{"id":5541,"date":"2025-01-14T11:30:42","date_gmt":"2025-01-14T03:30:42","guid":{"rendered":"https:\/\/nullthought.net\/?p=5541"},"modified":"2025-01-16T14:51:31","modified_gmt":"2025-01-16T06:51:31","slug":"%e5%a4%8d%e5%80%bc%e5%be%aa%e7%8e%af%e7%a5%9e%e7%bb%8f%e7%bd%91%e7%bb%9c%ef%bc%88complex-valued-recurrent-neural-network%ef%bc%8ccv-rnn%ef%bc%89%ef%bc%9a%e4%bb%8e%e6%95%b0%e5%ad%a6%e5%b1%82%e9%9d%a2","status":"publish","type":"post","link":"https:\/\/nullthought.net\/?p=5541","title":{"rendered":"\u590d\u503c\u5faa\u73af\u795e\u7ecf\u7f51\u7edc\uff08Complex-Valued Recurrent Neural Network\uff0ccv-RNN\uff09\uff1a\u4ece\u6570\u5b66\u5c42\u9762\u7406\u89e3\u795e\u7ecf\u7f51\u7edc\u7684\u51b3\u7b56\u8fc7\u7a0b"},"content":{"rendered":"\n<p>\u8bba\u6587<a href=\"https:\/\/www.pnas.org\/doi\/epdf\/10.1073\/pnas.2321319121\" target=\"_blank\" rel=\"noreferrer noopener\">Image segmentation with traveling waves in an exactly solvablerecurrent neural network<\/a>\u4ecb\u7ecd\u4e86\u4e00\u79cd\u65b0\u578b\u6570\u5b66\u6280\u672f\uff0c\u65e8\u5728\u6253\u5f00\u4eba\u5de5\u667a\u80fd\u7cfb\u7edf\u4e2d\u7684\u201c\u9ed1\u7bb1\u201d\uff0c\u4ece\u6570\u5b66\u5c42\u9762\u7406\u89e3\u795e\u7ecf\u7f51\u7edc\u7684\u51b3\u7b56\u8fc7\u7a0b\u3002<\/p>\n\n\n\n<p>\u5728\u5f53\u4eca\u6280\u672f\u9886\u57df\uff0c\u4ece\u8bed\u97f3\u52a9\u624b\uff08\u5982Siri\u548cChatGPT\uff09\u5230\u533b\u7597\u6210\u50cf\u548c\u81ea\u52a8\u9a7e\u9a76\u6c7d\u8f66\uff0c\u8bb8\u591a\u5173\u952e\u6280\u672f\u90fd\u4f9d\u8d56\u4e8e\u673a\u5668\u5b66\u4e60\u3002\u7136\u800c\uff0c\u5c3d\u7ba1\u795e\u7ecf\u7f51\u7edc\u662f\u673a\u5668\u5b66\u4e60\u7cfb\u7edf\u7684\u6838\u5fc3\uff0c\u4f46\u5b83\u4eec\u7684\u5185\u90e8\u8fd0\u4f5c\u673a\u5236\u4e00\u76f4\u96be\u4ee5\u88ab\u5b8c\u5168\u7406\u89e3\uff0c\u8fd9\u4f7f\u5f97\u8fd9\u4e9b\u7f51\u7edc\u88ab\u79f0\u4e3a\u201c<a href=\"https:\/\/nullthought.net\/?p=2959\" target=\"_blank\" rel=\"noreferrer noopener\">\u9ed1\u7bb1<\/a>\u201d\u3002\u795e\u7ecf\u7f51\u7edc\u6a21\u4eff\u4eba\u8111\u7684\u7ed3\u6784\u548c\u529f\u80fd\uff0c\u901a\u8fc7\u5c42\u5c42\u975e\u7ebf\u6027\u8ba1\u7b97\u5b8c\u6210\u4efb\u52a1\uff0c\u4f46\u5177\u4f53\u6bcf\u4e00\u6b65\u662f\u5982\u4f55\u8fbe\u6210\u7684\uff0c\u4ecd\u7136<a href=\"https:\/\/nullthought.net\/?p=2559\" target=\"_blank\" rel=\"noreferrer noopener\">\u7f3a\u4e4f\u76f4\u89c2\u7684\u89e3\u91ca<\/a>\u3002\u8fd9\u79cd\u201c\u9ed1\u7bb1\u201d\u7279\u6027\u5bfc\u81f4\u7814\u7a76\u4eba\u5458\u548c\u5f00\u53d1\u8005\u5728\u4fe1\u4efb\u548c\u4f18\u5316\u8fd9\u4e9b\u7cfb\u7edf\u65f6\u9762\u4e34\u56f0\u96be\uff0c\u5c24\u5176\u662f\u5728\u6d89\u53ca\u9ad8\u98ce\u9669\u7684\u9886\u57df\uff08\u5982\u533b\u7597\u3001\u91d1\u878d\u548c\u5b89\u5168\uff09\u65f6\u3002<\/p>\n\n\n\n<p>\u9488\u5bf9\u8fd9\u4e00\u95ee\u9898\uff0cWestern University\u6570\u5b66\u6559\u6388\u83b1\u5c14\u00b7\u7a46\u52d2\uff08Lyle Muller\uff09\u53ca\u5176\u56e2\u961f\u63d0\u51fa\u4e86\u4e00\u79cd\u521b\u65b0\u65b9\u6cd5\u3002\u4ed6\u4eec\u5f00\u53d1\u4e86\u80fd\u591f\u89e3\u51b3\u795e\u7ecf\u7f51\u7edc\u5185\u90e8\u6d3b\u52a8\u65b9\u7a0b\u7684\u6570\u5b66\u6280\u672f\uff0c\u4ece\u800c\u4f7f\u7f51\u7edc\u7684\u51b3\u7b56\u8fc7\u7a0b\u53ef\u88ab\u5168\u9762\u89e3\u6790\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"621\" src=\"https:\/\/nullthought.net\/wp-content\/uploads\/2025\/01\/image-13-1024x621.png\" alt=\"\" class=\"wp-image-5542\" srcset=\"https:\/\/nullthought.net\/wp-content\/uploads\/2025\/01\/image-13-1024x621.png 1024w, https:\/\/nullthought.net\/wp-content\/uploads\/2025\/01\/image-13-300x182.png 300w, https:\/\/nullthought.net\/wp-content\/uploads\/2025\/01\/image-13-768x466.png 768w, https:\/\/nullthought.net\/wp-content\/uploads\/2025\/01\/image-13.png 1127w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><a href=\"https:\/\/www.pnas.org\/doi\/epdf\/10.1073\/pnas.2321319121\" target=\"_blank\" rel=\"noreferrer noopener\">Image segmentation with traveling waves in an exactly solvablerecurrent neural network<\/a><\/figcaption><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">\u4e00\u3001\u6280\u672f\u65b9\u6cd5\u4e0e\u6570\u5b66\u6a21\u578b<\/h4>\n\n\n\n<h5 class=\"wp-block-heading\">\uff08\u4e00\uff09\u6a21\u578b\u7ed3\u6784\u4e0e\u8bbe\u8ba1<\/h5>\n\n\n\n<p>\u7814\u7a76\u56e2\u961f\u5f00\u53d1\u4e86\u4e00\u79cd\u57fa\u4e8e\u590d\u503c\u5faa\u73af\u795e\u7ecf\u7f51\u7edc\uff08Complex-Valued Recurrent Neural Network\uff0ccv-RNN\uff09\u7684\u65b0\u578b\u7f51\u7edc\u6a21\u578b\u3002\u5176\u5173\u952e\u7279\u70b9\u5305\u62ec\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u8f93\u5165\u4e0e\u8282\u70b9\u6620\u5c04\uff1a<\/strong> \u8f93\u5165\u56fe\u50cf\u7684\u6bcf\u4e2a\u50cf\u7d20\u88ab\u6295\u5c04\u5230cv-RNN\u4e2d\u7684\u4e00\u4e2a\u8282\u70b9\u4e0a\uff0c\u8fd9\u4e9b\u8282\u70b9\u88ab\u6392\u5217\u6210\u4e00\u4e2a\u4e8c\u7ef4\u7f51\u683c\u3002<\/li>\n\n\n\n<li><strong>\u5faa\u73af\u8fde\u63a5\u6743\u91cd\uff1a<\/strong> \u8282\u70b9\u4e4b\u95f4\u7684\u5faa\u73af\u8fde\u63a5\u6743\u91cd\u4ee5\u9ad8\u65af\u51fd\u6570\u8870\u51cf\uff0c\u6743\u91cd\u7684\u5f3a\u5f31\u4e0e\u8282\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u6210\u53cd\u6bd4\u3002\u8be5\u8bbe\u8ba1\u6a21\u62df\u4e86\u7269\u7406\u7cfb\u7edf\u4e2d\u7684\u5c40\u90e8\u76f8\u4e92\u4f5c\u7528\u89c4\u5f8b\uff0c\u4f7f\u7f51\u7edc\u80fd\u591f\u6355\u83b7\u56fe\u50cf\u4e2d\u7684\u5c40\u90e8\u7279\u5f81\u3002<\/li>\n\n\n\n<li><strong>\u590d\u6570\u52a8\u6001\u8868\u793a\uff1a<\/strong> \u6bcf\u4e2a\u8282\u70b9\u7684\u6d3b\u52a8\u7528\u590d\u5e73\u9762\u4e0a\u7684\u76f8\u4f4d\u548c\u5e45\u5ea6\u8868\u793a\uff0c\u8f93\u5165\u56fe\u50cf\u50cf\u7d20\u8c03\u5236\u8282\u70b9\u7684\u81ea\u7136\u9891\u7387\u3002\u8fd9\u79cd\u8bbe\u8ba1\u5141\u8bb8\u7f51\u7edc\u6355\u6349\u8f93\u5165\u6570\u636e\u7684\u590d\u6742\u65f6\u7a7a\u52a8\u6001\u7279\u5f81\u3002<\/li>\n\n\n\n<li><strong>\u65f6\u7a7a\u52a8\u6001\uff1a<\/strong> \u7f51\u7edc\u4e2d\u7684\u8282\u70b9\u901a\u8fc7\u5f7c\u6b64\u7684\u5faa\u73af\u8fde\u63a5\uff0c\u751f\u6210\u4e09\u79cd\u72ec\u7279\u7684\u65f6\u7a7a\u6a21\u5f0f\uff1a\u4e00\u79cd\u5bf9\u5e94\u80cc\u666f\uff0c\u4e00\u79cd\u5bf9\u5e94\u8f93\u5165\u56fe\u50cf\u4e2d\u7684\u7279\u5b9a\u51e0\u4f55\u5f62\u72b6\uff08\u5982\u6b63\u65b9\u5f62\u6216\u4e09\u89d2\u5f62\uff09\uff0c\u53e6\u4e00\u79cd\u5bf9\u5e94\u56fe\u50cf\u4e2d\u7684\u624b\u5199\u6570\u5b57\u3002<\/li>\n<\/ol>\n\n\n\n<h5 class=\"wp-block-heading\">\uff08\u4e8c\uff09\u6570\u5b66\u89e3\u6790\u4e0e\u539f\u7406<\/h5>\n\n\n\n<p>\u901a\u8fc7\u89e3\u6790\u7f51\u7edc\u7684\u5185\u90e8\u52a8\u6001\uff0c\u7814\u7a76\u56e2\u961f\u5b9e\u73b0\u4e86\u4ee5\u4e0b\u5173\u952e\u7a81\u7834\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u65b9\u7a0b\u6c42\u89e3\uff1a<\/strong> \u7814\u7a76\u4eba\u5458\u6784\u5efa\u4e86\u63cf\u8ff0cv-RNN\u6d3b\u52a8\u7684\u6570\u5b66\u65b9\u7a0b\uff0c\u5e76\u6210\u529f\u6c42\u89e3\u3002\u8fd9\u4e9b\u65b9\u7a0b\u63cf\u8ff0\u4e86\u7f51\u7edc\u8282\u70b9\u7684\u6d3b\u52a8\u968f\u65f6\u95f4\u6f14\u53d8\u7684\u89c4\u5f8b\uff0c\u63ed\u793a\u4e86\u8f93\u5165\u56fe\u50cf\u5982\u4f55\u4e0e\u7f51\u7edc\u7684\u52a8\u6001\u7279\u6027\u76f8\u4e92\u4f5c\u7528\u3002<\/li>\n\n\n\n<li><strong>\u7b80\u5316\u4e0e\u4f18\u5316\uff1a<\/strong> \u7814\u7a76\u56e2\u961f\u7b80\u5316\u4e86\u4f20\u7edf\u7f51\u7edc\u7684\u590d\u6742\u8ba1\u7b97\u8fc7\u7a0b\uff0c\u4f7f\u5f97\u7f51\u7edc\u4e0d\u4ec5\u5177\u5907\u66f4\u9ad8\u7684\u7075\u6d3b\u6027\uff0c\u8fd8\u5728\u5904\u7406\u672a\u89c1\u8fc7\u7684\u65b0\u8f93\u5165\u65f6\u8868\u73b0\u51fa\u8272\u3002\u4f8b\u5982\uff0c\u8be5\u7f51\u7edc\u80fd\u591f\u6210\u529f\u5206\u5272\u4ece\u672a\u8bad\u7ec3\u8fc7\u7684\u81ea\u7136\u573a\u666f\u56fe\u50cf\uff0c\u5982\u5317\u6781\u718a\u7684\u7167\u7247\u3002<\/li>\n\n\n\n<li><strong>\u52a8\u6001\u6a21\u5f0f\u5206\u6790\uff1a<\/strong> \u5b9e\u9a8c\u663e\u793a\uff0ccv-RNN\u53ef\u4ee5\u5728\u8f93\u5165\u56fe\u50cf\u4e2d\u4ea7\u751f\u6e05\u6670\u7684\u5206\u5272\u6548\u679c\uff0c\u5177\u4f53\u8868\u73b0\u4e3a\u8282\u70b9\u7684\u52a8\u6001\u6d3b\u52a8\u80fd\u591f\u533a\u5206\u56fe\u50cf\u4e2d\u7684\u80cc\u666f\u548c\u76ee\u6807\u3002\u8fd9\u79cd\u80fd\u529b\u6765\u81ea\u7f51\u7edc\u4e2d\u7cbe\u786e\u8bbe\u8ba1\u7684\u590d\u6570\u52a8\u6001\u4e0e\u5faa\u73af\u8fde\u63a5\u6a21\u5f0f\u3002<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading\">\u4e8c\u3001\u5b9e\u9a8c\u9a8c\u8bc1\u4e0e\u7ed3\u679c<\/h4>\n\n\n\n<p>\u7814\u7a76\u4eba\u5458\u9996\u5148\u5728\u7b80\u5355\u7684\u51e0\u4f55\u56fe\u50cf\u4e0a\u9a8c\u8bc1\u4e86cv-RNN\u7684\u6027\u80fd\uff0c\u4f8b\u5982\u5206\u5272\u7531\u6b63\u65b9\u5f62\u548c\u4e09\u89d2\u5f62\u7ec4\u6210\u7684\u56fe\u50cf\u3002\u7f51\u7edc\u80fd\u591f\u51c6\u786e\u5730\u5c06\u8fd9\u4e9b\u56fe\u50cf\u5212\u5206\u4e3a\u76ee\u6807\u533a\u57df\u548c\u80cc\u666f\u533a\u57df\u3002<\/p>\n\n\n\n<p>\u968f\u540e\uff0c\u7814\u7a76\u56e2\u961f\u8fdb\u4e00\u6b65\u6d4b\u8bd5\u4e86\u7f51\u7edc\u5728\u81ea\u7136\u56fe\u50cf\u4e0a\u7684\u8868\u73b0\uff0c\u5305\u62ec\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5317\u6781\u718a\u5728\u96ea\u5730\u884c\u8d70\u7684\u7167\u7247<\/li>\n\n\n\n<li>\u91ce\u5916\u9e1f\u7c7b\u7684\u56fe\u7247<\/li>\n<\/ul>\n\n\n\n<p>\u8fd9\u4e9b\u5b9e\u9a8c\u8868\u660e\uff0ccv-RNN\u4e0d\u4ec5\u9002\u7528\u4e8e\u4eba\u5de5\u5408\u6210\u7684\u7b80\u5355\u6570\u636e\u96c6\uff0c\u8fd8\u53ef\u4ee5\u5904\u7406\u66f4\u590d\u6742\u7684\u81ea\u7136\u573a\u666f\u3002\u8fd9\u79cd\u80fd\u529b\u4f7f\u5f97\u8be5\u6280\u672f\u5177\u6709\u66f4\u5e7f\u6cdb\u7684\u5e94\u7528\u6f5c\u529b\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u4e09\u3001\u8de8\u5b66\u79d1\u5e94\u7528\u4e0e\u62d3\u5c55<\/h4>\n\n\n\n<p>\u7814\u7a76\u56e2\u961f\u63d0\u51fa\uff0c\u8fd9\u79cd\u6570\u5b66\u6280\u672f\u4e0d\u4ec5\u9650\u4e8e\u56fe\u50cf\u5206\u5272\u4efb\u52a1\uff0c\u8fd8\u5728\u5176\u4ed6\u9886\u57df\u5c55\u73b0\u4e86\u5f3a\u5927\u7684\u9002\u5e94\u6027\u3002\u4f8b\u5982\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u903b\u8f91\u8fd0\u7b97\u4e0e\u4fe1\u606f\u5b89\u5168\uff1a<\/strong> \u5728\u76f8\u5173\u7814\u7a76\u4e2d\uff0ccv-RNN\u88ab\u7528\u4e8e\u6267\u884c\u57fa\u672c\u903b\u8f91\u8fd0\u7b97\u3001\u5b89\u5168\u4fe1\u606f\u4f20\u9012\u548c\u8bb0\u5fc6\u529f\u80fd\u3002\u8fd9\u4e9b\u4efb\u52a1\u7684\u6210\u529f\u8868\u660e\uff0c\u8be5\u7f51\u7edc\u5177\u6709\u5904\u7406\u591a\u4efb\u52a1\u7684\u6f5c\u529b\u3002<\/li>\n\n\n\n<li><strong>\u751f\u7269\u795e\u7ecf\u7f51\u7edc\u7ed3\u5408\uff1a<\/strong> 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