{"id":35842,"date":"2022-07-14T22:32:04","date_gmt":"2022-07-14T14:32:04","guid":{"rendered":"https:\/\/swarma.org\/?p=35842"},"modified":"2022-07-14T22:32:04","modified_gmt":"2022-07-14T14:32:04","slug":"%e5%a6%82%e4%bd%95%e9%80%9a%e8%bf%87%e5%9b%a0%e6%9e%9c%e6%b6%8c%e7%8e%b0%e6%89%be%e5%88%b0%e5%a4%8d%e6%9d%82%e7%bd%91%e7%bb%9c%e7%9a%84%e5%90%88%e9%80%82%e5%b0%ba%e5%ba%a6%ef%bc%9f","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=35842","title":{"rendered":"\u5982\u4f55\u901a\u8fc7\u56e0\u679c\u6d8c\u73b0\u627e\u5230\u590d\u6742\u7f51\u7edc\u7684\u5408\u9002\u5c3a\u5ea6\uff1f"},"content":{"rendered":"
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\u5218\u5fd7\u822a<\/span><\/strong><\/span><\/strong> <\/span>| <\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong>\u4f5c\u8005<\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/p>\n

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<\/span>Finding the right scale of a network: Efficient identification of causal  emergence through spectral clustering<\/span><\/p>\n

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https:\/\/arxiv.org\/abs\/1908.07565#<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n

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1. \u4ece\u5fae\u89c2\u5230\u5b8f\u89c2\uff1a\u590d\u6742\u7f51\u7edc\u7684\u56e0\u679c\u6d8c\u73b0<\/span><\/strong><\/strong><\/p>\n<\/section>\n

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<\/p>\n

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<\/p>\n

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<\/p>\n

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 <\/span><\/p>\n<\/section>\n<\/h3>\n

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<\/p>\n<\/section>\n<\/h3>\n

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<\/p>\n

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<\/p>\n

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<\/p>\n

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<\/p>\n

<\/p>\n

\u56fe3. \u56e0\u679c\u6d8c\u73b0\u8ba1\u7b97\u65b9\u6cd5\u7684\u6bd4\u8f83\u3002\u03b1 \u503c\u662f\u901a\u8fc7\u6dfb\u52a0\u8fde\u8fb9\u7684\u8fdb\u7a0b\u5728\u8c03\u7528\u6bcf\u4e2a\u51fd\u6570\u671f\u95f4\u4f7f\u7528\u7684\u7cfb\u7edf\u548c\u7528\u6237 CPU \u65f6\u95f4\u6765\u8ba1\u7b97\u7684\u3002\uff08A\uff09\u8d2a\u5a6a\u7b97\u6cd5\u548c\u68af\u5ea6\u4e0b\u964d\u6cd5\u90fd\u96be\u4ee5\u68c0\u6d4b \u03b1  =1.5 \u9644\u8fd1\u7684\u4e2d\u5c3a\u5ea6\uff0c\u800c\u8c31\u5206\u6790\u4fdd\u6301\u76f8\u5bf9\u4e0d\u53d8\u3002\uff08B\uff09\u8fd0\u884c\u65f6\u95f4\u4e0e\u7f51\u7edc\u5927\u5c0f\u3002\u8d2a\u5a6a\u7b97\u6cd5\u5728\u5c0f\u5b9e\u4f8b\u4e0a\u6bd4\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u66f4\u6709\u6548\uff0c\u800c\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u5728\u66f4\u5927\u7684\u7f51\u7edc\u4e0a\u66f4\u6709\u6548\uff0c\u8c31\u5206\u6790\u7684\u6027\u80fd\u4f18\u4e8e\u4e24\u8005\u3002\uff08C\uff09\u4e0d\u540c\u7b97\u6cd5\u53d1\u73b0 \u03b1 \u503c\u4e0d\u540c\u7684\u65e0\u6807\u5ea6\u7f51\u7edc\u7684\u56e0\u679c\u6d8c\u73b0\u3002\uff08D\uff09\u4e0e\u7f51\u7edc\u89c4\u6a21\u76f8\u6bd4\uff0c\u68c0\u6d4b\u5230\u7684\u56e0\u679c\u6d8c\u73b0\uff0c\u8c31\u5206\u6790\u7565\u4f18\u4e8e\u8d2a\u5a6a\u7b97\u6cd5\uff0c\u68af\u5ea6\u4e0b\u964d\u843d\u540e\u4e8e\u4e24\u8005\u3002<\/span><\/section>\n


<\/p>\n

\u56fe 3 \u5bf9\u6bd4\u4e86\u4e09\u79cd\u65b9\u6cd5\u6027\u80fd\uff0c\u4f5c\u8005\u5206\u6790\u4e86150 \u4e2a\u8282\u70b9\u7684\u4f18\u5148\u8fde\u63a5\u7f51\u7edc\u5728\u4e0d\u540c \u03b1 \u503c\u7684\u8fd0\u884c\u65f6\u95f4\u3002\u5f53\u03b1 = 1 \u65f6\u662f\u65e0\u6807\u5ea6\u7f51\u7edc\uff0c\u800c \u03b1 \u63a5\u8fd1 0 \u5219\u4ea7\u751f\u957f\u8def\u5f84\u7684\u6811\uff0c\u5f53\u03b1 > 2 \u5bfc\u81f4\u653e\u5c04\u5f0f\u6a21\u578b\u3002\u503c\u5f97\u6ce8\u610f\u5230\u7684\u662f\uff0c\u6781\u7aef\u5fae\u89c2\u5c3a\u5ea6<\/span>\uff08\u6700\u5c0f\u5230\u6ca1\u6709\u56e0\u679c\u6d8c\u73b0\uff09<\/span>\u548c\u6781\u7aef\u5b8f\u89c2\u5c3a\u5ea6<\/span>\uff08\u9ad8\u6c34\u5e73\u7684\u56e0\u679c\u6d8c\u73b0\uff09<\/span>\u4e0d\u9700\u8981\u592a\u591a\u7684\u8ba1\u7b97\u8d44\u6e90\u3002<\/span><\/p>\n


<\/p>\n

\u4e2d\u5c3a\u5ea6\u7ed3\u6784\u901a\u5e38\u662f\u7f51\u7edc\u4e2d\u8ba1\u7b97\u4e0a\u6700\u96be\u8bc6\u522b\u7684\u5c3a\u5ea6<\/span><\/strong>\u3002\u7136\u800c\uff0c\u8c31\u5206\u6790\u5728\u5f88\u5927\u7a0b\u5ea6\u4e0a\u907f\u514d\u4e86\u8fd9\u4e00\u95ee\u9898\uff0c\u5b83\u5177\u6709\u6700\u5f3a\u5927\u7684\u7b97\u6cd5\u6027\u80fd\uff0c\u5373\u4f7f\u5728\u5927\u578b\u7f51\u7edc\u4e2d\u4e5f\u80fd\u627e\u5230\u4fe1\u606f\u91cf\u5927\u4e14\u590d\u6742\u7684\u66f4\u9ad8\u5c3a\u5ea6<\/span>\uff08\u56fe3B\uff09<\/span>\u3002\u867d\u7136\u6240\u6709\u7b97\u6cd5\u90fd\u80fd\u8bc6\u522b\u56e0\u679c\u6d8c\u73b0\uff0c\u4f46\u8c31\u5206\u6790\u548c\u8d2a\u5a6a\u7b97\u6cd5\u4f3c\u4e4e\u90fd\u8868\u73b0\u5f97\u66f4\u597d\uff0c\u80fd\u627e\u5230\u7b49\u4ef7\u7684\u590d\u6742\u7f51\u7edc\u56e0\u679c\u6d8c\u73b0\u5c3a\u5ea6\u3002<\/strong><\/span><\/p>\n

\n
\n

 <\/span><\/p>\n<\/section>\n<\/h3>\n

\n
\n


<\/p>\n

\n
\n

<\/section>\n

<\/section>\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n
\n

3. \u590d\u6742\u7f51\u7edc\u7684\u5b8f\u89c2\u5c3a\u5ea6\u6027\u8d28<\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

<\/section>\n<\/section>\n<\/section>\n


<\/p>\n<\/section>\n<\/h3>\n

\u4e3a\u4e86\u63a2\u7d22\u5982\u4f55\u627e\u5230\u6709\u6548\u4fe1\u606f\u66f4\u5927\u7684\u7f51\u7edc\uff0c\u4f5c\u8005\u6a21\u62df\u4e86\u4f18\u5148\u8fde\u63a5\u89c4\u5219\u4e0b\u589e\u957f\u7684\u7f51\u7edc\uff0c\u901a\u8fc7\u5411\u7f51\u7edc\u4e2d\u6dfb\u52a0\u4e00\u4e2a\u65b0\u8282\u70b9\u548c\u5b83\u7684 m \u6761\u65b0\u8fb9\u6765\u589e\u52a0\u7f51\u7edc\u89c4\u6a21\uff0c\u901a\u8fc7\u64cd\u7eb5 \u03b1 \u4ee5\u53ef\u63a7\u7684\u65b9\u5f0f\u8de8\u8d8a\u4e00\u7cfb\u5217\u4e0d\u540c\u7684\u7f51\u7edc\u8fde\u63a5\u3002\u540c\u65f6\uff0c\u4f18\u5148\u8fde\u63a5\u7684\u7f51\u7edc\u53ef\u4ee5\u8de8\u8d8a\u56e0\u679c\u6d8c\u73b0\u7684\u8303\u56f4\uff0c\u4ece\u56e0\u679c\u9000\u5316<\/span>\uff08causal reduction\uff0c\u5373\u5f53 \u03b1 < 1 \u65f6\u901a\u8fc7\u964d\u7ef4\u65e0\u6cd5\u83b7\u5f97 EI \uff09<\/span>\u5230\u6240\u6709\u8282\u70b9\u88ab\u5206\u7ec4\u4e3a\u5355\u4e2a\u5b8f\u8282\u70b9<\/span>\uff08\u03b1 > 3\u65f6\uff09<\/span>\u3002<\/span><\/p>\n


<\/p>\n

<\/p>\n

\u56fe4.  \u7f51\u7edc\u7684\u5b8f\u5c3a\u5ea6\u793a\u4f8b\u3002\uff08A\uff0950\u4e2a\u8282\u70b9\uff08m = 1\uff09\u7684\u4f18\u5148\u8fde\u63a5\u7f51\u7edc\u968f\u7740 \u03b1 \u7684\u589e\u52a0\u800c\u5448\u73b0\u3002\u6211\u4eec\u7684\u8c31\u5206\u6790\u7528\u4e8e\u8bc6\u522b\u5b8f\u8282\u70b9\u3002\u901a\u8fc7\u7b97\u6cd5\u5206\u7ec4\u6210\u5b8f\u8282\u70b9\u7684\u8282\u70b9\u7528\u989c\u8272\u7f16\u7801\u3002\uff08B\uff09m = 3 \u7684\u4f18\u5148\u8fde\u63a5\u7f51\u7edc\uff0c\u8fd9\u610f\u5473\u7740\u968f\u7740\u6bcf\u4e00\u6b65\u589e\u52a0\u66f4\u591a\u7684\u8fb9\uff0c\u7f51\u7edc\u66f4\u52a0\u5bc6\u96c6\u3002\u4fe1\u606f\u5b8f\u8282\u70b9\u4e5f\u51fa\u73b0\u5728 \u03b1 \u7684\u66f4\u9ad8\u5c42\u6b21\u4e0a\u3002<\/span><\/section>\n


<\/p>\n

\u901a\u8fc7\u8c31\u5206\u6790\uff0c\u56fe4A \u663e\u793a\u4e86 50 \u4e2a\u8282\u70b9\u7f51\u7edc\u7684\u5b8f\u7ed3\u70b9\u6d8c\u73b0\u3002\u5982\u679c \u03b1 < 1\uff0c\u5bf9\u5e94\u4e8e\u4e9a\u7ebf\u6027\u4f18\u5148\u8fde\u63a5\u533a\u57df\uff0c\u5728\u8be5\u533a\u57df\u7f51\u7edc\u65e0\u6cd5\u5728\u66f4\u9ad8\u5c3a\u5ea6\u4e0a\u51fa\u73b0\u6709\u6548\u4fe1\u606f\u3002\u4e00\u65e6\u4f18\u5148\u8fde\u63a5\u662f\u8d85\u7ebf\u6027\u7684\uff0c\u56e0\u679c\u6d8c\u73b0\u5c31\u53d8\u5f97\u91cd\u8981\u3002\u90a3\u4e48\uff0c\u4e0d\u540c\u5c3a\u5ea6\u4e0b\u7684\u7f51\u7edc\u7684\u5c5e\u6027\u5b58\u5728\u4ec0\u4e48\u5dee\u5f02\u5462\uff1f<\/strong><\/span><\/p>\n


<\/p>\n

\u6211\u4eec\u4ece\u6709\u6548\u4fe1\u606f<\/span>\uff08EI\uff09<\/span>\u7684\u5b9a\u4e49\u53ef\u77e5\uff0c\u6709\u6548\u4fe1\u606f\u8d8a\u9ad8\u610f\u5473\u7740\u7f51\u7edc\u6709\u66f4\u9ad8\u7684\u786e\u5b9a\u6027\u6216\u66f4\u5c0f\u7684\u7b80\u5e76\u6027\u3002\u786e\u5b9a\u6027\u662f\u7f51\u7edc\u4e2d\u5e73\u5747\u6743\u91cd\u5411\u91cf\u7684\u9999\u519c\u71b5\uff0c\u800c\u6240\u8c13\u7b80\u5e76\u6027\u5219\u662f\u7f51\u7edc\u6743\u503c\u5206\u5e03\u4e0d\u5747\u5300\u7a0b\u5ea6\u7684\u4e00\u4e2a\u5ea6\u91cf\u3002\u4ece\u56fe5B \u53ef\u4ee5\u770b\u51fa\uff0c\u56e0\u679c\u6d8c\u73b0\u7684\u5b8f\u89c2\u7f51\u7edc\u7684\u4e0d\u786e\u5b9a\u6027\u51cf\u5c0f\uff0c\u800c\u56fe5C \u5219\u663e\u793a\u4e86\u5728\u5b8f\u89c2\u5c3a\u5ea6\u4e0b\u7b80\u5e76\u6027\u7684\u51cf\u5c0f\u3002\u8fd9\u610f\u5473\u7740\u968f\u673a\u6e38\u8d70\u8005\u5728\u7f51\u7edc\u7684\u5b8f\u89c2\u5c3a\u5ea6\u4e0a\u9762\u4e34\u66f4\u5c11\u7684\u4e0d\u786e\u5b9a\u6027\u3002\u5728\u56fe5D \u4e2d\uff0c\u5c55\u793a\u4e86\u968f\u673a\u6e38\u8d70\u8005\u7684\u71b5\u7387<\/span>\uff08\u6bcf\u4e00\u65f6\u95f4\u6b65\u4ea7\u751f\u7684\u4e0d\u786e\u5b9a\u5ea6\u5927\u5c0f\uff09<\/span>\u5982\u4f55\u5728\u56e0\u679c\u6d8c\u73b0\u7684\u5b8f\u89c2\u5c3a\u5ea6\u4e0b\u6bd4\u5728\u5fae\u89c2\u5c3a\u5ea6\u4e0b\u4f4e\u5f97\u591a\u3002<\/span><\/p>\n


<\/p>\n

<\/p>\n

\u56fe5. \u4e0d\u540c\u5c3a\u5ea6\u4e0b\u7684\u4f18\u5148\u8fde\u63a5\u7f51\u7edc\u7684\u5c5e\u6027\u3002\uff08A\uff09\u5bf9\u4e8e\u4e0d\u540c\u7684\u03b1 \u503c\u7684\u56e0\u679c\u6d8c\u73b0\u91cf\u3002\uff08B\uff09\u66f4\u9ad8\u7684\u5c3a\u5ea6\u4e0a\u786e\u5b9a\u6027\u7684\u589e\u52a0\u3002\uff08C\uff09\u66f4\u9ad8\u5c3a\u5ea6\u4e0a\u7b80\u5e76\u6027\u7684\u51cf\u5c0f\u3002\uff08D\uff09\u968f\u673a\u6e38\u8d70\u5728\u5fae\u89c2\u548c\u5b8f\u89c2\u5c3a\u5ea6\u4e0a\u5bf9\u7f51\u7edc\u5e73\u7a33\u5206\u5e03\u7684\u71b5\u7387\u3002\uff08E\uff09\u7f51\u7edc\u7684\u6548\u7387\u63d0\u9ad8\u3002\uff08F\uff09\u4e2d\u4ecb\u6027\u4e2d\u5fc3\u6027\u3002\uff08G\uff09\u4e2d\u5fc3\u6027\u3002\uff08H\uff09\u7f51\u7edc\u4e2d\u8282\u70b9\u7684\u53ef\u4ea4\u6d41\u6027\u5e8f\u5217\u71b5\u3002\uff08I\uff09\u7f51\u7edc\u7684\u5e73\u5747\u5ea6\u964d\u4f4e\u3002\uff08J\uff09\u8282\u70b9\u5ea6\u65b9\u5dee\u968f\u7740 \u03b1 \u7684\u589e\u52a0\u800c\u589e\u52a0\u3002\uff08K\uff09\u968f\u7740\u03b1\u7684\u589e\u52a0\uff0c\u5ea6\u5173\u8054\u6027\u964d\u4f4e\u3002\uff08L\uff09\u6838\u7ef4\u6570\u4e0e\u7f51\u7edc\u7684\u7b80\u5e76\u6027\u6709\u5173\u3002\u5b83\u4ece\u6982\u7387\u7684\u89d2\u5ea6\u91cf\u5316\u4e86\u4ece\u4e00\u4e2a\u65f6\u95f4\u6b65\u5230\u4e0b\u4e00\u4e2a\u65f6\u95f4\u6b65\u6536\u655b\u5230\u76f8\u540c\u5206\u5e03\u7684\u968f\u673a\u6e38\u8d70\u7684\u5206\u5e03\u7a7a\u95f4\u3002<\/span><\/section>\n


<\/p>\n

\u5728\u56e0\u679c\u5173\u7cfb\u6d8c\u73b0\u7684\u60c5\u51b5\u4e0b\uff0c\u5b8f\u89c2\u4e0a\u7684\u5168\u5c40\u7f51\u7edc\u6548\u7387\u4e5f\u53ef\u80fd\u66f4\u9ad8<\/span>\uff08\u56fe5E\uff09<\/span>\u3002\u8fd9\u8868\u660e\u5b8f\u8282\u70b9\u901a\u4fe1\u6216\u4ea4\u4e92\u6bd4\u5b83\u4eec\u7684\u5e95\u5c42\u5fae\u89c2\u5c3a\u5ea6\u66f4\u6709\u6548\uff0c\u56e0\u4e3a\u5e73\u5747\u8def\u5f84\u957f\u5ea6\u8981\u4f4e\u5f97\u591a\u3002\u540c\u65f6\uff0c\u5728\u56e0\u679c\u6d8c\u73b0\u540e\uff0c\u7f51\u7edc\u8282\u70b9\u7684\u5e73\u5747\u4e2d\u5fc3\u6027\u663e\u8457\u589e\u52a0<\/span>\uff08\u56fe5F\uff09<\/span>\u3002\u7531\u4e8e\u4e2d\u4ecb\u4e2d\u5fc3\u6027\u53ef\u4ee5\u88ab\u89e3\u91ca\u4e3a\u7f51\u7edc\u4e2d\u8282\u70b9\u5bf9\u4fe1\u606f\u4f20\u8f93\u7684\u63a7\u5236\u7a0b\u5ea6\u7684\u91cf\u5316\uff0c\u8fd9\u8868\u660e\u5b8f\u89c2\u5c3a\u5ea6\u6bd4\u5fae\u89c2\u5c3a\u5ea6\u5bf9\u7f51\u7edc\u4fe1\u606f\u4f20\u8f93\u52a8\u6001\u7684\u63a7\u5236\u7a0b\u5ea6\u66f4\u9ad8\u3002\u968f\u7740 \u03b1 \u7684\u589e\u52a0\uff0c\u5b8f\u8282\u70b9\u7684\u5e73\u5747\u7279\u5f81\u5411\u91cf\u4e2d\u5fc3\u6027\u5f00\u59cb\u589e\u52a0<\/span>\uff08\u56fe5G\uff09<\/span>\u3002<\/span><\/p>\n


<\/p>\n

\u7f51\u7edc\u7279\u6027\u7684\u8fd9\u4e9b\u5e7f\u6cdb\u800c\u663e\u8457\u7684\u53d8\u5316\u8868\u660e\u4e86\u7f51\u7edc\u4e2d\u5b8f\u89c2\u5c3a\u5ea6\u7684\u6709\u6548\u8bc6\u522b\u662f\u591a\u4e48\u91cd\u8981\uff0c\u4ee5\u53ca\u4e3a\u4ec0\u4e48\u91cd\u8981\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u5c3d\u7ba1\u5b8f\u89c2\u5c3a\u5ea6\u548c\u5fae\u89c2\u5c3a\u5ea6\u7684\u8fd9\u4e9b\u5c5e\u6027\u53d1\u751f\u4e86\u53d8\u5316\uff0c\u4f46\u5b83\u4eec\u5728\u968f\u673a\u6e38\u8d70\u52a8\u529b\u5b66\u65b9\u9762\u4ecd\u7136\u662f\u4e00\u81f4\u7684\uff0c\u8fd9\u8868\u660e\u7f51\u7edc\u5c5e\u6027\u901a\u5e38\u4f9d\u8d56\u4e8e\u5c3a\u5ea6\u3002<\/span><\/strong><\/span><\/p>\n

\n
\n

 <\/span><\/p>\n<\/section>\n<\/h3>\n

\n
\n


<\/p>\n

\n
\n

<\/section>\n

<\/section>\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n
\n

4. \u5bfb\u627e\u66f4\u9ad8\u7684\u7f51\u7edc\u5c3a\u5ea6\u5e76\u4e0d\u662f\u793e\u533a\u68c0\u6d4b<\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

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

[1] Hoel, E. P., Albantakis, L., & Tononi, G. (2013). Quantifying causal emergence shows that macro can beat micro. Proceedings of the National Academy of Sciences, 110(49), 19790-19795.<\/span><\/p>\n

[2] Klein, B., & Hoel, E. (2020). The emergence of informative higher scales in complex networks. Complexity.<\/span><\/p>\n


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