9009\u62e9\u610f\u5473\u7740\u6bcf\u4e2a\u50cf\u7d20\u70b9\u7684\u65b0\u503c\u662f\u7531\u5176\u81ea\u8eab\u548c\u5468\u56f48\u4e2a\u50cf\u7d20\u70b9\uff08\u57283\u00d73\u90bb\u57df\u4e2d\uff09\u901a\u8fc7\u5377\u79ef\u6838\u52a0\u6743\u6c42\u548c\u5f97\u5230\u7684\u3002\u4e0e\u79bb\u6563\u5377\u79ef\u4e0d\u540c\uff0c\u8fde\u7eed\u5377\u79ef\u6d89\u53ca\u4e00\u4e2a\u52a8\u6001\u751f\u6210\u7684\u5377\u79ef\u6838\uff0c\u8fd9\u4e2a\u6838\u7684\u503c\u662f\u6839\u636e\u622a\u65ad\u53d8\u91cfC<\/em>\u6216\u5176\u76ee\u6807\u8282\u70b9\u7684\u90bb\u5c45\u6570\u91cf\u8ba1\u7b97\u7684\u3002\u7531\u4e8e\u56fe\u6570\u636e\u7684\u4e0d\u89c4\u5219\u6027\uff0c\u5373\u4f7f\u622a\u65ad\u53d8\u91cfC<\/em>\u56fa\u5b9a\uff0c\u6bcf\u4e2a\u56fe\u5c40\u90e8\u8303\u56f4\u4e0b\u7684\u90bb\u5c45\u6570\u91cf\u5927\u6982\u7387\u662f\u4e0d\u540c\u7684\u3002<\/p>\n\n\n\n

1.2 SchNet\u4e0eGNN<\/h3>\n\n\n\n

\u6700\u540e\uff0c\u4eceGNN\u6a21\u578b\u6846\u67b6\u7684\u89d2\u5ea6\u6765\u8bb2\u89e3\u4e00\u4e0bSchNet\u3002\u9996\u5148\uff0c\u56de\u987e\u4e00\u4e0bGNN \u7684\u6838\u5fc3\u8ba1\u7b97\u6d41\u7a0b\uff0c\u5982\u56fe6\u6240\u793a\u3002<\/p>\n\n\n

\n
\"\"
\u56fe6 GNN\u6838\u5fc3\u8ba1\u7b97\u6d41\u7a0b<\/figcaption><\/figure><\/div>\n\n\n

\u5176\u4e2d\u7684\u5173\u952e\u70b9\u6709\u4e09\u65b9\u9762\uff0c\u5176\u4e00\u662f\u5bf9\u8f93\u5165\u6570\u636e\u7684\u5411\u91cf\u5316\uff08Embedding\uff09\uff1b\u5176\u4e8c\u662f\u5bf9\u8282\u70b9\u3001\u8fb9\u6216\u5168\u5c40\u7279\u5f81\u8fdb\u884c\u6d88\u606f\u4f20\u9012\u4e0e\u66f4\u65b0\uff0c\u6700\u540e\u662f\u5bf9\u6a21\u578b\u9876\u5c42\u7684\u8bbe\u8ba1\u6765\u9002\u5e94\u5177\u4f53\u7684\u4efb\u52a1\uff0c\u5c06SchNet\u5bf9\u5e94\u5230GNN\u7684\u6846\u67b6\u4e2d\u5982\u56fe7\u6240\u793a\u3002<\/p>\n\n\n

\n
\"\"
\u56fe7 \u6a21\u5757\u5bf9\u5e94<\/figcaption><\/figure><\/div>\n\n\n

SchNet\u4e2d\u5bf9\u8f93\u5165\u6570\u636e\u7684\u5411\u91cf\u5316\u76f8\u5bf9\u76f4\u63a5\u800c\u7b80\u5355\u3002\u5b83\u901a\u8fc7\u5c06\u539f\u5b50\u7c7b\u578b\u6620\u5c04\u6210\u9ad8\u7ef4\u7a7a\u95f4\u4e2d\u7684\u5411\u91cf\u6765\u5b9e\u73b0\u3002\u8fd9\u4e00\u8fc7\u7a0b\u901a\u5e38\u6d89\u53ca\u4e00\u4e2a\u53ef\u5b66\u4e60\u7684\u795e\u7ecf\u7f51\u7edc\u5c42\uff0c\u8be5\u5c42\u5c06\u6bcf\u4e2a\u539f\u5b50\u7c7b\u578b\u7684one-hot\u7f16\u7801\u8f6c\u6362\u4e3a\u4e00\u4e2a\u56fa\u5b9a\u957f\u5ea6\u7684\u5411\u91cf\u8868\u793a\u3002\u8fd9\u4e9b\u8868\u793a\u53ef\u4ee5\u901a\u8fc7\u6a21\u578b\u8bad\u7ec3\u6355\u6349\u539f\u5b50\u4e4b\u95f4\u6f5c\u5728\u7684\u76f8\u4f3c\u6027\u548c\u5dee\u5f02\u6027\u3002<\/p>\n\n\n\n

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