{"id":38848,"date":"2022-12-02T22:39:43","date_gmt":"2022-12-02T14:39:43","guid":{"rendered":"https:\/\/swarma.org\/?p=38848"},"modified":"2022-12-02T22:39:43","modified_gmt":"2022-12-02T14:39:43","slug":"hopfield%e6%a8%a1%e5%9e%8b%e7%9a%84%e7%bb%9f%e8%ae%a1%e7%89%a9%e7%90%86%ef%bc%88%e4%ba%8c%ef%bc%89-%e5%91%a8%e5%85%ad%e7%9b%b4%e6%92%ad%c2%b7%e7%a5%9e%e7%bb%8f%e7%bd%91%e7%bb%9c%e7%9a%84%e7%bb%9f","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=38848","title":{"rendered":"Hopfield\u6a21\u578b\u7684\u7edf\u8ba1\u7269\u7406\uff08\u4e8c\uff09 | \u5468\u516d\u76f4\u64ad\u00b7\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66\u8bfe\u7a0b\u7b2c\u4e5d\u8bb2"},"content":{"rendered":"<div class='wxsyncmain'>\n<section powered-by=\"xiumi.us\" style=\"margin-bottom: 0px;outline: 0px;letter-spacing: 0.544px;white-space: normal;color: rgb(63, 63, 63);font-family: PingFangSC-light;font-size: 15px;background-color: rgb(255, 255, 255);visibility: visible;\" data-mpa-powered-by=\"yiban.io\">\n<section style=\"outline: 0px;display: inline-block;width: 661px;vertical-align: top;background-color: rgb(246, 246, 246);visibility: visible;\">\n<section style=\"outline: 0px;visibility: visible;\">\n<p style=\"text-align: center;\"><img class=\"rich_pages wxw-img js_insertlocalimg\" data-backh=\"392\" data-backw=\"578\" data-ratio=\"0.67734375\" data-s=\"300,640\"  data-type=\"jpeg\" data-w=\"1280\" style=\"width: 100%;height: auto;\" src=\"\/wp-content\/uploads\/2022\/12\/wxsync-2022-12-e8caa2f70f1d474fb5992754b36e5dec.jpeg\"  \/><\/p>\n<\/section>\n<section powered-by=\"xiumi.us\" style=\"margin-top: 10px;outline: 0px;letter-spacing: 0.544px;visibility: visible;\">\n<section style=\"outline: 0px;width: 661px;visibility: visible;\">\n<section style=\"padding-right: 3px;outline: 0px;float: left;line-height: 1;visibility: visible;\">\n<section powered-by=\"xiumi.us\" style=\"outline: 0px;text-align: left;visibility: visible;\">\n<section style=\"padding-left: 10px;outline: 0px;display: inline-block;width: auto;vertical-align: top;min-width: 10%;height: auto;border-left: 3px solid rgb(33, 166, 210);border-bottom-left-radius: 0px;line-height: 0;visibility: visible;\">\n<section powered-by=\"xiumi.us\" style=\"outline: 0px;transform: translate3d(-13px, 0px, 0px);visibility: visible;\">\n<section style=\"outline: 0px;display: inline-block;width: 25px;height: 10px;vertical-align: top;overflow: hidden;line-height: 0;border-style: solid solid none;border-width: 3px 3px 2px;border-radius: 0px;border-color: rgb(33, 166, 210) rgb(33, 166, 210) rgb(15, 76, 129);visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<\/section>\n<section powered-by=\"xiumi.us\" style=\"outline: 0px;transform: translate3d(-1px, 0px, 0px);visibility: visible;\">\n<section style=\"outline: 0px;text-align: justify;color: rgb(33, 166, 210);font-size: 16px;line-height: 1.5;visibility: visible;\">\n<p style=\"outline: 0px;visibility: visible;\"><strong style=\"outline: 0px;visibility: visible;\">\u5bfc\u8bed<\/strong><\/p>\n<\/section>\n<\/section>\n<section powered-by=\"xiumi.us\" style=\"outline: 0px;transform: translate3d(-13px, 0px, 0px) rotateX(180deg);visibility: visible;\">\n<section style=\"outline: 0px;display: inline-block;width: 24px;height: 10px;vertical-align: top;overflow: hidden;line-height: 0;border-style: solid solid none;border-width: 3px 3px 2px;border-radius: 0px;border-color: rgb(33, 166, 210) rgb(33, 166, 210) rgb(15, 76, 129);visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<section style=\"padding-right: 4px;padding-left: 4px;outline: 0px;clear: right;box-shadow: rgb(0, 0, 0) 0px 0px 0px;visibility: visible;min-height: 4.5em !important;\">\n<section powered-by=\"xiumi.us\" style=\"margin-top: 5px;margin-bottom: 5px;outline: 0px;visibility: visible;\">\n<section style=\"padding-right: 8px;padding-left: 8px;outline: 0px;font-size: 13px;line-height: 2;letter-spacing: 0.544px;visibility: visible;\">\n<p style=\"outline: 0px;clear: none;line-height: 2em;visibility: visible;\"><strong style=\"text-indent: 0em;letter-spacing: 0.544px;font-size: 15px;\"><span style=\"font-size: 13px;letter-spacing: 0.544px;text-decoration-style: solid;text-decoration-color: rgb(63, 63, 63);\">\u7edf\u8ba1\u7269\u7406\u65b9\u6cd5\u662f\u4e00\u5ea7\u67b6\u8d77\u5fae\u89c2\u4f5c\u7528\u5230\u5b8f\u89c2\u6d8c\u73b0\u7684\u6865\u6881\uff0c2021\u5e74\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u5f97\u4e3b\u5e15\u91cc\u897f\u5728\u65e0\u5e8f\u7cfb\u7edf\u65b9\u9762\u4f5c\u51fa\u5f00\u521b\u4e4b\u4e3e\uff0c\u4ed6\u63d0\u51fa\u590d\u672c\u5bf9\u79f0\u7834\u7f3a\u65b9\u6cd5\u89e3\u51b3\u81ea\u65cb\u73bb\u7483\u95ee\u9898\uff0c\u8fd9\u4e00\u65b9\u6cd5\u4e5f\u5bf9\u795e\u7ecf\u7f51\u7edc\u7b49\u4ea4\u53c9\u5b66\u79d1\u4ea7\u751f\u6df1\u539a\u5f71\u54cd\uff0c\u6fc0\u53d1\u5b66\u8005\u5bf9\u4eba\u5de5\u667a\u80fd\u548c\u4eba\u8111\u7b49\u590d\u6742\u7cfb\u7edf\u7684\u8fdb\u4e00\u6b65\u7814\u7a76\u3002\u7531\u4e2d\u5c71\u5927\u5b66\u9ec4\u6d77\u5e73\u6559\u6388\u7ec4\u7ec7\u7684<\/span><\/strong><strong><span style=\"letter-spacing: 0.544px;\">\u3010<a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247628086&amp;idx=2&amp;sn=32c39ccfc209a0ac02d8995e0a64f54b&amp;chksm=e899afbbdfee26ad74fe0809f477e061095857882da0dde32640c94906424e20818d3404dd6a&amp;scene=21#wechat_redirect\" textvalue=\"\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66\" linktype=\"text\" imgurl=\"\" imgdata=\"null\" data-itemshowtype=\"0\" tab=\"innerlink\" data-linktype=\"2\" rel=\"noopener noreferrer\">\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66<\/a>\u3011\u7cfb\u5217\u8bfe\u7a0b<\/span><\/strong><strong style=\"text-indent: 0em;letter-spacing: 0.544px;font-size: 15px;\"><span style=\"font-size: 13px;letter-spacing: 0.544px;text-decoration-style: solid;text-decoration-color: rgb(63, 63, 63);\">\uff0c\u7cfb\u7edf\u6027\u68b3\u7406\u7edf\u8ba1\u529b\u5b66\u7684\u57fa\u672c\u539f\u7406\u53ca\u5176\u5728\u7406\u89e3\u795e\u7ecf\u7f51\u7edc\u5185\u90e8\u5de5\u4f5c\u539f\u7406\u7684\u5e94\u7528\uff0c\u81ea2022\u5e749\u6708\u6301\u7eed\u52302023\u5e746\u6708\uff0c\u5468\u516d\u6388\u8bfe\u3002\u8bfe\u7a0b\u89c6\u9891\u5c06\u5728\u96c6\u667a\u5b66\u56ed\u7f51\u7ad9\u540c\u6b65\uff0c\u8d2d\u8bfe\u56de\u770b\u5f55\u64ad\u8bf7\u626b\u4e8c\u7ef4\u7801\u6216\u4e0b\u62c9\u81f3\u6587\u672b\u62a5\u540d\u3002<\/span><\/strong><\/p>\n<p style=\"outline: 0px;clear: none;line-height: 2em;visibility: visible;\"><strong style=\"text-indent: 0em;letter-spacing: 0.544px;font-size: 15px;\"><span style=\"font-size: 13px;letter-spacing: 0.544px;text-decoration-style: solid;text-decoration-color: rgb(63, 63, 63);\"><strong><span style=\"color: rgb(63, 63, 63);letter-spacing: 0.544px;text-decoration: none solid rgb(63, 63, 63);\"><br  \/><\/span><\/strong><\/span><\/strong><\/p>\n<p style=\"outline: 0px;clear: none;line-height: 2em;visibility: visible;\"><strong style=\"text-indent: 0em;letter-spacing: 0.544px;font-size: 15px;\"><span style=\"font-size: 13px;letter-spacing: 0.544px;text-decoration-style: solid;text-decoration-color: rgb(63, 63, 63);\">12\u67083\u65e5\uff08\u5468\u516d\uff0914:00-16:00 \u5c06\u8fdb\u884c\u7cfb\u5217\u8bfe\u7a0b\u7684\u7b2c\u4e5d\u8bb2\uff0c\u5173\u4e8e Hopfield \u6a21\u578b\u7b2c\u4e8c\u6b21\u8bfe\u7a0b\u3002Hopfield \u6a21\u578b\u53ef\u4ee5\u5efa\u6a21\u8054\u60f3\u8bb0\u5fc6\u8fc7\u7a0b\uff0c\u56e0\u6b64\u5bf9\u8ba1\u7b97\u795e\u7ecf\u79d1\u5b66\uff0c\u4e43\u81f3\u4e8e\u73b0\u4ee3\u673a\u5668\u5b66\u4e60\u90fd\u6709\u5f88\u91cd\u8981\u7684\u610f\u4e49\u3002\u672c\u8282\u8bfe\u6211\u4eec\u7ee7\u7eed\u5b66\u4e60 Hopfield \u6a21\u578b\u7684\u89e3\u6790\u8ba1\u7b97\uff0c\u63a5\u7740\u4e0a\u8282\u8bfe\u7684\u5185\u5bb9\u5c06\u8bb2\u89e3\u978d\u70b9\u5206\u6790\uff0c\u4ee5\u53ca Hopfield \u6a21\u578b\u7684\u76f8\u56fe\uff0c\u5e76\u7ed3\u5408 21 \u5e74\u7684\u6700\u65b0\u5de5\u4f5c\u5bf9\u62d3\u5c55\u7684 Hopfield \u6a21\u578b\u8fdb\u884c\u4ecb\u7ecd\u3002\u672c\u8282\u8bfe\u7a0b\u4f1a\u5728\u96c6\u667a\u5b66\u56ed\u89c6\u9891\u53f7\u548cB\u7ad9\u76f4\u64ad\uff0c\u9884\u7ea6\u53ca\u4ed8\u8d39\u62a5\u540d\u65b9\u5f0f\u89c1\u4e0b\u6587\u3002<\/span><\/strong><\/p>\n<\/section>\n<section style=\"padding-right: 8px;padding-left: 8px;outline: 0px;font-size: 13px;line-height: 2;letter-spacing: 0.544px;visibility: visible;\">\n<section><strong style=\"letter-spacing: 0.544px;text-align: justify;text-indent: 0em;font-size: 15px;\"><\/strong><\/section>\n<section class=\"channels_iframe_wrp\"><mpvideosnap class=\"js_uneditable custom_select_card channels_live_iframe\" data-pluginname=\"videosnap\" data-headimgurl=\"https:\/\/wx.qlogo.cn\/finderhead\/ajNVdqHZLLDkhV6hTgHRHksyS5fIwv7eAAhSpic1M5pDQQG7h9VN84g\/0\" data-username=\"v2_060000231003b20faec8c5ea891bc3dcc80ce934b077144e6416ea45d7e19afb464dfa855442@finder\" data-nickname=\"\u96c6\u667a\u5b66\u56ed\" data-desc=\"\u5c06\u572812\u670803\u65e5 14:00 \u76f4\u64ad\" data-intro=\"Hopfield\u6a21\u578b\u7684\u7edf\u8ba1\u7269\u7406\uff08\u4e8c\uff09\" data-noticeid=\"finderlivenotice-v2_060000231003b20faec8c5ea891bc3dcc80ce934b077144e6416ea45d7e19afb464dfa855442@finder-1669953663388676-1610590779\" data-type=\"live\"><\/mpvideosnap><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<section powered-by=\"xiumi.us\" style=\"margin-top: 10px;outline: 0px;visibility: visible;\">\n<section style=\"outline: 0px;width: 661px;visibility: visible;\">\n<section style=\"outline: 0px;clear: both;line-height: 0;visibility: visible;\">\n<section style=\"outline: 0px;line-height: 0;width: 0px;visibility: visible;\"><svg viewbox=\"0 0 1 1\" style=\"vertical-align: top;visibility: visible;\"><\/svg><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<section powered-by=\"xiumi.us\" style=\"margin-top: 10px;margin-bottom: 10px;outline: 0px;letter-spacing: 0.544px;white-space: normal;color: rgb(63, 63, 63);font-family: PingFangSC-light;font-size: 15px;background-color: rgb(255, 255, 255);text-align: center;visibility: visible;\">\n<section style=\"outline: 0px;vertical-align: middle;display: inline-block;line-height: 0;visibility: visible;\"><img class=\"rich_pages wxw-img\" data-fileid=\"100098753\" data-ratio=\"0.07314814814814814\"  data-type=\"png\" data-w=\"1080\" style=\"outline: 0px;box-sizing: border-box;vertical-align: middle;display: initial;visibility: visible !important;width: 677px !important;\" src=\"\/wp-content\/uploads\/2022\/12\/wxsync-2022-12-b8becffe5d1a6c877515894a0e4f617b.png\"  \/><strong style=\"outline: 0px;letter-spacing: 0.544px;text-align: right;font-size: 13px;color: rgb(0, 0, 0);visibility: visible;\"><\/strong><\/section>\n<\/section>\n<section powered-by=\"xiumi.us\" style=\"margin-top: 0pt;margin-bottom: 0pt;outline: 0px;letter-spacing: 0.544px;white-space: normal;color: rgb(73, 73, 73);line-height: 1.7;font-family: PingFangSC-light;background-color: rgb(255, 255, 255);text-align: right;visibility: visible;\">\n<p style=\"outline: 0px;visibility: visible;\"><br  \/><\/p>\n<\/section>\n<section style=\"text-align: center;margin-left: 8px;margin-right: 8px;\"><img class=\"rich_pages wxw-img js_insertlocalimg\" data-ratio=\"1.83359375\" data-s=\"300,640\"  data-type=\"jpeg\" data-w=\"1280\" style=\"\" src=\"\/wp-content\/uploads\/2022\/12\/wxsync-2022-12-696456b5a3aac767a8d282b0adc3241e.jpeg\"  \/><\/section>\n<section style=\"text-align: center;margin-left: 8px;margin-right: 8px;\"><br  \/><\/section>\n<h3 style=\"margin-bottom: 0em;outline: 0px;color: rgb(34, 34, 34);letter-spacing: 0.544px;white-space: normal;font-family: mp-quote, -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;background-color: rgb(255, 255, 255);visibility: visible;\">\n<section powered-by=\"xiumi.us\" style=\"outline: 0px;letter-spacing: 0.544px;text-align: right;font-size: 13px;visibility: visible;\">\n<section powered-by=\"xiumi.us\" style=\"margin-top: 10px;margin-bottom: 10px;outline: 0px;letter-spacing: 0.544px;text-align: center;visibility: visible;\">\n<section style=\"outline: 0px;display: inline-block;vertical-align: middle;visibility: visible;\">\n<section style=\"margin-bottom: -2px;outline: 0px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;visibility: visible;\">\n<section style=\"outline: 0px;float: left;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<section style=\"outline: 0px;float: right;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<section style=\"outline: 0px;clear: both;line-height: 0;visibility: visible;\">\n<section style=\"outline: 0px;line-height: 0;width: 0px;visibility: visible;\"><svg viewbox=\"0 0 1 1\" style=\"vertical-align: top;visibility: visible;\"><\/svg><\/section>\n<\/section>\n<\/section>\n<section style=\"padding-right: 10px;padding-left: 10px;outline: 0px;border-left: 3px solid rgb(33, 166, 210);border-right: 3px solid rgb(33, 166, 210);border-top-color: rgb(33, 166, 210);border-bottom-color: rgb(33, 166, 210);font-size: 16px;color: rgb(0, 0, 0);line-height: 1.4;visibility: visible;\">\n<p style=\"outline: 0px;visibility: visible;\"><strong style=\"outline: 0px;visibility: visible;\"><strong style=\"outline: 0px;text-align: left;color: rgb(33, 166, 210);letter-spacing: 0.544px;visibility: visible;\"><span style=\"outline: 0px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;caret-color: rgb(89, 89, 89);visibility: visible;\">\u8bfe\u7a0b\u7b80\u4ecb<\/span><\/strong><\/strong><\/p>\n<\/section>\n<section style=\"margin-top: -2px;outline: 0px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;visibility: visible;\">\n<section style=\"outline: 0px;float: left;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<section style=\"outline: 0px;float: right;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;outline: 0px;color: rgb(34, 34, 34);font-family: system-ui, -apple-system, &quot;system-ui&quot;, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;letter-spacing: 0.544px;white-space: normal;background-color: rgb(255, 255, 255);line-height: 1.75em;visibility: visible;\"><br  \/><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u672c\u8282\u8bfe\u7a0b\u662f\u7cfb\u5217\u8bfe\u7a0b\u7684\u7b2c 9 \u8282\uff0c\u5173\u4e8e Hopfield \u6a21\u578b\u7b2c\u4e8c\u6b21\u8bfe\u7a0b\u3002Hopfield \u6a21\u578b\u53ef\u4ee5\u5efa\u6a21\u8054\u60f3\u8bb0\u5fc6\u8fc7\u7a0b\uff0c\u56e0\u6b64\u5bf9\u8ba1\u7b97\u795e\u7ecf\u79d1\u5b66\uff0c\u4e43\u81f3\u4e8e\u73b0\u4ee3\u673a\u5668\u5b66\u4e60\u90fd\u6709\u5f88\u91cd\u8981\u7684\u610f\u4e49\u3002\u672c\u8282\u8bfe\u6211\u4eec\u7ee7\u7eed\u5b66\u4e60 Hopfield \u6a21\u578b\u7684\u89e3\u6790\u8ba1\u7b97\uff0c\u63a5\u7740\u4e0a\u8282\u8bfe\u7684\u5185\u5bb9\u5c06\u8bb2\u89e3\u978d\u70b9\u5206\u6790\uff0c\u4ee5\u53ca Hopfield \u6a21\u578b\u7684\u76f8\u56fe\uff0c\u5e76\u7ed3\u5408 21 \u5e74\u7684\u6700\u65b0\u5de5\u4f5c\u5bf9\u62d3\u5c55\u7684 Hopfield \u6a21\u578b\u8fdb\u884c\u4ecb\u7ecd\u3002<\/span><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"><br  \/><\/span><\/section>\n<p style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;margin-bottom: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u672c\u4e3b\u9898\u5bf9\u5e94<\/span><a href=\"https:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247634469&amp;idx=3&amp;sn=36d67d75c21f6ce172cc03704f40f34a&amp;scene=21#wechat_redirect\" data-linktype=\"2\" style=\"color: rgb(63, 63, 63);font-size: 15px;\">SMNN\u4e66\u7c4d<\/a><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u7684\u7b2c\u516b\u7ae0\uff0c\u5177\u4f53\u4e3a\uff1a<\/span><\/p>\n<p style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;margin-bottom: 8px;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">Chapter 8: &nbsp;Statistical Mechanical Theory of Hopfield Model<\/span><\/p>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;width: 577.422px;white-space: normal;\">\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<p style=\"line-height: 1.75em;margin-bottom: 8px;text-align: left;\">8.1 Hopfield Model<\/p>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;width: 577.422px;white-space: normal;\">\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<p style=\"line-height: 1.75em;margin-bottom: 8px;text-align: left;\">8.2 Replica Method<\/p>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;width: 577.422px;white-space: normal;\">\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<p style=\"line-height: 1.75em;margin-bottom: 8px;text-align: left;\">8.3 Phase Diagram<\/p>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;width: 577.422px;white-space: normal;\">\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<p style=\"line-height: 1.75em;margin-bottom: 8px;text-align: left;\">8.4 Hopfield Model with Arbitrary Hebbian Length<\/p>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u8bf4\u660e\uff1aSMNN\u4e66\u7c4d\u7b2c\u516d\u3001\u4e03\u7ae0\u5c06\u5ef6\u540e\u8bb2\u89e3\u3002<\/span><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><br  \/><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u9ec4\u6d77\u5e73\u7814\u7a76\u7ec4 21 \u5e74\u76f8\u5173\u7684\u6700\u65b0\u5de5\u4f5c<\/span><\/section>\n<section style=\"margin-right: 8px;margin-left: 8px;white-space: normal;text-align: left;line-height: normal;margin-bottom: 8px;\"><span style=\"font-family: mp-quote, -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;font-size: 13px;\">1. Jiang, Z., Zhou, J., Hou, T., Wong, K. M., &amp; Huang, H. (2021). Associative memory model with arbitrary Hebbian length. Physical Review E, 104(6), 064306. https:\/\/journals.aps.org\/pre\/abstract\/10.1103\/PhysRevE.104.064306<\/span><\/section>\n<p style=\"margin-right: 8px;margin-left: 8px;white-space: normal;text-align: left;line-height: normal;margin-bottom: 0px;\"><span style=\"font-family: mp-quote, -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;font-size: 13px;\">2. Zhou, J., Jiang, Z., Hou, T., Chen, Z., Wong, K. M., &amp; Huang, H. (2021). Eigenvalue spectrum of neural networks with arbitrary Hebbian length. Physical Review E, 104(6), 064307. https:\/\/journals.aps.org\/pre\/abstract\/10.1103\/PhysRevE.104.064307<\/span><\/p>\n<ol start=\"2\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;width: 577.422px;white-space: normal;\"><\/ol>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><br  \/><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><br  \/><\/section>\n<h3 style=\"margin-bottom: 0em;white-space: normal;outline: 0px;color: rgb(34, 34, 34);letter-spacing: 0.544px;font-family: mp-quote, -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;background-color: rgb(255, 255, 255);visibility: visible;\">\n<section powered-by=\"xiumi.us\" style=\"outline: 0px;letter-spacing: 0.544px;text-align: right;font-size: 13px;visibility: visible;\">\n<section powered-by=\"xiumi.us\" style=\"margin-top: 10px;margin-bottom: 10px;outline: 0px;letter-spacing: 0.544px;text-align: center;visibility: visible;\">\n<section style=\"outline: 0px;display: inline-block;vertical-align: middle;visibility: visible;\">\n<section style=\"margin-bottom: -2px;outline: 0px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;visibility: visible;\">\n<section style=\"outline: 0px;float: left;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<section style=\"outline: 0px;float: right;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<section style=\"outline: 0px;clear: both;line-height: 0;visibility: visible;\">\n<section style=\"outline: 0px;line-height: 0;width: 0px;visibility: visible;\"><svg viewbox=\"0 0 1 1\" style=\"vertical-align: top;visibility: visible;\"><\/svg><\/section>\n<\/section>\n<\/section>\n<section style=\"padding-right: 10px;padding-left: 10px;outline: 0px;border-left: 3px solid rgb(33, 166, 210);border-right: 3px solid rgb(33, 166, 210);border-top-color: rgb(33, 166, 210);border-bottom-color: rgb(33, 166, 210);font-size: 16px;color: rgb(0, 0, 0);line-height: 1.4;visibility: visible;\">\n<p style=\"outline: 0px;visibility: visible;\"><strong style=\"outline: 0px;visibility: visible;\"><strong style=\"outline: 0px;text-align: left;color: rgb(33, 166, 210);letter-spacing: 0.544px;visibility: visible;\"><span style=\"outline: 0px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;caret-color: rgb(89, 89, 89);visibility: visible;\">\u672c\u8282\u8bfe\u7a0b\u5927\u7eb2<\/span><\/strong><\/strong><\/p>\n<\/section>\n<section style=\"margin-top: -2px;outline: 0px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;visibility: visible;\">\n<section style=\"outline: 0px;float: left;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<section style=\"outline: 0px;float: right;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;outline: 0px;color: rgb(34, 34, 34);font-family: system-ui, -apple-system, &quot;system-ui&quot;, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;letter-spacing: 0.544px;background-color: rgb(255, 255, 255);line-height: 1.75em;visibility: visible;\"><br  \/><\/section>\n<ol start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;width: 577.422px;white-space: normal;\">\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<p style=\"line-height: 1.75em;margin-bottom: 8px;\">\u590d\u672c\u8ba1\u7b97\u7684\u978d\u70b9\u5206\u6790<\/p>\n<\/li>\n<\/ol>\n<ol start=\"2\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;width: 577.422px;white-space: normal;\">\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<p style=\"line-height: 1.75em;margin-bottom: 8px;\">\u4ece\u978d\u70b9\u65b9\u7a0b\u4e2d\u53d1\u73b0\u76f8\u53d8<\/p>\n<\/li>\n<\/ol>\n<ol start=\"3\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;width: 577.422px;white-space: normal;\">\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<p style=\"line-height: 1.75em;margin-bottom: 8px;\">Hopfield\u6a21\u578b\u7684\u76f8\u53d8<\/p>\n<\/li>\n<\/ol>\n<ol start=\"4\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;width: 577.422px;white-space: normal;\">\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<p style=\"line-height: 1.75em;margin-bottom: 8px;\">\u5e26\u6709\u4efb\u610fHebbian\u957f\u5ea6\u7684Hopfield\u6a21\u578b<\/p>\n<\/li>\n<\/ol>\n<ol start=\"5\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;width: 577.422px;white-space: normal;\">\n<li style=\"font-size: 15px;color: rgb(63, 63, 63);\">\n<p style=\"line-height: 1.75em;margin-bottom: 8px;\">\u6587\u732e\u62d3\u5c55\u90e8\u5206<\/p>\n<\/li>\n<\/ol>\n<p style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;margin-bottom: 0px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u5173\u952e\u8bcd\uff1aHopfield\u6a21\u578b\uff0c\u76f8\u53d8\uff0c\u978d\u70b9\u65b9\u7a0b<\/span><\/p>\n<p style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;margin-bottom: 0px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"><br  \/><\/span><\/p>\n<section style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;margin-bottom: 0px;\"><br  \/><\/section>\n<h3 style=\"margin-bottom: 0em;outline: 0px;white-space: normal;font-family: mp-quote, -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;letter-spacing: 0.544px;background-color: rgb(255, 255, 255);visibility: visible;\">\n<section powered-by=\"xiumi.us\" style=\"outline: 0px;letter-spacing: 0.544px;text-align: right;font-size: 13px;visibility: visible;\">\n<section powered-by=\"xiumi.us\" style=\"margin-top: 10px;margin-bottom: 10px;outline: 0px;letter-spacing: 0.544px;text-align: center;visibility: visible;\">\n<section style=\"outline: 0px;display: inline-block;vertical-align: middle;visibility: visible;\">\n<section style=\"margin-bottom: -2px;outline: 0px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;visibility: visible;\">\n<section style=\"outline: 0px;float: left;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<section style=\"outline: 0px;float: right;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<section style=\"outline: 0px;clear: both;line-height: 0;visibility: visible;\">\n<section style=\"outline: 0px;line-height: 0;width: 0px;visibility: visible;\"><svg viewbox=\"0 0 1 1\" style=\"vertical-align: top;visibility: visible;\"><\/svg><\/section>\n<\/section>\n<\/section>\n<section style=\"padding-right: 10px;padding-left: 10px;outline: 0px;border-left: 3px solid rgb(33, 166, 210);border-right: 3px solid rgb(33, 166, 210);border-top-color: rgb(33, 166, 210);border-bottom-color: rgb(33, 166, 210);font-size: 16px;color: rgb(0, 0, 0);line-height: 1.4;visibility: visible;\">\n<p style=\"outline: 0px;visibility: visible;\"><strong style=\"outline: 0px;visibility: visible;\"><strong style=\"outline: 0px;text-align: left;color: rgb(33, 166, 210);letter-spacing: 0.544px;visibility: visible;\"><span style=\"outline: 0px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;caret-color: rgb(89, 89, 89);visibility: visible;\">\u8d1f\u8d23\u4eba\u4ecb\u7ecd<\/span><\/strong><\/strong><\/p>\n<\/section>\n<section style=\"margin-top: -2px;outline: 0px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;visibility: visible;\">\n<section style=\"outline: 0px;float: left;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<section style=\"outline: 0px;float: right;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br style=\"outline: 0px;visibility: visible;\"  \/><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;outline: 0px;white-space: normal;line-height: 1.75em;\"><br  \/><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;margin-bottom: 0px;line-height: 1.75em;text-align: center;\"><img class=\"rich_pages wxw-img\" data-height=\"233\" data-ratio=\"1.2459893048128343\"  data-type=\"png\" data-w=\"187\" data-width=\"187\" src=\"\/wp-content\/uploads\/2022\/12\/wxsync-2022-12-300899bd8278443984819ff5ded47bb8.png\"  \/><\/section>\n<p style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;margin-bottom: 8px;\"><strong><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u9ec4\u6d77\u5e73<\/span><\/strong><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\uff0c\u4e2d\u5c71\u5927\u5b66\u7269\u7406\u5b66\u9662\u6559\u6388\u3002\u672c\u79d1\u6bd5\u4e1a\u4e8e\u4e2d\u5c71\u5927\u5b66\u7406\u5de5\u5b66\u9662\uff0c\u535a\u58eb\u6bd5\u4e1a\u4e8e\u4e2d\u56fd\u79d1\u5b66\u9662\u7406\u8bba\u7269\u7406\u7814\u7a76\u6240\uff0c\u968f\u540e\u5728\u9999\u6e2f\u79d1\u6280\u5927\u5b66\u7269\u7406\u7cfb\u3001\u4e1c\u4eac\u5de5\u4e1a\u5927\u5b66\u8ba1\u7b97\u667a\u80fd\u7cfb &nbsp;(2012\u5e74\u83b7\u65e5\u672c\u5b66\u672f\u632f\u5174\u4f1a\u8d44\u52a9) \u4ee5\u53ca\u65e5\u672c\u7406\u5316\u5b66\u7814\u7a76\u6240 (RIKEN) \u8111\u79d1\u5b66\u4e2d\u5fc3\u4ece\u4e8b\u7edf\u8ba1\u7269\u7406\u4e0e\u673a\u5668\u5b66\u4e60\u3001 &nbsp;\u795e\u7ecf\u8ba1\u7b97\u4ea4\u53c9\u7684\u57fa\u7840\u7406\u8bba\u7814\u7a76\uff0c2017\u5e74\u56e0\u5728\u65e0\u76d1\u7763\u5b66\u4e60\u65b9\u9762\u7684\u7814\u7a76\u83b7\u5f97 RIKEN &nbsp;\u6770\u51fa\u7814\u7a76\u5956\u3002\u4e8e2018\u5e74\u5165\u9009\u4e2d\u5c71\u5927\u5b66\u767e\u4eba\u8ba1\u5212\uff0c\u5728\u7269\u7406\u5b66\u9662\u7ec4\u5efa\u4e86\u201c\u7269\u7406\u3001\u673a\u5668\u4e0e\u667a\u80fd\u201d &nbsp;\uff08PMI\uff09\u7814\u7a76\u5c0f\u7ec4\uff0c\u4e13\u6ce8\u4e8e\u5404\u79cd\u795e\u7ecf\u8ba1\u7b97\u7684\u7406\u8bba\u57fa\u7840\uff0c\u957f\u671f\u76ee\u6807\u662f\u4f7f\u7528\u57fa\u4e8e\u7269\u7406\u7684\u8fd1\u4f3c\u6765\u63ed\u793a\u673a\u5668\u53ca\u5927\u8111\u667a\u80fd\u7684\u57fa\u672c\u539f\u7406\u3002\u66fe\u4e3b\u6301\u56fd\u5bb6\u81ea\u7136\u79d1\u5b66\u57fa\u91d1\u9752\u5e74\u57fa\u91d1\u3001\u4f18\u79c0\u9752\u5e74\u57fa\u91d1\u7b49\u56fd\u5bb6\u7ea7\u9879\u76ee\u3002<\/span><\/p>\n<section style=\"margin-left: 8px;margin-right: 8px;margin-bottom: 0px;line-height: 1.75em;text-align: left;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">PMI Lab\uff1ahttps:\/\/www.labxing.com\/hphuang2018<\/span><\/section>\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><br  \/><\/section>\n<p style=\"margin-bottom: 0px;outline: 0px;color: rgb(34, 34, 34);font-family: system-ui, -apple-system, &quot;system-ui&quot;, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;letter-spacing: 0.544px;white-space: normal;background-color: rgb(255, 255, 255);\"><br  \/><\/p>\n<h3 style=\"margin-bottom: 0em;outline: 0px;color: rgb(34, 34, 34);letter-spacing: 0.544px;white-space: normal;font-family: mp-quote, -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;background-color: rgb(255, 255, 255);visibility: visible;\">\n<section powered-by=\"xiumi.us\" style=\"outline: 0px;letter-spacing: 0.544px;text-align: right;font-size: 13px;visibility: visible;\">\n<section powered-by=\"xiumi.us\" style=\"margin-top: 10px;margin-bottom: 10px;outline: 0px;letter-spacing: 0.544px;text-align: center;visibility: visible;\">\n<section style=\"outline: 0px;display: inline-block;vertical-align: middle;visibility: visible;\">\n<section style=\"margin-bottom: -2px;outline: 0px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;visibility: visible;\">\n<section style=\"outline: 0px;float: left;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br  \/><\/section>\n<section style=\"outline: 0px;float: right;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br  \/><\/section>\n<section style=\"outline: 0px;clear: both;line-height: 0;visibility: visible;\">\n<section style=\"outline: 0px;line-height: 0;width: 0px;visibility: visible;\"><svg viewbox=\"0 0 1 1\" style=\"vertical-align: top;visibility: visible;\"><\/svg><\/section>\n<\/section>\n<\/section>\n<section style=\"padding-right: 10px;padding-left: 10px;outline: 0px;border-left: 3px solid rgb(33, 166, 210);border-right: 3px solid rgb(33, 166, 210);border-top-color: rgb(33, 166, 210);border-bottom-color: rgb(33, 166, 210);font-size: 16px;color: rgb(0, 0, 0);line-height: 1.4;visibility: visible;\">\n<p style=\"outline: 0px;visibility: visible;\"><strong style=\"outline: 0px;visibility: visible;\"><strong style=\"outline: 0px;text-align: left;color: rgb(33, 166, 210);letter-spacing: 0.544px;visibility: visible;\"><span style=\"outline: 0px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;caret-color: rgb(89, 89, 89);visibility: visible;\">\u76f4\u64ad\u4fe1\u606f<\/span><\/strong><\/strong><\/p>\n<\/section>\n<section style=\"margin-top: -2px;outline: 0px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;visibility: visible;\">\n<section style=\"outline: 0px;float: left;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br  \/><\/section>\n<section style=\"outline: 0px;float: right;width: 8px;height: 3px;background-color: rgb(33, 166, 210);line-height: 0;visibility: visible;\"><br  \/><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n<section style=\"margin-left: 8px;margin-right: 8px;margin-bottom: 0px;line-height: 1.75em;\"><strong><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u76f4\u64ad\u65f6\u95f4\uff1a<\/span><\/strong><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;margin-bottom: 0px;line-height: 1.75em;\"><span style=\"color: rgb(63, 63, 63);font-size: 15px;\">2022\u5e7411\u670826\u65e5\uff08\u5468\u516d\uff09\u4e0b\u534814:00-16:00<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;margin-bottom: 0px;line-height: 1.75em;\"><br  \/><\/section>\n<p style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;margin-bottom: 8px;\"><strong><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u53c2\u4e0e\u65b9\u5f0f\u4e00\uff1a\u89c6\u9891\u53f7\u9884\u7ea6\u76f4\u64ad<\/span><\/strong><\/p>\n<ul class=\"list-paddingleft-1\" style=\"list-style-type: disc;\">\n<li style=\"font-size: 15px;\">\n<p style=\"line-height: 1.75em;margin-bottom: 8px;\"><span style=\"color: rgb(63, 63, 63);font-size: 15px;\">\u96c6\u667a\u5b66\u56ed\u89c6\u9891\u53f7\u9884\u7ea6<\/span><\/p>\n<\/li>\n<\/ul>\n<section class=\"channels_iframe_wrp\"><mpvideosnap class=\"js_uneditable custom_select_card channels_live_iframe\" data-pluginname=\"videosnap\" data-headimgurl=\"https:\/\/wx.qlogo.cn\/finderhead\/ajNVdqHZLLDkhV6hTgHRHksyS5fIwv7eAAhSpic1M5pDQQG7h9VN84g\/0\" data-username=\"v2_060000231003b20faec8c5ea891bc3dcc80ce934b077144e6416ea45d7e19afb464dfa855442@finder\" data-nickname=\"\u96c6\u667a\u5b66\u56ed\" data-desc=\"\u5c06\u572812\u670803\u65e5 14:00 \u76f4\u64ad\" data-intro=\"Hopfield\u6a21\u578b\u7684\u7edf\u8ba1\u7269\u7406\uff08\u4e8c\uff09\" data-noticeid=\"finderlivenotice-v2_060000231003b20faec8c5ea891bc3dcc80ce934b077144e6416ea45d7e19afb464dfa855442@finder-1669953663388676-1610590779\" data-type=\"live\"><\/mpvideosnap><\/section>\n<ul class=\"list-paddingleft-1\" style=\"list-style-type: disc;\">\n<li>\n<section style=\"margin-bottom: 0px;line-height: 1.75em;text-align: left;\"><span style=\"color: rgb(63, 63, 63);font-size: 15px;\">\u96c6\u667a\u5b66\u56ed B <\/span><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u7ad9\u514d\u8d39\u76f4\u64ad\uff0c\u623f\u95f4\u53f7https:\/\/live.bilibili.com\/6782735<\/span><\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-left: 8px;margin-right: 8px;margin-bottom: 0px;line-height: 1.75em;\"><br  \/><\/section>\n<p style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;margin-bottom: 8px;\"><strong><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u53c2\u4e0e\u65b9\u5f0f\u4e8c\uff1a\u4ed8\u8d39\u52a0\u5165\u8bfe\u7a0b\uff0c\u67e5\u770b\u8bfe\u7a0b\u56de\u653e<\/span><\/strong><\/p>\n<p style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;margin-bottom: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u4ed8\u8d39\u540e\uff0c\u53ef\u53c2\u4e0e\u96c6\u667a\u5b66\u56ed\u5e73\u53f0\u76f4\u64ad\u5e76\u52a0\u5165\u4ea4\u6d41\u7fa4\u83b7\u5f97\u89c6\u9891\u56de\u653e\u6743\u9650\u3002\u6b22\u8fce\u5bf9\u7edf\u8ba1\u529b\u5b66\u7684\u57fa\u672c\u539f\u7406\u611f\u5174\u8da3\u7684\u4f60\uff0c\u52a0\u5165\u3010<a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247628086&amp;idx=2&amp;sn=32c39ccfc209a0ac02d8995e0a64f54b&amp;chksm=e899afbbdfee26ad74fe0809f477e061095857882da0dde32640c94906424e20818d3404dd6a&amp;scene=21#wechat_redirect\" textvalue=\"\u9ec4\u6d77\u5e73\uff1a\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66\u8bfe\u7a0b | 50\u4eba\u514d\u8d39\u540d\u989d\" linktype=\"text\" imgurl=\"\" imgdata=\"null\" data-itemshowtype=\"0\" tab=\"innerlink\" data-linktype=\"2\" rel=\"noopener noreferrer\">\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66<\/a>\u3011\u8bfe\u7a0b\uff01<\/span><\/p>\n<p style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;margin-bottom: 8px;\"><strong><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u8bfe\u7a0b\u5b9a\u4ef7<\/span><\/strong><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\uff1a499\u5143<\/span><\/p>\n<p style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;margin-bottom: 8px;\"><strong><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u8bfe\u7a0b\u65f6\u95f4\uff1a<\/span><\/strong><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u4ece2022\u5e749\u670817\u65e5\u8d77\uff0c\u6bcf\u5468\u516d 14:00-16:00\uff08\u8282\u5047\u65e5\u9664\u5916\uff09<\/span><\/p>\n<section style=\"margin-left: 8px;margin-right: 8px;margin-bottom: 0px;line-height: 1.75em;text-align: center;\"><img class=\"rich_pages wxw-img\" data-height=\"260\" data-ratio=\"1\"  data-type=\"png\" data-w=\"260\" data-width=\"260\" style=\"width: 130px;height: 130px;\" src=\"\/wp-content\/uploads\/2022\/12\/wxsync-2022-12-81453595b432ca6e46c7737e67c92285.png\"  \/><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;margin-bottom: 0px;line-height: 1.75em;text-align: center;\"><span style=\"color: rgb(136, 136, 136);font-size: 13px;\">\u626b\u7801\u4ed8\u8d39\u62a5\u540d\u8bfe\u7a0b<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;margin-bottom: 0px;line-height: 1.75em;text-align: center;\"><span style=\"color: rgb(136, 136, 136);font-size: 13px;\">https:\/\/campus.swarma.org\/course\/4543<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;margin-bottom: 0px;line-height: 1.75em;\"><br  \/><\/section>\n<p style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;margin-bottom: 8px;\"><strong><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u4ed8\u8d39\u6d41\u7a0b\uff1a<\/span><\/strong><\/p>\n<p style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;margin-bottom: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u7b2c\u4e00\u6b65\uff1a\u626b\u7801\u4ed8\u8d39<\/span><\/p>\n<p style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;margin-bottom: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u7b2c\u4e8c\u6b65\uff1a\u5728\u8bfe\u7a0b\u8be6\u60c5\u9875\u9762\uff0c\u586b\u5199\u201c\u5b66\u5458\u4fe1\u606f\u767b\u8bb0\u8868\u201d<\/span><\/p>\n<p style=\"margin-left: 8px;margin-right: 8px;line-height: 1.75em;margin-bottom: 8px;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u7b2c\u4e09\u6b65\uff1a\u626b\u7801\u6dfb\u52a0\u52a9\u6559\u5fae\u4fe1\uff0c\u5165\u7fa4<\/span><\/p>\n<section style=\"margin-left: 8px;margin-right: 8px;margin-bottom: 0px;line-height: 1.75em;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\">\u672c\u8bfe\u7a0b\u53ef\u5f00\u53d1\u7968\u3002<\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;margin-bottom: 0px;line-height: 1.75em;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"><br  \/><\/span><\/section>\n<section style=\"margin-left: 8px;margin-right: 8px;margin-bottom: 0px;line-height: 1.75em;\"><span style=\"font-size: 15px;color: rgb(63, 63, 63);\"><br  \/><\/span><\/section>\n<section style=\"margin-top: 10px;outline: 0px;letter-spacing: 0.544px;color: rgb(136, 136, 136);font-size: 14px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;text-align: center;justify-content: center;margin-bottom: 0px;\">\n<section style=\"outline: 0px;display: inline-block;width: auto;vertical-align: top;min-width: 10%;height: auto;box-shadow: rgb(0, 0, 0) 0px 0px 0px;border-bottom: 9px solid rgb(169, 215, 227);border-bottom-right-radius: 0px;\">\n<section powered-by=\"xiumi.us\" style=\"margin-bottom: -15px;outline: 0px;\">\n<section style=\"padding-right: 10px;padding-left: 10px;outline: 0px;color: rgb(12, 130, 169);font-size: 16px;line-height: 2;letter-spacing: 3px;\">\n<p style=\"outline: 0px;\"><strong style=\"outline: 0px;\">\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66<\/strong><\/p>\n<p style=\"outline: 0px;\"><strong style=\"outline: 0px;\">\u6bcf\u5468\u66f4\u65b0\uff0c\u6301\u7eed\u62a5\u540d\u4e2d<br style=\"outline: 0px;\"  \/><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;letter-spacing: 0.544px;color: rgb(136, 136, 136);font-size: 14px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;line-height: 1.75em;margin-bottom: 0px;\"><br  \/><\/section>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;letter-spacing: 0.544px;color: rgb(136, 136, 136);font-size: 14px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;line-height: 2em;margin-bottom: 0px;\"><strong style=\"outline: 0px;color: rgb(33, 166, 210);font-size: 16px;font-family: mp-quote, -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;\"><span style=\"outline: 0px;font-size: 15px;\">\u7cfb\u5217\u8bfe\u7a0b\u5927\u7eb2<\/span><\/strong><\/section>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;letter-spacing: 0.544px;color: rgb(136, 136, 136);font-size: 14px;font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;line-height: 2em;margin-bottom: 0px;\"><strong style=\"outline: 0px;color: rgb(33, 166, 210);font-size: 16px;font-family: mp-quote, -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;\"><span style=\"outline: 0px;font-size: 15px;\"><br  \/><\/span><\/strong><\/section>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;margin-bottom: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\u8bfe\u7a0b\u4e3b\u8981\u76ee\u7684\u662f\u57f9\u517b\u4e00\u6279\u6709\u671b\u5728\u795e\u7ecf\u7f51\u7edc\u7406\u8bba\u6df1\u8015\u7684\u9752\u5e74\u5b66\u8005\uff08\u4fa7\u91cd\u5b66\u751f\uff09\uff0c\u8bfe\u7a0b\u6d89\u53ca\u9ec4\u6d77\u5e73\u8001\u5e08\u6700\u65b0\u51fa\u7248\u7684\u4e66\u7c4d\u300aStatistical Mechanics of Neural Networks\u300b\u7684\u5927\u90e8\u5206\u5185\u5bb9\uff0c\u76ee\u6807\u662f\u5b66\u4e60\u7edf\u8ba1\u529b\u5b66\u7684\u57fa\u672c\u539f\u7406\u53ca\u5176\u5728\u7406\u89e3\u795e\u7ecf\u7f51\u7edc\u5185\u90e8\u5de5\u4f5c\u539f\u7406\u7684\u5e94\u7528\u3002\u4e66\u7c4d\u6db5\u76d6\u4e86\u7528\u4e8e\u7406\u89e3\u795e\u7ecf\u7f51\u7edc\u539f\u7406\u7684\u5fc5\u8981\u7edf\u8ba1\u529b\u5b66\u77e5\u8bc6\uff0c\u5305\u62ec\u590d\u672c\u65b9\u6cd5\u3001\u7a7a\u8154\u65b9\u6cd5\u3001\u5e73\u5747\u573a\u8fd1\u4f3c\u3001\u53d8\u5206\u6cd5\u3001\u968f\u673a\u80fd\u91cf\u6a21\u578b\u3001Nishimori\u6761\u4ef6\u3001\u52a8\u529b\u5b66\u5e73\u5747\u573a\u7406\u8bba\u3001\u5bf9\u79f0\u6027\u7834\u7f3a\u3001\u968f\u673a\u77e9\u9635\u7406\u8bba\u7b49\uff0c\u540c\u65f6\u8be6\u7ec6\u63cf\u8ff0\u4e86\u76d1\u7763\u5b66\u4e60\u3001\u65e0\u76d1\u7763\u5b66\u4e60\u3001\u8054\u60f3\u8bb0\u5fc6\u7f51\u7edc\u3001\u611f\u77e5\u5668\u7f51\u7edc\u3001\u968f\u673a\u5faa\u73af\u7f51\u7edc\u7b49\u795e\u7ecf\u7f51\u7edc\u53ca\u5176\u529f\u80fd\u7684\u7269\u7406\u6a21\u578b\u4ee5\u53ca\u89e3\u6790\u7406\u8bba\u3002\u672c\u4e66\u901a\u8fc7\u7b80\u6d01\u7684\u6a21\u578b\u5c55\u793a\u4e86\u795e\u7ecf\u7f51\u7edc\u539f\u7406\u7684\u6570\u5b66\u7f8e\u548c\u7269\u7406\u6df1\u5ea6\uff0c\u5e76\u4ecb\u7ecd\u4e86\u76f8\u5173\u5386\u53f2\u548c\u5c55\u671b\u672a\u6765\u7814\u7a76\u7684\u91cd\u8981\u8bfe\u9898\uff0c\u53ef\u4f9b\u5bf9\u795e\u7ecf\u7f51\u7edc\u539f\u7406\u611f\u5174\u8da3\u7684\u5b66\u751f\u3001\u7814\u7a76\u4eba\u5458\u4ee5\u53ca\u5de5\u7a0b\u5e08\u9605\u8bfb\u53c2\u8003\u3002<\/span><\/section>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;margin-bottom: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\"><br style=\"outline: 0px;\"  \/><\/span><\/section>\n<section style=\"outline: 0px;text-align: center;margin-bottom: 0px;\"><img class=\"rich_pages wxw-img\" data-height=\"865\" data-ratio=\"1.476109215017065\"  data-type=\"png\" data-w=\"586\" data-width=\"586\" style=\"height: 286px;white-space: normal;width: 194px;\" src=\"\/wp-content\/uploads\/2022\/12\/wxsync-2022-12-ed8c9705e79d477628bcba8a0ac79458.png\"  \/><\/section>\n<p><br  \/><\/p>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;margin-bottom: 0px;\"><strong style=\"outline: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\u4e66\u7c4d\u76ee\u5f55\uff08\u8be6\u7248\uff09\uff1a<\/span><\/strong><\/section>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">Chapter 1: &nbsp;Introduction<\/span><\/section>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">Chapter 2: &nbsp;Spin Glass Models and Cavity Method<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">2.1 Multi-spin Interaction Models<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">2.2 Cavity Method<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">2.3 From Cavity Method to Message Passing Algorithms<\/span><\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">Chapter 3: &nbsp;Variational Mean-Field Theory and Belief Propagation<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">3.1 Variational Method<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">3.2 Variational Free Energy<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">3.3 Mean-Field Inverse Ising Problem<\/span><\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">Chapter 4: &nbsp;Monte Carlo Simulation Methods<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">4.1 Monte Carlo Method<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">4.2 Importance Sampling<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">4.3 Markov Chain Sampling<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">4.4 Monte Carlo Simulations in Statistical Physics<\/span><\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">Chapter 5: &nbsp;High-Temperature Expansion<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">5.1 Statistical Physics Setting<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">5.2 High-Temperature Expansion<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">5.3 Properties of the TAP Equation<\/span><\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">Chapter 6: &nbsp;Nishimori Line<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">6.1 Model Setting<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">6.2 Exact Result for Internal Energy<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">6.3 Proof of No RSB Effects on the Nishimori Line<\/span><\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">Chapter 7: &nbsp;Random Energy Model<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">7.1 Model Setting<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">7.2 Phase Diagram<\/span><\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">Chapter 8: &nbsp;Statistical Mechanical Theory of Hopfifield Model<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">8.1 Hopfifield Model<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">8.2 Replica Method<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">8.3 Phase Diagram<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">8.4 Hopfifield Model with Arbitrary Hebbian Length<\/span><\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">Chapter 9: &nbsp;Replica Symmetry and Replica Symmetry Breaking<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">9.1 Generalized Free Energy and Complexity of States<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">9.2 Applications to Constraint Satisfaction Problems<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">9.3 More Steps of Replica Symmetry Breaking<\/span><\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">Chapter 10: &nbsp;Statistical Mechanics of Restricted Boltzmann Machine<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">10.1 Boltzmann Machine<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">10.2 Restricted Boltzmann Machine<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">10.3 Free Energy Calculation<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">10.4 Thermodynamic Quantities Related to Learning<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">10.5 Stability Analysis<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">10.6 Variational Mean-Field Theory for Training Binary RBMs<\/span><\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">Chapter 11: &nbsp;Simplest Model of Unsupervised Learning with Binary<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">11.1 Model Setting<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">11.2 Derivation of sMP and AMP Equations<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">11.3 Replica Computation<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">11.4 Phase Transitions<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">11.5 Measuring the Temperature of Dataset<\/span><\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">Chapter 12: &nbsp;Inherent-Symmetry Breaking in Unsupervised Learning<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">12.1 Model Setting<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">12.2 Phase Diagram<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">12.3 Hyper-Parameters Inference<\/span><\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">Chapter 13: &nbsp;Mean-Field Theory of Ising Perceptron<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">13.1 Ising Perceptron model<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">13.2 Message-Passing-Based Learning<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">13.3 Replica Analysis<\/span><\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">Chapter 14: &nbsp;Mean-Field Model of Multi-layered Perceptron<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">14.1 Random Active Path Model<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">14.2 Mean-Field Training Algorithms<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">14.3 Spike and Slab Model<\/span><\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">Chapter 15: &nbsp;Mean-Field Theory of Dimension Reduction in Neural Networks<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">15.1 Mean-Field Model<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">15.2 Linear Dimensionality and Correlation Strength<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">15.3 Dimension Reduction with Correlated Synapses<\/span><\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">Chapter 16: &nbsp;Chaos Theory of Random Recurrent Neural Networks<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">16.1 Spiking and Rate Models<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">16.2 Dynamical Mean-Field Theory<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">16.3 Lyapunov Exponent and Chaos<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">16.4 Excitation-Inhibition Balance Theory<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">16.5 Training Recurrent Neural Networks<\/span><\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">Chapter 17: &nbsp;Statistical Mechanics of Random Matrices<\/span><\/section>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">17.1 Spectral Density<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">17.2 Replica Method and Semi-circle Law<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">17.3 Cavity Approach and Marchenko<\/span><\/section>\n<\/li>\n<\/ul>\n<ul start=\"1\" class=\"list-paddingleft-1\" style=\"margin-right: 8px;margin-left: 8px;padding-left: 1.5em;outline: 0px;\">\n<li style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\n<section style=\"outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;\">17.4 Spectral Densities of Random Asymmetric Matrices<\/span><\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;text-align: left;margin-bottom: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">Chapter 18: &nbsp;Perspectives<\/span><\/section>\n<h3 style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;margin-bottom: 0px;\"><br  \/><\/h3>\n<h3 style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;margin-bottom: 0px;\"><span style=\"outline: 0px;color: rgb(33, 166, 210);\"><strong style=\"outline: 0px;\"><span style=\"outline: 0px;font-size: 15px;\">\u62a5\u540d\u52a0\u5165\u8bfe\u7a0b<\/span><\/strong><\/span><\/h3>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;margin-bottom: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\u6b22\u8fce\u5bf9\u7edf\u8ba1\u529b\u5b66\u7684\u57fa\u672c\u539f\u7406\u611f\u5174\u8da3\u7684\u4f60\uff0c\u52a0\u5165\u3010\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66\u3011\u8bfe\u7a0b\uff01<\/span><\/section>\n<p style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;margin-bottom: 8px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\u8bfe\u7a0b\u4ef7\u683c\uff1a499\u5143<\/span><\/p>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;text-align: center;margin-bottom: 0px;\"><img class=\"rich_pages wxw-img\" data-height=\"260\" data-ratio=\"1\"  data-type=\"png\" data-w=\"260\" data-width=\"260\" style=\"outline: 0px;display: initial;box-sizing: border-box !important;width: 134px;visibility: visible !important;height: 134px;\" src=\"\/wp-content\/uploads\/2022\/12\/wxsync-2022-12-01bb6a5922018f2f204dc6210787e2a5.png\"  \/><\/section>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;text-align: center;margin-bottom: 0px;\"><span style=\"outline: 0px;color: rgb(136, 136, 136);font-size: 13px;\">\u626b\u7801\u4ed8\u8d39\u62a5\u540d\u8bfe\u7a0b<\/span><\/section>\n<p style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;margin-bottom: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\u7b2c\u4e00\u6b65\uff1a\u626b\u7801\u4ed8\u8d39<\/span><\/p>\n<p style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;margin-bottom: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\u7b2c\u4e8c\u6b65\uff1a\u5728\u8bfe\u7a0b\u8be6\u60c5\u9875\u9762\uff0c\u586b\u5199\u201c\u5b66\u5458\u4fe1\u606f\u767b\u8bb0\u8868\u201d<\/span><\/p>\n<p style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;margin-bottom: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\u7b2c\u4e09\u6b65\uff1a\u626b\u7801\u6dfb\u52a0\u52a9\u6559\u5fae\u4fe1\uff0c\u5165\u7fa4<\/span><\/p>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;margin-bottom: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\u672c\u8bfe\u7a0b\u53ef\u5f00\u53d1\u7968\u3002<\/span><\/section>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;margin-bottom: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\"><br style=\"outline: 0px;\"  \/><\/span><\/section>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;margin-bottom: 0px;\"><span style=\"outline: 0px;font-size: 15px;color: rgb(63, 63, 63);\">\u8bfe\u7a0b\u8d1f\u8d23\u4eba\u9ec4\u6d77\u5e73\u7684\u8bc4\u8bba\u6587\u7ae0\uff1a<\/span><\/section>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;margin-bottom: 0px;\"><a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247634468&amp;idx=1&amp;sn=3cba5dbd1ba494176182eaf6fc13ec00&amp;chksm=e89994a9dfee1dbf1cfa3d7a2fc35c66ef2980cdcdc14977e81fad5c52dd00c4af39266abd8f&amp;scene=21#wechat_redirect\" textvalue=\"\u7edf\u8ba1\u7269\u7406\u3001\u65e0\u5e8f\u7cfb\u7edf\u548c\u795e\u7ecf\u7f51\u7edc\" linktype=\"text\" imgurl=\"\" imgdata=\"null\" data-itemshowtype=\"11\" tab=\"innerlink\" data-linktype=\"2\" hasload=\"1\" style=\"outline: 0px;text-decoration: underline;-webkit-tap-highlight-color: rgba(0, 0, 0, 0);cursor: pointer;font-size: 15px;\" rel=\"noopener noreferrer\"><span style=\"outline: 0px;\">\u7edf\u8ba1\u7269\u7406\u3001\u65e0\u5e8f\u7cfb\u7edf\u548c\u795e\u7ecf\u7f51\u7edc<\/span><\/a><br style=\"outline: 0px;\"  \/><\/section>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;margin-bottom: 0px;\"><span style=\"outline: 0px;color: rgb(63, 63, 63);font-size: 15px;\">\u70b9\u51fb\u4e86\u89e3\u7cfb\u5217\u8bfe\u7a0b\u8be6\u60c5\uff1a<\/span><\/section>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;margin-bottom: 0px;\"><a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247628086&amp;idx=2&amp;sn=32c39ccfc209a0ac02d8995e0a64f54b&amp;chksm=e899afbbdfee26ad74fe0809f477e061095857882da0dde32640c94906424e20818d3404dd6a&amp;scene=21#wechat_redirect\" textvalue=\"\u9ec4\u6d77\u5e73\uff1a\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66\u8bfe\u7a0b | 50\u4eba\u514d\u8d39\u540d\u989d\" linktype=\"text\" imgurl=\"\" imgdata=\"null\" data-itemshowtype=\"0\" tab=\"innerlink\" data-linktype=\"2\" hasload=\"1\" style=\"outline: 0px;text-decoration: underline;-webkit-tap-highlight-color: rgba(0, 0, 0, 0);cursor: pointer;font-size: 15px;\" rel=\"noopener noreferrer\"><span style=\"outline: 0px;\">\u9ec4\u6d77\u5e73\uff1a\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66\u8bfe\u7a0b | 50\u4eba\u514d\u8d39\u540d\u989d<\/span><\/a><br style=\"outline: 0px;\"  \/><\/section>\n<section style=\"margin-right: 8px;margin-left: 8px;outline: 0px;line-height: 1.75em;margin-bottom: 0px;\"><br  \/><\/section>\n<section style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;margin-bottom: 8px;\"><span style=\"color: rgb(33, 166, 210);\"><strong><span style=\"font-size: 15px;\">\u5f80\u671f\u56de\u987e\uff1a<\/span><\/strong><\/span><\/section>\n<ul class=\"list-paddingleft-1\" style=\"list-style-type: circle;\">\n<li>\n<section style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;margin-bottom: 8px;\"><a href=\"https:\/\/mp.weixin.qq.com\/s?__biz=MzI0MjY5NTM2MQ==&amp;mid=2247506134&amp;idx=1&amp;sn=54254605dab9320714a4b0d67c04ba23&amp;scene=21#wechat_redirect\" data-linktype=\"2\" style=\"text-decoration: underline;font-size: 15px;\">\u7b2c\u4e8c\u8bb2\uff1a\u81ea\u65cb\u73bb\u7483\u6a21\u578b\u7b80\u4ecb\u548c\u7a7a\u8154\u6cd5<\/a><\/section>\n<\/li>\n<li>\n<section style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;margin-bottom: 8px;\"><a href=\"https:\/\/mp.weixin.qq.com\/s?__biz=MzI0MjY5NTM2MQ==&amp;mid=2247506173&amp;idx=1&amp;sn=950d650ead6c5485aef020a8d33b9679&amp;scene=21#wechat_redirect\" data-linktype=\"2\" style=\"text-decoration: underline;font-size: 15px;\">\u7b2c\u4e09\u8bb2\uff1a\u81ea\u65cb\u73bb\u7483\u6a21\u578b\u7b80\u4ecb\u548c\u7a7a\u8154\u6cd5\u4e0b<\/a><\/section>\n<\/li>\n<li>\n<section style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;margin-bottom: 8px;\"><a href=\"https:\/\/mp.weixin.qq.com\/s?__biz=MzI0MjY5NTM2MQ==&amp;mid=2247506190&amp;idx=2&amp;sn=8154741a618b3b05b05d94d98af51a33&amp;scene=21#wechat_redirect\" data-linktype=\"2\" style=\"text-decoration: underline;font-size: 15px;\">\u7b2c\u56db\u8bb2\uff1a\u53d8\u5206\u5e73\u5747\u573a\u7406\u8bba\u4e0e\u4fe1\u5ff5\u4f20\u64ad<\/a><\/section>\n<\/li>\n<li>\n<section style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;margin-bottom: 8px;\"><a href=\"https:\/\/mp.weixin.qq.com\/s?__biz=MzI0MjY5NTM2MQ==&amp;mid=2247506365&amp;idx=1&amp;sn=c4e8b01384a91aa0f6441fa45562a6b4&amp;scene=21#wechat_redirect\" data-linktype=\"2\" style=\"text-decoration: underline;font-size: 15px;\">\u7b2c\u4e94\u8bb2\uff1a\u8499\u7279\u5361\u7f57\u65b9\u6cd5\uff08\u4e00\uff09<\/a><\/section>\n<\/li>\n<li>\n<p style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;margin-bottom: 8px;\"><a href=\"https:\/\/mp.weixin.qq.com\/s?__biz=MzI0MjY5NTM2MQ==&amp;mid=2247506598&amp;idx=1&amp;sn=4bf4024e467d89099836b32deef0d9cf&amp;scene=21#wechat_redirect\" data-linktype=\"2\" style=\"text-decoration: underline;font-size: 15px;\">\u7b2c\u516d\u8bb2\uff1a\u8499\u7279\u5361\u7f57\u65b9\u6cd5\uff08\u4e8c\uff09<\/a><\/p>\n<\/li>\n<li style=\"font-size: 15px;\">\n<p style=\"margin-right: 8px;margin-left: 8px;white-space: normal;line-height: 1.75em;margin-bottom: 8px;\"><a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247645814&amp;idx=3&amp;sn=5e0f1c38c4f896fbed4c51071b30784b&amp;chksm=e899e0fbdfee69edded916ee564b2c8f9dcbc7d4f9ada5592e96c7f077f67c2dab1071ed2ab4&amp;scene=21#wechat_redirect\" textvalue=\"\" linktype=\"text\" imgurl=\"\" imgdata=\"null\" data-itemshowtype=\"0\" tab=\"innerlink\" data-linktype=\"2\" rel=\"noopener noreferrer\"><\/a><a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247645814&amp;idx=3&amp;sn=5e0f1c38c4f896fbed4c51071b30784b&amp;chksm=e899e0fbdfee69edded916ee564b2c8f9dcbc7d4f9ada5592e96c7f077f67c2dab1071ed2ab4&amp;scene=21#wechat_redirect\" textvalue=\"\u9ad8\u6e29\u5c55\u5f00 | \u5468\u516d\u76f4\u64ad\u00b7\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66\u8bfe\u7a0b\u7b2c\u4e03\u8bb2\" linktype=\"text\" imgurl=\"\" imgdata=\"null\" data-itemshowtype=\"0\" tab=\"innerlink\" style=\"font-size: 15px;text-decoration: underline;\" data-linktype=\"2\" rel=\"noopener noreferrer\"><span style=\"font-size: 15px;\">\u7b2c\u4e03\u8bb2\uff1a\u9ad8\u6e29\u5c55\u5f00<\/span><\/a><\/p>\n<\/li>\n<li style=\"font-size: 15px;\">\n<section style=\"margin-right: 8px;margin-bottom: 0px;margin-left: 8px;white-space: normal;line-height: 1.75em;\"><a target=\"_blank\" href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIzMjQyNzQ5MA==&amp;mid=2247648686&amp;idx=4&amp;sn=67cc3efd6c4e94c696dc328fbb284e9b&amp;chksm=e899df23dfee56350bfd631de67767de2806fc3531c23d360f4d6e9ee152eaf7e19b0e213789&amp;scene=21#wechat_redirect\" textvalue=\"Hopfield\u6a21\u578b\u7684\u7edf\u8ba1\u7269\u7406 | \u5468\u516d\u76f4\u64ad\u00b7\u795e\u7ecf\u7f51\u7edc\u7684\u7edf\u8ba1\u529b\u5b66\u8bfe\u7a0b\u7b2c\u516b\u8bb2\" linktype=\"text\" imgurl=\"\" imgdata=\"null\" data-itemshowtype=\"0\" tab=\"innerlink\" style=\"text-decoration: underline;\" data-linktype=\"2\" rel=\"noopener noreferrer\">\u7b2c\u516b\u8bb2\uff1aHopfield\u6a21\u578b\u7684\u7edf\u8ba1\u7269\u7406<\/a><br  \/><\/section>\n<\/li>\n<\/ul>\n<section style=\"margin-bottom: 0px;\"><br  \/><\/section>\n<section style=\"margin-bottom: 0px;\"><br  \/><\/section>\n<section style=\"outline: 0px;margin-bottom: 0px;\"><strong style=\"outline: 0px;letter-spacing: 0.544px;font-size: 15px;text-align: left;color: rgb(255, 255, 255);font-family: PingFangSC-light;\"><span style=\"outline: 0px;background-color: rgb(12, 130, 169);\">\u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u62a5\u540d\u8bfe\u7a0b<\/span><\/strong><\/section>\n<p style=\"display: none;\"><mp-style-type data-value=\"3\"><\/mp-style-type><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5bfc\u8bed 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