{"id":2500,"date":"2024-12-27T22:37:49","date_gmt":"2024-12-27T14:37:49","guid":{"rendered":"https:\/\/www.gnn.club\/?p=2500"},"modified":"2025-06-24T14:18:50","modified_gmt":"2025-06-24T06:18:50","slug":"gvp-gnn","status":"publish","type":"post","link":"http:\/\/gnn.club\/?p=2500","title":{"rendered":"GVP-GNN"},"content":{"rendered":"\n

1\u3001Geometric Vector Perceptron<\/h2>\n\n\n\n

GVP-GNN\u5305\u542b\u6807\u91cf\u548c\u5411\u91cf\u4e24\u4e2a\u5904\u7406\u901a\u9053\uff0c\u5982\u56fe1\u6240\u793a\u3002\u5411\u91cf\u901a\u9053\u5904\u7406\u5411\u91cf\u7279\u5f81\\(\\text{V}\\)\uff0c\u8fd9\u4e9b\u7279\u5f81\u662f\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u7684\u5411\u91cf\uff0c\u901a\u5e38\u4ee3\u8868\u65b9\u5411\u6027\u6570\u636e\u3002\\(\\text{V}\\)\u4e58\u4ee5\u6743\u91cd\u77e9\u9635\\(W_{\\nu h}\\)\u548c\\(W_{\\nu\\mu}\\)\uff0c\u53ef\u4ee5\u5206\u522b\u5f97\u5230\u4e24\u4e2a\u65b0\u7684\u5411\u91cf\u96c6\u5408 \\(V_{h}\\)\u548c\\(V_{\\mu}\\)\u3002\u63a5\u7740\uff0c\u8fd9\u4e9b\u5411\u91cf\u4f7f\u7528L2\u8303\u6570\u8fdb\u884c\u5f52\u4e00\u5316\uff0c\u5176\u4e2d\\(V_{h}\\)\u5f52\u4e00\u5316\u540e\u7684\u7ed3\u679c\u4e0e\u6807\u91cf\u7279\u5f81\\(\\text{s}\\)\u8fdb\u884c\u62fc\u63a5\u53c2\u4e0e\u540e\u7eed\u6807\u91cf\u4fe1\u606f\u7684\u66f4\u65b0\uff1b\\(V_{\\mu}\\)\u5f52\u4e00\u5316\u540e\u7684\u7ed3\u679c\u7ecf\u8fc7\u6fc0\u6d3b\u51fd\u6570\\(\\sigma^{+}\\)\u7684\u5904\u7406\u5f97\u5230\u4e00\u4e2a\u975e\u8d1f\u7684\u7f29\u653e\u56e0\u5b50\\(\\sigma^+(V_\\mu)\\)\u3002\u6fc0\u6d3b\u51fd\u6570\\(\\sigma^{+}\\)\u53ef\u4ee5\u5c06\u5176\u89c6\u4e3a\u4e00\u79cd\u4fee\u6539\u7248\u7684ReLU\u51fd\u6570\uff0c\u4e13\u95e8\u88ab\u5e94\u7528\u4e8e\u5411\u91cf\\(V_{\\mu}\\)\u7684L2\u8303\u6570\uff0c\u5f97\u5230\u4e00\u4e2a\u975e\u8d1f\u7684\u7f29\u653e\u56e0\u5b50\uff0c\u8fd9\u4e2a\u7f29\u653e\u56e0\u5b50\u8d77\u5230\u4e00\u79cd\u95e8\u63a7\u51fd\u6570\u7684\u4f5c\u7528\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u6fc0\u6d3b\u51fd\u6570\\(\\sigma^{+}\\)\u5bf9\u4e8e\u4efb\u4f55\u8d1f\u8f93\u5165\u548c\u4ecb\u4e8e0\u4e0e\ud835\udf16\u4e4b\u95f4\u7684\u8f93\u5165\u8f93\u51fa\u4e00\u4e2a\u5c0f\u7684\u6b63\u5e38\u6570\ud835\udf16\u3002\u5bf9\u4e8e\u5927\u4e8e\ud835\udf16\u7684\u6b63\u8f93\u5165\uff0c\u8f93\u51fa\u7b49\u4e8e\u8f93\u5165\u503c\u3002\u516c\u5f0f\u8868\u793a\u4e3a\uff1a<\/p>\n\n\n

\\(\\sigma^+(x)=\\max(\\epsilon,x)\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (1)<\/p>\n\n\n

\u7f29\u653e\u56e0\u5b50\\(\\sigma^{+}(V_{\\mu})\\)\u5c06\u4e0e\\(V_{\\mu}\\)\u4e2d\u76f8\u5bf9\u5e94\u4f4d\u7f6e\u7684\u5143\u7d20\u8fdb\u884c\u9010\u5143\u7d20\u4e58\u6cd5\uff0c\u8fd9\u4e2a\u64cd\u4f5c\u5728\u51e0\u4f55\u5b66\u4e0a\u53ef\u4ee5\u88ab\u7406\u89e3\u4e3a\u6309\u5143\u7d20\u7f29\u653e\u6bcf\u4e2a\u5411\u91cf\uff0c\u8fd9\u79cd\u9010\u5143\u7d20\u7684\u4e58\u6cd5\u4f7f\u5f97\u7f51\u7edc\u80fd\u591f\u8c03\u6574\u6bcf\u4e2a\u5411\u91cf\u65b9\u5411\u4e0a\u7684\u5927\u5c0f\uff0c\u800c\u4e0d\u6539\u53d8\u5176\u65b9\u5411\u3002\u7ed3\u679c\\(V^{\\prime}\\)\u662f\u66f4\u65b0\u540e\u7684\u5411\u91cf\u7279\u5f81\uff0c\u5176\u7ef4\u5ea6\u4ecd\u7136\u662f\\(R^{\\mu\\times3}\\)\uff0c\u6bcf\u4e2a\u5411\u91cf\u7684\u5927\u5c0f\u5df2\u7ecf\u88ab\u8c03\u6574\u8fc7\uff0c\u4f46\u65b9\u5411\u4fdd\u6301\u4e0d\u53d8\u3002<\/p>\n\n\n

\n
\"\"
\u56fe1 GVP-GNN\u6a21\u578b\u7ed3\u6784<\/figcaption><\/figure><\/div>\n\n\n

\u503c\u5f97\u6ce8\u610f\u7684\u662f\u5f52\u4e00\u5316\u64cd\u4f5c\u4e00\u822c\u662f\u89c4\u8303\u5411\u91cf\u7684\u5927\u5c0f\uff0c\u800c\u6700\u540e\u7684\u95e8\u63a7\u673a\u5236\u53c8\u5728\u8c03\u6574\u5411\u91cf\u7684\u5927\u5c0f\uff0c\u8fd9\u5728\u903b\u8f91\u4e0a\u770b\u8d77\u6765\u6709\u4e9b\u81ea\u76f8\u77db\u76fe\uff0c\u4f46\u5b9e\u9645\u4e0a\u8fd9\u4e24\u4e2a\u8fc7\u7a0b\u662f\u76f8\u8f85\u76f8\u6210\u7684\u3002\u5177\u4f53\u800c\u8a00\uff0c\u5f52\u4e00\u5316\u5904\u7406\u53ef\u4ee5\u786e\u4fdd\u5411\u91cf\u7684\u65b9\u5411\u88ab\u4fdd\u7559\u4e0b\u6765\uff0c\u540c\u65f6\u5c06\u5b83\u4eec\u7684\u5927\u5c0f\u6807\u51c6\u5316\u5230\u76f8\u4f3c\u7684\u89c4\u6a21\uff0c\u8fd9\u4e3b\u8981\u662f\u4e3a\u4e86\u6570\u503c\u8ba1\u7b97\u7684\u7a33\u5b9a\u6027\u548c\u4f18\u5316\u7b97\u6cd5\u7684\u6548\u7387\u3002\u5f52\u4e00\u5316\u4e4b\u540e\u7684\u5411\u91cf\u5728\u8fdb\u884c\u795e\u7ecf\u7f51\u7edc\u7684\u8bad\u7ec3\u65f6\u4e0d\u4f1a\u56e0\u4e3a\u5927\u5c0f\u5dee\u5f02\u8fc7\u5927\u800c\u5bfc\u81f4\u68af\u5ea6\u95ee\u9898\u3002\u63a5\u7740\uff0c\u5c3d\u7ba1\u5f52\u4e00\u5316\u5c06\u6240\u6709\u5411\u91cf\u7684\u5927\u5c0f\u7edf\u4e00\uff0c\u795e\u7ecf\u7f51\u7edc\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u5b66\u4e60\u5230\u7684\u6743\u91cd\u548c\u5176\u4ed6\u53c2\u6570\uff0c\u5374\u53ef\u4ee5\u4f7f\u7f51\u7edc\u52a8\u6001\u8c03\u6574\u5411\u91cf\u7684\u5927\u5c0f\u6765\u9002\u5e94\u4e0d\u540c\u7684\u4efb\u52a1\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u7f51\u7edc\u53ef\u4ee5\u51b3\u5b9a\u54ea\u4e9b\u65b9\u5411\u7684\u7279\u5f81\u66f4\u91cd\u8981\uff0c\u5e76\u76f8\u5e94\u5730\u589e\u52a0\u8fd9\u4e9b\u7279\u5f81\u5411\u91cf\u7684\u5927\u5c0f\uff08\u6743\u91cd\uff09\uff0c\u800c\u4e0d\u662f\u901a\u8fc7\u6539\u53d8\u5b83\u4eec\u7684\u65b9\u5411\u3002\u7b80\u5355\u8bf4\u5f52\u4e00\u5316\u7684\u4f5c\u7528\u662f\u63d0\u4f9b\u6570\u503c\u7a33\u5b9a\u6027\u548c\u4f18\u5316\u6548\u7387\uff0c\u540c\u65f6\u4fdd\u6301\u5411\u91cf\u65b9\u5411\u7684\u4fe1\u606f\u3002\u5411\u91cf\u5927\u5c0f\u8c03\u6574\u662f\u4e3a\u4e86\u7f51\u7edc\u5b66\u4e60\u7684\u8fc7\u7a0b\u4e2d\u53ef\u4ee5\u52a8\u6001\u8c03\u6574\u5411\u91cf\u5927\u5c0f\uff0c\u6765\u5f3a\u8c03\u67d0\u4e9b\u7279\u5f81\u7684\u91cd\u8981\u6027\u3002<\/p>\n\n\n\n

\u6807\u91cf\u901a\u9053\u5904\u7406\u6807\u91cf\u7279\u5f81\\(\\text{s}\\)\uff0c\u8fd9\u4e9b\u7279\u5f81\u6ca1\u6709\u65b9\u5411\u6027\uff0c\u901a\u5e38\u4ee3\u8868\u7269\u4f53\u7684\u5927\u5c0f\u3001\u5f3a\u5ea6\u7b49\u5c5e\u6027\u3002\u9996\u5148\uff0c\u6807\u91cf\u4fe1\u606f\\(\\text{s}\\)\u4e0e\u5411\u91cf\u901a\u9053\u5f52\u4e00\u5316\u540e\u7684\u8f93\u51fa\\(V_{h}\\)\u8fdb\u884c\u62fc\u63a5\uff0c\u5f62\u6210\u4e00\u4e2a\u65b0\u7684\u5411\u91cf\\(s_{h+n}\\)\u3002\u7136\u540e\uff0c\u901a\u8fc7\u6743\u91cd\u77e9\u9635\\(W_{m}\\)\u8fdb\u884c\u53d8\u6362\uff0c\u518d\u7ecf\u8fc7\u4e00\u4e2a\u6fc0\u6d3b\u51fd\u6570\\(\\sigma\\)\uff0c\u5f97\u5230\u6700\u7ec8\u7684\u8f93\u51fa\u6807\u91cf\u7279\u5f81\\(s^{\\prime}\\)\u3002<\/p>\n\n\n\n

2\u3001GVP\u7ed3\u5408GNN<\/h2>\n\n\n\n

GVP-GNN\u91c7\u7528\u4e86GNN\u7684\u4fe1\u606f\u4f20\u9012\u673a\u5236\u4f7f\u7528GVP\u6765\u66f4\u65b0\u56fe\u4e2d\u8282\u70b9\u7684\u7279\u6027\u5411\u91cf\u3002\u4e0b\u9762\u516c\u5f0f\u9010\u6b65\u89e3\u6790\u5b83\u7684\u5173\u952e\u90e8\u5206\uff1a<\/p>\n\n\n

\\(\\boldsymbol{h}_m^{(j\\to i)}:=g\\left(\\operatorname{concat}\\left(\\boldsymbol{h}_\\nu^{(j)},\\boldsymbol{h}_e^{(j\\to i)}\\right)\\right)\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(2)<\/p>\n

\\(\\boldsymbol{h}_\\nu^{(i)}\\leftarrow\\text{LayerNorm}\\Bigg(\\boldsymbol{h}_\\nu^{(i)}+\\frac1{k'}\\text{Dropout}\\Bigg(\\sum_{j:\\boldsymbol{e}_{j\\to i}\\in\\mathcal{E}}\\boldsymbol{h}_m^{(j\\to i)}\\Bigg)\\Bigg)\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (3)<\/p>\n

\\(\\boldsymbol{h}_\\nu^{(i)}\\leftarrow\\text{LayerNorm}\\left(\\boldsymbol{h}_\\nu^{(i)}+\\text{Dropout}\\left(g\\left(\\boldsymbol{h}_\\nu^{(i)}\\right)\\right)\\right)\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (4)<\/p>\n\n\n

\u5176\u4e2d\u5f0f(2)\u662f\u6d88\u606f\u805a\u5408\u7684\u4f53\u73b0\uff0c\\(h_m^{(j\\to i)}\\)\u662f\u4ece\u8282\u70b9\\(\\mathrm{j}\\)\u4f20\u9012\u7ed9\u8282\u70b9\\(\\mathrm{i}\\)\u7684\u6d88\u606f\uff0c\\(\\mathrm{g}\\)\u662f\u4e09\u4e2a\u51e0\u4f55\u5411\u91cf\u611f\u77e5\u673a\uff0c\u7528\u4e8e\u66f4\u65b0\u8f6c\u6362\u8282\u70b9\u548c\u8fb9\u7684\u7279\u5f81\u3002 \\(h_{\\nu}^{(j)}\\)\u548c\\(h_e^{(j\\to i)}\\)\u5206\u522b\u8868\u793a\u6ca1\u6709\u88abGVP\u66f4\u65b0\u524d\u7684\u8282\u70b9\\(\\mathrm{j}\\)\u548c\u8fb9\\((j\\to i)\\)\u7684\u7279\u5f81\u3002\\(\\mathrm{concat}\\left(\\boldsymbol{h}_\\nu^{(j)},\\boldsymbol{h}_e^{(j\\to i)}\\right)\\)\u8868\u793a\u5c06\u8282\u70b9\u548c\u8fb9\u7684\u7279\u5f81\u5411\u91cf\u8fdb\u884c\u62fc\u63a5\uff0c\u4e00\u8d77\u4f5c\u4e3aGVP\u7684\u8f93\u5165\u3002<\/p>\n\n\n\n

\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u5728\u5173\u4e8eGVP\u7684\u8bb2\u89e3\u4e2d\u63d0\u5230\u5176\u8f93\u5165\u662f\u6807\u91cf\u4fe1\u606f\u548c\u5411\u91cf\u4fe1\u606f\u4e24\u90e8\u5206\uff0c\u800c\u5f0f(2\u53c8\u53d8\u6210\u4e86\u8282\u70b9\u7279\u5f81\\(h_{\\nu}^{(j)}\\)\u548c\u8fb9\u7279\u5f81\\(h_e^{(j\\rightarrow i)}\\)\u3002\u5b9e\u9645\u4e0a\uff0c\u8fd9\u91cc\u7684\u8282\u70b9\u7279\u5f81\u548c\u8fb9\u7279\u5f81\u672c\u8eab\u5df2\u7ecf\u5305\u542b\u4e86\u6807\u91cf\u548c\u5411\u91cf\u4fe1\u606f\uff0c\u53ea\u662f\u516c\u5f0f\u4e2d\u6ca1\u6709\u663e\u793a\u7684\u8868\u8fbe\u800c\u5df2\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u8282\u70b9\u7279\u5f81\\(h_{\\nu}^{(j)}\\)\u8981\u6c42\u5305\u542b\u4e86\u8282\u70b9\u7684\u6807\u91cf\u4fe1\u606f\uff08\u5982\u6c28\u57fa\u9178\u7684\u7c7b\u578b\u3001\u7535\u8377\u7b49\uff09 \u548c\u5411\u91cf\u4fe1\u606f\uff08\u5982\u5176\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u7684\u65b9\u5411\u5411\u91cf\uff09\u3002\u540c\u7406\uff0c\u8fb9\u7279\u5f81\u4e5f\u8981\u6c42\u5305\u542b\u4e86\u6807\u91cf\u548c\u5411\u91cf\u4fe1\u606f\uff0c\u5982\u8fde\u63a5\u8282\u70b9\u7684\u8ddd\u79bb\u3001\u65b9\u5411\u7b49\u3002<\/p>\n\n\n\n

\u5f0f(3)\u548c(4)\u90fd\u8868\u793a\u8282\u70b9\u7279\u5f81\u7684\u66f4\u65b0\u3002\u5728\u5f0f(3)\u4e2d\uff0cLayerNorm\u662f\u4e00\u79cd\u89c4\u8303\u5316\u6280\u672f\uff0c\u7528\u4e8e\u6807\u51c6\u5316\u6bcf\u4e2a\u6837\u672c\u5185\u90e8\u7684\u7279\u5f81\uff0c\u5b83\u5728\u795e\u7ecf\u7f51\u7edc\u4e2d\u5e38\u7528\u4e8e\u7a33\u5b9a\u548c\u52a0\u901f\u8bad\u7ec3\u3002\\(h_{\\nu}^{(i)}+\\frac{1}{k^{^{\\prime}}}\u2026\\)\u8fd9\u90e8\u5206\u8868\u793a\u5f53\u524d\u8282\u70b9\u7279\u5f81\\(h_{\\nu}^{(i)}\\) \u4e0e\u7ecf\u8fc7Dropout\u548c\u805a\u5408\u90bb\u5c45\u4fe1\u606f\u540e\u5f97\u5230\u7684\u65b0\u7279\u5f81\u7684\u548c\uff0c\u8fd9\u662f\u4e00\u79cd\u5178\u578b\u7684\u6b8b\u5dee\u8fde\u63a5\u673a\u5236\uff0c\u6709\u52a9\u4e8e\u7f13\u89e3\u68af\u5ea6\u6d88\u5931\u95ee\u9898\uff0c\u5e76\u5141\u8bb8\u66f4\u6df1\u5c42\u6b21\u7684\u7f51\u7edc\u8bad\u7ec3\u3002\\(\\frac{1}{k^{\\prime}}\\)\u662f\u4e00\u4e2a\u5f52\u4e00\u5316\u56e0\u5b50\uff0c\u5176\u4e2d\\({k^{\\prime}}\\)\u662f\u5b9e\u9645\u63a5\u6536\u5230\u7684\u6d88\u606f\u6570\u91cf\uff0c\u7b49\u4e8e\u8282\u70b9\\(\\mathrm{i}\\)\u7684\u90bb\u5c45\u6570\u91cf\u3002\u8fd9\u4e2a\u56e0\u5b50\u786e\u4fdd\u4e86\uff1a\u4e0d\u8bba\u8282\u70b9\u6709\u591a\u5c11\u4e2a\u90bb\u5c45\uff0c\u805a\u5408\u540e\u7684\u4fe1\u606f\u90fd\u4f1a\u4fdd\u6301\u4e00\u81f4\u7684\u89c4\u6a21\u3002Dropout \u662f\u4e00\u79cd\u6b63\u5219\u5316\u6280\u672f\uff0c\u901a\u8fc7\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u968f\u673a\u201c\u4e22\u5f03\u201d\uff08\u5373\u5c06\u53c2\u6570\u8bbe\u7f6e\u4e3a0) \u4e00\u4e9b\u795e\u7ecf\u5143\u7684\u8f93\u51fa\u6765\u9632\u6b62\u7f51\u7edc\u8fc7\u62df\u5408\u3002\u5728\u8fd9\u91cc\uff0cDropout \u88ab\u5e94\u7528\u4e8e\u6240\u6709\u90bb\u5c45\u8282\u70b9\\(\\mathrm{j}\\)\u7684\u6d88\u606f\\(h_{m}^{(j\\rightarrow i)}\\)\u7684\u603b\u548c\uff0c\u800c\u4e0d\u662f\u968f\u673a\u9009\u62e9\u90bb\u5c45\u8282\u70b9\u3002\u603b\u7684\u6765\u8bf4\uff0c\u5f0f(3)\u8868\u793a\u7684\u662f\u8282\u70b9\\(\\mathrm{i}\\)\u7684\u7279\u5f81\u5982\u4f55\u901a\u8fc7\u4e0e\u5b83\u7684\u6240\u6709\u90bb\u5c45\\(\\mathrm{j}\\)\u7684\u4fe1\u606f\u6c47\u603b\uff08\u5e76\u4e14\u8fd9\u4e2a\u6c47\u603b\u7684\u4fe1\u606f\u53d7\u5230Dropout\u7684\u5f71\u54cd\uff09\u540e\uff0c\u7ed3\u5408\u6b8b\u5dee\u8fde\u63a5\u8fdb\u884c\u66f4\u65b0\u3002\u8fd9\u79cd\u66f4\u65b0\u673a\u5236\u5141\u8bb8\u6bcf\u4e2a\u8282\u70b9\u4fdd\u7559\u81ea\u5df1\u7684\u4fe1\u606f\u7684\u540c\u65f6\u4e5f\u878d\u5408\u90bb\u5c45\u8282\u70b9\u7684\u4fe1\u606f\uff0c\u4ece\u800c\u5728\u6574\u4e2a\u7f51\u7edc\u4e2d\u4f20\u9012\u548c\u6269\u6563\u4fe1\u606f\u3002<\/p>\n\n\n\n

\u5f0f(4)\u5219\u8d1f\u8d23\u5c06\u5f0f(3)\u5f97\u5230\u7684\u8282\u70b9\u7279\u5f81\u8fdb\u884c\u8fdb\u4e00\u6b65\u7684\u66f4\u65b0\u8fed\u4ee3\uff0c\u5176\u6838\u5fc3\u6b65\u9aa4\u662f\\(g\\left(h_{\\nu}^{(i)}\\right)\\)\u3002\\(\\mathrm{g}\\)\u662f\u4e09\u4e2a\u51e0\u4f55\u5411\u91cf\u611f\u77e5\u673a\uff0c\u5bf9\u5f53\u524d\u7684\u8282\u70b9\u7279\u5f81\\(h_\\nu^{(i)}\\)\u8fdb\u884c\u5904\u7406\uff0c\u8fdb\u4e00\u6b65\u5b66\u4e60\u66f4\u590d\u6742\u7684\u7279\u5f81\u53d8\u6362\u3002\u81f3\u4e8e\u5f0f(4)\u4e2d\u7684Dropout\u3001LayerNorm\u548c\u6b8b\u5dee\u8fde\u63a5\u7684\u4f5c\u7528\u5219\u4e0e\u5f0f(3)\u7c7b\u4f3c\uff0c\u8fd9\u91cc\u4e0d\u518d\u8d58\u8ff0\u3002<\/p>\n\n\n\n

3\u3001GVP-GNN\u7b49\u53d8\u6027\u7684\u8ba8\u8bba<\/h2>\n\n\n\n

GVP-GNN\u6a21\u578b\u901a\u8fc7\u878d\u5408\u6807\u91cf\u548c\u5411\u91cf\u4fe1\u606f\u6765\u589e\u5f3a\u5bf9\u51e0\u4f55\u7ed3\u6784\u7684\u8868\u5f81\u80fd\u529b\u3002\u5728\u8be5\u6a21\u578b\u4e2d\uff0c\u6807\u91cf\u4fe1\u606f\u901a\u5e38\u662f\u4e0d\u53d8\u6027\u7684\uff0c\u56e0\u4e3a\u6807\u91cf\u503c\uff08\u5982\u6e29\u5ea6\u3001\u8d28\u91cf\u7b49\uff09\u901a\u5e38\u4e0d\u968f\u53c2\u8003\u7cfb\u7684\u65cb\u8f6c\u6216\u5e73\u79fb\u800c\u6539\u53d8\u3002\u5411\u91cf\u4fe1\u606f\u5982\u4f4d\u7f6e\u6216\u65b9\u5411\u5411\u91cf\uff0c\u5219\u662f\u7b49\u53d8\u6027\u7684\uff0c\u56e0\u4e3a\u5b83\u4eec\u4f1a\u968f\u7740\u53c2\u8003\u7cfb\u7684\u65cb\u8f6c\u6216\u5e73\u79fb\u800c\u76f8\u5e94\u5730\u53d8\u6362\u3002\u5728GVP-GNN\u4e2d\u5b9e\u73b0\u7b49\u53d8\u6027\uff0c\u662f\u901a\u8fc7\u8bbe\u8ba1\u7f51\u7edc\u7684\u64cd\u4f5c\u6765\u4fdd\u6301\u8f93\u5165\u5411\u91cf\u7684\u65cb\u8f6c\u7b49\u53d8\u6027\u3002\u8fd9\u610f\u5473\u7740\uff1a\u5982\u679c\u8f93\u5165\u7684\u5411\u91cf\u6570\u636e\uff08\u5982\u539f\u5b50\u5750\u6807\uff09\u53d1\u751f\u65cb\u8f6c\uff0c\u7f51\u7edc\u7684\u5411\u91cf\u8f93\u51fa\u4e5f\u5e94\u5f53\u4ee5\u76f8\u540c\u7684\u65b9\u5f0f\u53d1\u751f\u65cb\u8f6c\u3002 <\/p>\n\n\n\n

GVP-GNN\u6a21\u578b\u7684\u7b49\u53d8\u6027\u4e0d\u4ec5\u4ec5\u6765\u6e90\u4e8e\u6807\u91cf\u548c\u5411\u91cf\u4e24\u79cd\u5904\u7406\u901a\u9053\uff0c\u66f4\u91cd\u8981\u7684\u662f\u6a21\u578b\u7684\u8bbe\u8ba1\u5141\u8bb8\u5728\u66f4\u65b0\u8282\u70b9\u7279\u5f81\u65f6\uff0c\u5411\u91cf\u4fe1\u606f\u7684\u65b9\u5411\u88ab\u4fdd\u7559\u5e76\u6b63\u786e\u5904\u7406\u3002\u4f8b\u5982\uff0c\u5728GVP\u7684\u5411\u91cf\u5904\u7406\u901a\u9053\u4e2d\uff0c\u53ea\u6539\u53d8\u5411\u91cf\u5927\u5c0f\uff0c\u4e0d\u6539\u53d8\u65b9\u5f0f\u5c31\u662f\u4e3a\u4e86\u4fdd\u8bc1\u7b49\u53d8\u6027\u3002\u8fd9\u610f\u5473\u7740\u5982\u679c\u8f93\u5165\u6570\u636e\uff08\u5982\u5206\u5b50\u7ed3\u6784\uff09\u7ecf\u5386\u4e86\u7a7a\u95f4\u65cb\u8f6c\uff0c\u8f93\u51fa\u7684\u5411\u91cf\u7279\u5f81\u4e5f\u4f1a\u4ee5\u540c\u6837\u7684\u65b9\u5f0f\u8fdb\u884c\u65cb\u8f6c\u3002\u800c\u4e14\uff0c\u5728\u5411\u91cf\u5904\u7406\u901a\u9053\u4e2d\uff0c\u4e5f\u4e0d\u5b58\u5728\u975e\u7ebf\u6027\u7684\u64cd\u4f5c\uff0c\u76ee\u7684\u4e5f\u662f\u4e3a\u4e86\u4fdd\u8bc1\u7b49\u53d8\u6027\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u5411\u91cf\\(\\mathrm{V}\\)\u4e0e\u6743\u91cd\u77e9\u9635\\(W_{\\nu h}\\)\u548c\\(W_{\\nu\\mu}\\)\u76f8\u4e58\uff0c\u5f97\u5230\u4e24\u4e2a\u65b0\u7684\u5411\u91cf\u96c6\u5408\\(V_{h}\\)\u548c\\(V_{\\mu}\\)\u3002\u8fd9\u79cd\u53d8\u6362\u662f\u7ebf\u6027\u7684\uff0c\u5e76\u4e14\u4fdd\u6301\u7b49\u53d8\u6027\u3002\\(V_{h}\\)\u901a\u8fc7L2\u8303\u6570\u5f52\u4e00\u5316\u5e76\u4e0e\u6807\u91cf\u7279\u5f81\\(\\mathrm{s}\\)\u8fdb\u884c\u62fc\u63a5\uff0c\u8fd9\u4e2a\u62fc\u63a5\u64cd\u4f5c\u4fdd\u6301\u5411\u91cf\u7684\u65b9\u5411\uff0c\u540c\u65f6\u4e3a\u6807\u91cf\u901a\u9053\u63d0\u4f9b\u4e86\u5927\u5c0f\u4fe1\u606f\u3002\\(V_{\\mu}\\)\u901a\u8fc7L2\u8303\u6570\u5f52\u4e00\u5316\u540e\uff0c\u5176\u7ed3\u679c\u901a\u8fc7\u6fc0\u6d3b\u51fd\u6570\\(\\sigma^{+}\\)\uff08\u5982ReLU\u53d8\u4f53\uff09\u5904\u7406\uff0c\u751f\u6210\u975e\u8d1f\u7684\u7f29\u653e\u56e0\u5b50\uff0c\u8be5\u56e0\u5b50\u4e0e\\(V_{\\mu}\\)\u8fdb\u884c\u9010\u5143\u7d20\u4e58\u6cd5\uff0c\u8fd9\u4e2a\u64cd\u4f5c\u5728\u4fdd\u6301\u65b9\u5411\u4e0d\u53d8\u7684\u540c\u65f6\u8c03\u6574\u5927\u5c0f\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

1\u3001Geometric Vector Perceptron GVP-GNN\u5305\u542b\u6807\u91cf\u548c\u5411\u91cf\u4e24\u4e2a\u5904\u7406\u901a\u9053\uff0c\u5982\u56fe1\u6240 […]<\/p>\n","protected":false},"author":1,"featured_media":2501,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[27,23],"tags":[],"class_list":["post-2500","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\/2500","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=2500"}],"version-history":[{"count":3,"href":"http:\/\/gnn.club\/index.php?rest_route=\/wp\/v2\/posts\/2500\/revisions"}],"predecessor-version":[{"id":2505,"href":"http:\/\/gnn.club\/index.php?rest_route=\/wp\/v2\/posts\/2500\/revisions\/2505"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/gnn.club\/index.php?rest_route=\/wp\/v2\/media\/2501"}],"wp:attachment":[{"href":"http:\/\/gnn.club\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2500"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/gnn.club\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2500"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/gnn.club\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2500"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}