{"id":45749,"date":"2025-09-23T18:00:48","date_gmt":"2025-09-23T10:00:48","guid":{"rendered":"https:\/\/case.ntu.edu.tw\/blog\/?p=45749"},"modified":"2025-09-22T09:47:31","modified_gmt":"2025-09-22T01:47:31","slug":"%e5%be%9e%e7%a3%81%e6%80%a7%e5%95%9f%e7%99%bc%e5%88%b0%e7%a5%9e%e7%b6%93%e7%b6%b2%e8%b7%af","status":"publish","type":"post","link":"https:\/\/case.ntu.edu.tw\/blog\/?p=45749","title":{"rendered":"\u5f9e\u78c1\u6027\u555f\u767c\u5230\u795e\u7d93\u7db2\u8def"},"content":{"rendered":"<p><span style=\"color: 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style=\"color: #99cc00;\"><strong>\u81ea\u65cb\u73bb\u7483<\/strong> <strong>\u963b\u632b\u73fe\u8c61<\/strong><\/span><\/h6>\n<p>\u78c1\u6027\u6750\u6599\u7684\u6bcf\u500b\u6676\u683c\u9ede\u4e0a\u5b58\u5728\u8457\u81ea\u65cb\uff0c\u9019\u4e9b\u81ea\u65cb\u7336\u5982\u4e00\u500b\u5c0f\u78c1\u9435\u822c\u5e36\u6709\u78c1\u6027\u3002\u5018\u82e5\u662f\u9435\u78c1\u6027\u6750\u6599\u5247\u5927\u90e8\u5206\u7684\u81ea\u65cb\u90fd\u559c\u6b61\u671d\u540c\u4e00\u65b9\u5411\uff0c\u4e26\u4e14\u8b93\u6574\u9ad4\u7522\u751f\u81ea\u767c\u78c1\u6027\u3002\u5047\u4f7f\u662f\u53cd\u9435\u78c1\u6750\u6599\uff0c\u5247\u6676\u683c\u9ede\u4e0a\u7684\u81ea\u65cb\uff0c\u6703\u559c\u6b61\u4e00\u4e0a\u4e00\u4e0b\u4ea4\u932f\u6392\u5217\uff0c\u5982\u6b64\u78c1\u6027\u6703\u88ab\u76f8\u4e92\u62b5\u92b7\u4e0d\u7522\u751f\u78c1\u6027\u3002\u7136\u800c\uff0c\u6709\u4e00\u7a2e\u6750\u6599\u7a31\u4e4b\u70ba\u81ea\u65cb\u73bb\u7483\uff0c\u88e1\u9762\u7684\u81ea\u65cb\u65b9\u5411\u96dc\u4e82\u7121\u7ae0\u5448\u73fe\u7121\u5e8f\u72c0\u614b\uff0c\u88e1\u9762\u7684\u81ea\u65cb\u53c8\u6703\u76f8\u4e92\u727d\u5236\u3002\u8209\u4f8b\u4f86\u8aaa\uff0c\u6709\u4e09\u500b\u6676\u683c\u9ede\u4e0a\u5206\u5225\u5b58\u5728A\u3001B\u3001C\u4e09\u500b\u81ea\u65cb\uff0c\u5047\u8a2d\u4e09\u500b\u81ea\u65cb\u7686\u559c\u6b61\u53cd\u5411\u6392\u5217\uff0c\u5047\u4f7fA\u671d\u4e0a\uff0cB\u5c31\u6703\u671d\u4e0b\uff0c\u4f46C\u5c31\u6703\u6709\u671d\u4e0a\u8207\u671d\u4e0b\u5169\u7a2e\u9078\u64c7\uff0c\u600e\u9ebc\u9078\u90fd\u7121\u6cd5\u8b93\u4e09\u500b\u81ea\u65cb\u90fd\u76f8\u4e92\u53cd\u5411\uff0c\u8ab0\u4e5f\u6eff\u8db3\u4e0d\u4e86\uff0c\u9019\u500b\u73fe\u8c61\u7a31\u4e4b\u70ba\u963b\u632b\u3002\u56e0\u70ba\u963b\u632b\u73fe\u8c61\u7cfb\u7d71\u7121\u6cd5\u9054\u5230\u6700\u8212\u670d\u7684\u72c0\u614b\uff0c\u4e5f\u5c31\u662f\u80fd\u91cf\u6700\u4f4e\u7684\u72c0\u614b\u3002\u9435\u78c1\u8207\u53cd\u9435\u78c1\u7684\u8a71\u5c31\u6709\u8fa6\u6cd5\u9054\u5230\u6700\u4f4e\u72c0\u614b\u3002\u65e2\u7136\u7121\u6cd5\u9054\u5230\u80fd\u91cf\u6700\u4f4e\u72c0\u614b\uff0c\u53ea\u80fd\u9000\u800c\u6c42\u5176\u6b21\uff0c\u8b93\u7cfb\u7d71\u8655\u65bc\u5c40\u90e8\u6700\u4f4e\u72c0\u614b\u3002\u5c55\u958b\u80fd\u91cf\u5716\u53ef\u4ee5\u767c\u73fe\u5230\u6703\u5b58\u5728\u8a31\u591a\u5c0f\u5c71\u8c37\uff0c\u6709\u8457\u8907\u96dc\u7684\u5730\u5f62\u5716\u3002\u6bcf\u4e00\u500b\u5c0f\u5c71\u8c37\u90fd\u662f\u4ee3\u8868\u8457\u7279\u5b9a\u7684\u81ea\u65cb\u6392\u5217\u65b9\u5f0f\uff0c\u53ef\u4ee5\u7528\u4f86\u5b58\u653e\u4e00\u7d44\u8cc7\u6599\u3002\u6211\u5011\u53ef\u4ee5\u5c07\u81ea\u65cb\u73bb\u7483\u7684\u7cfb\u7d71\uff0c\u7d93\u7531\u6f14\u7b97\u6cd5\u5beb\u5165\u96fb\u8166\u4e2d\uff0c\u7a31\u4e4b\u70ba\u795e\u7d93\u7db2\u8def\u3002<\/p>\n<p>&nbsp;<\/p>\n<h6><span style=\"color: #99cc00;\"><strong>\u4eff\u6548\u795e\u7d93<\/strong> 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Joseph Hopfield)\u57281982\u5e74\u63d0\u51fa\u3002\u5f9e\u81ea\u65cb\u7684\u89d2\u5ea6\u51fa\u767c\uff0c\u53ef\u4ee5\u5c07\u7cfb\u7d71\u7684\u7e3d\u80fd\u91cf\u4ee5\u6613\u8f9b\u6a21\u578b\u63cf\u8ff0\u70ba\u4e0b\u5f0f\u6240\u793a\u3002<\/p>\n<p><img decoding=\"async\" class=\"aligncenter  wp-image-45750\" src=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2025\/09\/\u65b9\u7a0b\u5f0f-1.png\" alt=\"\" width=\"258\" height=\"57\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2025\/09\/\u65b9\u7a0b\u5f0f-1.png 775w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2025\/09\/\u65b9\u7a0b\u5f0f-1-300x66.png 300w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2025\/09\/\u65b9\u7a0b\u5f0f-1-768x169.png 768w\" sizes=\"(max-width: 258px) 100vw, 258px\" 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\/>\n<p><strong>\u53c3\u8003\u6587\u737b<\/strong><\/p>\n<ol>\n<li>Krotov, \u201cA new frontier for Hopfield networks,\u201d<em> Nature Reviews Physics<\/em>, vol. 5, pp. 366\u2013367, 2023.<\/li>\n<li>C. Marullo and E. Agliari, \u201cBoltzmann machines as generalized Hopfield networks: a review of recent results and outlooks,\u201d <em>Entropy<\/em>, vol. 23, p. 34, 2021.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u6211\u5011\u7684\u5927\u8166\u80fd\u5728\u6a21\u7cca\u3001\u5c40\u90e8\u8a0a\u606f\u4e2d\u8fc5\u901f\u8fa8\u8b58\u4e8b\u7269\uff0c\u9019\u7a2e\u5f37\u5927\u7684\u5b78\u7fd2\u8207\u8a18\u61b6\u80fd\u529b\u6210\u70ba\u4eba\u5de5\u667a\u6167\u6a21\u4eff\u7684\u5c0d\u8c61\u3002\u672c\u6587\u4ecb\u7d39\u4e00\u7a2e\u7531\u78c1\u6027\u6750\u6599\u4e2d\u81ea\u65cb\u73bb\u7483\u555f\u767c\u7684\u795e\u7d93\u7db2\u8def\u6a21\u578b\uff0c\u5373Hopfield\u7db2\u8def\u3002\u81ea\u65cb\u73bb\u7483\u56e0\u5167\u90e8\u81ea\u65cb\u7121\u6cd5\u6eff\u8db3\u5f7c\u6b64\u76f8\u65a5\u7684\u6392\u5217\u9700\u6c42\uff0c\u5448\u73fe\u51fa\u591a\u500b\u7a69\u5b9a\u4f46\u4e0d\u552f\u4e00\u7684\u80fd\u91cf\u8c37\uff0c\u6bcf\u500b\u8c37\u53ef\u8996\u70ba\u4e00\u7a2e\u8a18\u61b6\u72c0\u614b\u3002Hopfield\u7db2\u8def\u4eff\u6b64\u539f\u7406\uff0c\u5c07\u795e\u7d93\u5143\u72c0\u614b\u985e\u6bd4\u70ba\u81ea\u65cb\uff0c\u900f\u904e\u5f7c\u6b64\u9593\u7684\u9023\u7d50\u5f37\u5ea6\u5132\u5b58\u8cc7\u8a0a\uff0c\u4e26\u5728\u64fe\u52d5\u5f8c\u81ea\u52d5\u56de\u5fa9\u81f3\u7a69\u5b9a\u8a18\u61b6\u3002\u96d6\u7136\u8a72\u7db2\u8def\u6709\u5bb9\u91cf\u9650\u5236\uff0c\u4f46\u5b83\u5960\u5b9a\u4e86\u795e\u7d93\u8a08\u7b97\u7684\u7269\u7406\u57fa\u790e\u3002\u96a8\u8457\u6df1\u5ea6\u5b78\u7fd2\u8207\u65b0\u578b\u67b6\u69cb\u7684\u51fa\u73fe\uff0c\u9019\u7a2e\u7531\u7269\u7406\u555f\u767c\u7684\u795e\u7d93\u7db2\u8def\u4e0d\u50c5\u62d3\u5c55\u4e86\u6211\u5011\u5c0d\u4eba\u5de5\u667a\u6167\u7684\u7406\u89e3\uff0c\u4e5f\u8b93\u96fb\u8166\u8a18\u61b6\u7cfb\u7d71\u9081\u5411\u66f4\u5f37\u5927\u8207\u62bd\u8c61\u7684\u5c64\u6b21\u3002<\/p>\n","protected":false},"author":20,"featured_media":45751,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3293,39,6512],"tags":[2869,3792,7050],"aioseo_notices":[],"jetpack_featured_media_url":"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2025\/09\/\u5f9e\u78c1\u6027\u5230\u795e\u7d93\u7db2\u8def-scaled.jpg","_links":{"self":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/45749"}],"collection":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/users\/20"}],"replies":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=45749"}],"version-history":[{"count":1,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/45749\/revisions"}],"predecessor-version":[{"id":45752,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/45749\/revisions\/45752"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/media\/45751"}],"wp:attachment":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=45749"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=45749"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=45749"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}