{"id":8508,"date":"2023-07-01T21:37:09","date_gmt":"2023-07-01T12:37:09","guid":{"rendered":"https:\/\/agirobots.com\/?p=8508"},"modified":"2023-07-02T00:53:00","modified_gmt":"2023-07-01T15:53:00","slug":"classical-hopfield-network","status":"publish","type":"post","link":"https:\/\/developers.agirobots.com\/jp\/classical-hopfield-network\/","title":{"rendered":"(Classical) Hopfield Network\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac"},"content":{"rendered":"\n<p>\u672c\u8a18\u4e8b\u3067\u306f1982\u5e74\u306b\u63d0\u6848\u3055\u308c\u305fClassical\u306aHopfield Network\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u77e5\u308b\u3053\u3068\u3092\u76ee\u6a19\u306b\u3001\u89e3\u8aac\u3057\u3066\u3044\u304d\u305f\u3044\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u9023\u60f3\u8a18\u61b6\u3068Hopfield Network<\/h2>\n\n\n\n<p>\u9023\u60f3\u8a18\u61b6\u3068\u306f\u3001\u3042\u308b\u7279\u5b9a\u306e\u4e8b\u67c4\u304b\u3089\u95a2\u9023\u6027\u306e\u3042\u308b\u5225\u306e\u4e8b\u67c4\u3092\u601d\u3044\u51fa\u3059\u80fd\u529b\u3001\u3059\u306a\u308f\u3061\u7279\u5b9a\u306e\u8a18\u61b6\u304c\u5225\u306e\u8a18\u61b6\u3092\u5f15\u304d\u51fa\u3059\u3068\u3044\u3046\u73fe\u8c61\u3092\u6307\u3057\u307e\u3059\u3002\u3053\u306e\u9023\u60f3\u8a18\u61b6\u306f\u3001\u4eba\u9593\u306e\u601d\u8003\u30d1\u30bf\u30fc\u30f3\u3084\u77e5\u6027\u306e\u5f62\u6210\u306b\u5927\u3044\u306b\u5f71\u97ff\u3092\u53ca\u307c\u3057\u3066\u3044\u308b\u3068\u8003\u3048\u3089\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" width=\"1024\" height=\"296\" src=\"https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-9-1024x296.png\" alt=\"\" class=\"wp-image-8509\" srcset=\"https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-9-1024x296.png 1024w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-9-300x87.png 300w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-9-768x222.png 768w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-9-1536x443.png 1536w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-9-2048x591.png 2048w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/div>\n\n\n<p>\u4e0a\u306e\u56f3\u306f\u3001\u300c\u30ea\u30f3\u30b4\u300d\u306b\u95a2\u9023\u3059\u308b\u9023\u60f3\u306e\u5177\u4f53\u4f8b\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u79c1\u305f\u3061\u306f\u300c\u30ea\u30f3\u30b4\u306f\u679c\u7269\u300d\u3001\u300c\u679c\u7269\u306f\u98df\u3079\u7269\u300d\u3001\u300c\u30ea\u30f3\u30b4\u306f\u8d64\u3044\u300d\u306a\u3069\u3001\u591a\u7a2e\u591a\u69d8\u306a\u6027\u8cea\u3084\u5074\u9762\u304b\u3089\u9023\u60f3\u3092\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u79c1\u305f\u3061\u306f\u3001\u7269\u4e8b\u3092\u69d8\u3005\u306a\u5074\u9762\u304b\u3089\u8003\u3048\u305f\u308a\u3001\u30a2\u30a4\u30c7\u30a3\u30a2\u3092\u51fa\u3057\u305f\u308a\u3059\u308b\u3068\u304d\u3001\u57fa\u672c\u7684\u306b\u306f\u81ea\u5206\u306e\u8a18\u61b6\u3092\u30d9\u30fc\u30b9\u306b\u9023\u60f3\u3092\u91cd\u306d\u3001\u305d\u306e\u9023\u60f3\u304c\u8ad6\u7406\u7684\u306b\u7b4b\u304c\u901a\u3066\u3044\u308b\u304b\u306a\u3069\u3092\u982d\u306e\u4e2d\u3067\u7e70\u308a\u8fd4\u3057\u691c\u8a3c\u3057\u305f\u308a\u3057\u3066\u3044\u307e\u3059\u3002\u79c1\u305f\u3061\u306e\u601d\u8003\u3084\u77e5\u6027\u306e\u69cb\u7bc9\u306b\u304a\u3044\u3066\u3001\u3053\u306e\u3088\u3046\u306a\u9023\u60f3\u7684\u306a\u30d7\u30ed\u30bb\u30b9\u304c\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3059\u3053\u3068\u306f\u7406\u89e3\u3044\u305f\u3060\u3051\u308b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u305d\u308c\u3067\u306f\u3001\u3053\u306e\u9023\u60f3\u8a18\u61b6\u306e\u6a5f\u80fd\u3092\u3069\u306e\u3088\u3046\u306b\u5b9f\u73fe\u3059\u308c\u3070\u826f\u3044\u306e\u3067\u3057\u3087\u3046\u304b\uff1f\u3053\u306e\u554f\u3044\u306b\u5bfe\u3059\u308b\u89e3\u3068\u3057\u3066\u63d0\u6848\u3055\u308c\u305f\u306e\u304c\u3001Hopfield Network[1]\u3068\u3044\u3046\u9023\u60f3\u8a18\u61b6\u30e2\u30c7\u30eb\u3067\u3059\u3002Hopfield Network\u306f\u30011982\u5e74\u306bJohn Hopfield\u304c\u63d0\u5531\u3057\u305f\u3082\u306e\u3067\u3059\u3002Hopfield\u304c\u63d0\u6848\u3057\u305f\u3053\u306e\u30e2\u30c7\u30eb\u306f\u300110\u5e74\u524d\u306b\u7518\u5229\u6c0f\u304c\u63d0\u5531\u3057\u305f\u30e2\u30c7\u30eb[2]\u3068\u5168\u304f\u540c\u4e00\u3067\u3042\u3063\u305f\u305f\u3081\u3001\u6642\u6298\u3001Amari-Hopfield\u30e2\u30c7\u30eb[3]\u3068\u3082\u547c\u3070\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u30e2\u30c7\u30eb\u306f\u3001\u8133\u304c<strong>\u60c5\u5831\u3092\u51e6\u7406\u3057<\/strong>\u3001<strong>\u95a2\u9023\u4ed8\u3051<\/strong>\u3001<strong>\u601d\u3044\u51fa\u3059<\/strong>\u3088\u3046\u306a\u6a5f\u80fd\u3092\u5b9f\u73fe\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u305d\u3057\u3066\u3001\u3053\u308c\u3089\u306fHopfield Network\u306e\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u69cb\u9020\u3001\u5b66\u7fd2\u65b9\u6cd5\u3001\u9023\u60f3\u65b9\u6cd5\u306b\u3064\u3044\u3066\u7406\u89e3\u3059\u308b\u3053\u3068\u3067\u3001\u305d\u308c\u3089\u306e\u6a5f\u80fd\u306e\u5b9f\u73fe\u65b9\u6cd5\u3092\u77e5\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u60c5\u5831\u306e\u51e6\u7406\u3000\u3000\uff1aHopfield Network\u306e<strong>\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u69cb\u9020<\/strong><br>\u60c5\u5831\u306e\u95a2\u9023\u4ed8\u3051\uff1aHopfield Network\u306e<strong>\u5b66\u7fd2\u65b9\u6cd5<\/strong><br>\u60c5\u5831\u3092\u601d\u3044\u51fa\u3059\uff1aHopfield Network\u306e<strong>\u60f3\u8d77\u65b9\u6cd5<\/strong><\/p>\n\n\n\n<p>\u3053\u308c\u3089\u306b\u3064\u3044\u3066\u9806\u306b\u8aac\u660e\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Hopfield Network\u306e\u8a73\u7d30<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u69cb\u9020<\/h3>\n\n\n\n<p>\u307e\u305a\u306f\u3001\u60c5\u5831\u51e6\u7406\u3092\u884c\u3046\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u69cb\u9020\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002Hopfield Network\u3067\u306f\u76f8\u4e92\u7d50\u5408\u578b\u306e\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u304c\u63a1\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u305d\u306e\u7406\u7531\u3092\u77e5\u308b\u306b\u306f\u3001\u79c1\u305f\u3061\u306e\u8133\u306b\u304a\u3044\u3066\u9023\u60f3\u8a18\u61b6\u3092\u53f8\u3063\u3066\u3044\u308b\u3068\u8003\u3048\u3089\u308c\u3066\u3044\u308b\u6d77\u99ac\u306e\u69cb\u9020\u306b\u3064\u3044\u3066\u8aac\u660e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u6d77\u99ac\u3068\u306f\u5927\u8133\u8fba\u7e01\u7cfb\u3092\u69cb\u6210\u3059\u308b\u90e8\u4f4d\u306e\uff11\u3064\u3067\u3001\u65ad\u9762\u306fCA1\u3001CA2\u3001CA3\u3068\u3044\u3046\u4e09\u3064\u306e\u9818\u57df\u306b\u533a\u5206\u3067\u304d\u307e\u3059\u3002\u3053\u3053\u3067\u7279\u7b46\u3059\u3079\u304d\u306a\u306e\u306f\u3001CA3\u3068\u547c\u3070\u308c\u308b\u90e8\u4f4d\u304c\u9023\u60f3\u8a18\u61b6\u3068\u5bc6\u63a5\u306a\u95a2\u9023\u6027\u304c\u3042\u308b\u3068\u8003\u3048\u3089\u308c\u3066\u3044\u308b\u70b9\u3067\u3059\u3002CA3\u3067\u306f\u3001\u795e\u7d4c\u7d30\u80de\u304c\u4e92\u3044\u306b\u76f8\u4e92\u63a5\u7d9a\u3092\u5f62\u6210\u3057\u3001\u8907\u96d1\u306a\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u69cb\u9020\u3092\u69cb\u7bc9\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u4e8b\u5b9f\u306b\u57fa\u3065\u3044\u3066\u3001Hopfield Network\u3067\u76f8\u4e92\u7d50\u5408\u578b\u306e\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u3092\u63a1\u7528\u3059\u308b\u3068\u3044\u3046\u306e\u306f\u3001\u751f\u7269\u5b66\u7684\u306a\u8996\u70b9\u304b\u3089\u3082\u9ad8\u3044\u59a5\u5f53\u6027\u3092\u6301\u3063\u3066\u3044\u308b\u3068\u8a00\u3048\u308b\u3067\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1024\" height=\"407\" src=\"https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-10-1024x407.png\" alt=\"\" class=\"wp-image-8511\" srcset=\"https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-10-1024x407.png 1024w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-10-300x119.png 300w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-10-768x305.png 768w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-10-1536x610.png 1536w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-10-2048x814.png 2048w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>\u4e0a\u56f3\u53f3\u306b\u793a\u3057\u305f\u76f8\u4e92\u7d50\u5408\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306f\u3001\u4ee5\u964d\u306e\u8aac\u660e\u306b\u304a\u3044\u3066\u4e0d\u4fbf\u306a\u306e\u3067\u3001\u6539\u3081\u3066\u76f8\u4e92\u7d50\u5408\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306e\u30b0\u30e9\u30d5\u69cb\u9020\u306b\u3064\u3044\u3066\u3001\u3053\u3053\u3067\u5b9a\u7fa9\u3057\u3066\u304a\u304d\u307e\u3059\u3002\u4e0a\u56f3\u53f3\u306e\u76f8\u4e92\u7d50\u5408\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u3092\u305d\u306e\u307e\u307e\u30b0\u30e9\u30d5\u306b\u8868\u3057\u305f\u306e\u304c\u4e0b\u56f3\u5de6\u3067\u3059\u3002\u3053\u3053\u3067\u3001\u9752\u4e38\u306f\u30cb\u30e5\u30fc\u30ed\u30f3\u3092\u3001\u9ed2\u7dda\u306f\u7d50\u5408\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3057\u304b\u3057\u3001Hopfield Network\u306f\u4e0b\u56f3\u5de6\u306e\u76f8\u4e92\u7d50\u5408\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u3092\u305d\u306e\u307e\u307e\u4f7f\u308f\u305a\u3001\u5e7e\u3064\u304b\u306e\u5236\u7d04\u3092\u52a0\u3048\u305f\u4e0b\u56f3\u53f3\u306b\u793a\u3059\u3088\u3046\u306a\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u69cb\u9020\u3092\u63a1\u7528\u3057\u3066\u3044\u307e\u3059\u3002\u8a73\u3057\u304f\u8aac\u660e\u3057\u307e\u3059\u3002\u3042\u308b\u30cb\u30e5\u30fc\u30ed\u30f3\\(i\\)\u3068\\(j\\)\u9593\u306e\u91cd\u307f\u306b\u3064\u3044\u3066\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u3053\u306e\u91cd\u307f\u306b\u306f\u3001\\(i\\rightarrow j\\)\u306e\u91cd\u307f\\(w_{ij}\\)\u3068\u9006\u65b9\u5411\u306e\\(j\\rightarrow i\\)\u306e\u91cd\u307f\\(w_{ji}\\)\u306e2\u3064\u304c\u8003\u3048\u3089\u308c\u307e\u3059\u3002\u5de6\u306e\u56f3\u3067\u306f\u305d\u308c\u305e\u308c\u304c\u5225\u306e\u30d1\u30b9\u3068\u3057\u3066\u8868\u3055\u308c\u3066\u304a\u308a\u3001\u305d\u308c\u3089\u306e\u91cd\u307f\u306e\u9593\u306b\u5236\u7d04\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u3057\u304b\u3057\u3001Hopfield Network\u3067\u306f\u3001\u305d\u308c\u3089\u306e\u91cd\u307f\u306e\u9593\u306b\\(w_{ij}=w_{ji}\\)\u3068\u3044\u3046\u5236\u7d04\u3092\u8a2d\u3051\u307e\u3059\u3002\u4e00\u898b\u3059\u308b\u3068\u3001\u5de6\u5074\u306e\u56f3\u306e\u3088\u3046\u306b\u5236\u7d04\u3092\u8a2d\u3051\u305a\u306b\u7406\u8ad6\u3092\u767a\u5c55\u3055\u305b\u305f\u65b9\u304c\u3001\u3088\u308a\u8c4a\u5bcc\u306a\u8868\u73fe\u304c\u53ef\u80fd\u306b\u306a\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u304c\u3001\u53f3\u5074\u306e\u5f62\u5f0f\u306b\u3088\u3063\u3066Hopfield Network\u306e\u7406\u8ad6\u306f\u9032\u5316\u3057\u3066\u304d\u307e\u3057\u305f\u3002\u3053\u308c\u306f\u3001\u305d\u306e\u7279\u6027\u3068\u3057\u3066\u53d7\u3051\u5165\u308c\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u3067\u3057\u3087\u3046\u3002\u7406\u7531\u306b\u3064\u3044\u3066\u306f\u79c1\u306f\u5b58\u3058\u4e0a\u3052\u307e\u305b\u3093\u304c\u3001\u3082\u3057\u304b\u3057\u305f\u3089\u8a08\u7b97\u30b3\u30b9\u30c8\u3084\u7406\u8ad6\u306e\u69cb\u7bc9\u306e\u3057\u3084\u3059\u3055\u306a\u3069\u304c\u95a2\u308f\u3063\u3066\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" width=\"1024\" height=\"604\" src=\"https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-14-1024x604.png\" alt=\"\" class=\"wp-image-8524\" srcset=\"https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-14-1024x604.png 1024w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-14-300x177.png 300w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-14-768x453.png 768w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-14-1536x905.png 1536w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-14-2048x1207.png 2048w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/div>\n\n\n<p>\u76f8\u4e92\u7d50\u5408\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306e\u30a4\u30e9\u30b9\u30c8\u306b\u304a\u3044\u3066\u3001\u7d50\u5408\u3092\u8868\u3059\u7dda\u306e\u5148\u7aef\u306e\u77e2\u5370\u306f\u4e00\u822c\u7684\u306b\u7701\u7565\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u7d50\u5408\u306b\u65b9\u5411\u6027\u304c\u306a\u3044\u305f\u3081\u3067\u3059\u3002\u307e\u305f\u3001\u8996\u899a\u7684\u306a\u89b3\u70b9\u304b\u3089\u898b\u3066\u3082\u3001\u7dda\u306e\u7aef\u306b\u77e2\u5370\u3092\u3064\u3051\u305a\u306b\u63cf\u304f\u3053\u3068\u3067\u3001\u56f3\u5168\u4f53\u304c\u7169\u96d1\u306b\u306a\u308b\u3053\u3068\u3092\u907f\u3051\u3001\u8996\u8a8d\u6027\u3092\u9ad8\u3081\u308b\u3053\u3068\u304c\u53ef\u80fd\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u4ee5\u4e0b\u306e\u56f3\u306f\u3001\u30cb\u30e5\u30fc\u30ed\u30f3\u6570\u304c\u5897\u52a0\u3057\u305fHopfield Network\u306e\u30a4\u30e9\u30b9\u30c8\u3067\u3059\u3002\u3053\u3053\u3067\u306f\u7dda\u306e\u4e21\u7aef\u306b\u77e2\u5370\u3092\u4ed8\u3051\u305a\u306b\u63cf\u3044\u3066\u3044\u3066\u3001\u77e2\u5370\u90e8\u5206\u304c\u91cd\u306a\u3063\u3066\u898b\u3065\u3089\u304f\u306a\u308b\u3068\u3044\u3046\u4e8b\u614b\u3092\u907f\u3051\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u4ee5\u964d\u306e\u8aac\u660e\u3067\u3082\u3001Hopfield Network\u306e\u30ce\u30fc\u30c9\u9593\u306e\u30a8\u30c3\u30b8\u306b\u3064\u3044\u3066\u306f\u77e2\u5370\u3092\u7701\u7565\u3057\u3001\u30b7\u30f3\u30d7\u30eb\u306a\u7dda\u3067\u8868\u73fe\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1024\" height=\"1024\" src=\"https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-1-1024x1024.png\" alt=\"\" class=\"wp-image-8421\" srcset=\"https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-1-1024x1024.png 1024w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-1-300x300.png 300w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-1-150x150.png 150w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-1-768x767.png 768w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-1-100x100.png 100w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-1.png 1470w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>\u3067\u306f\u3001Hopfield Network\u3067\u7528\u3044\u3089\u308c\u308b\u30cb\u30e5\u30fc\u30ed\u30f3\u306e\u30e2\u30c7\u30eb\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u4f7f\u7528\u3055\u308c\u308b\u30cb\u30e5\u30fc\u30ed\u30f3\u306f\u3001\u72b6\u614b\u30922\u3064\u3057\u304b\u6301\u305f\u306a\u3044\u30d0\u30a4\u30ca\u30ea\u30cb\u30e5\u30fc\u30ed\u30f3\u3067\u3059\u3002\u6d3b\u6027\u5316\u95a2\u6570\u306b\u306f\u7b26\u53f7\u95a2\u6570\\(\\text{sgn}\\)\u304c\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\\(\\text{sgn}\\)\u95a2\u6570\u306f\u6b21\u306e\u5f0f\u3067\u8868\u3055\u308c\u3001\u30b0\u30e9\u30d5\u3067\u8868\u3059\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$<br>\\text{sgn}(x) = \\begin{cases} <br>1 &amp; \\text{if } x &gt; 0\\\\<br>0 &amp; \\text{if } x = 0\\\\ <br>-1 &amp; \\text{if } x &lt; 0<br>\\end{cases}<br>$$<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"601\" height=\"438\" src=\"https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-11.png\" alt=\"\" class=\"wp-image-8512\" srcset=\"https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-11.png 601w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-11-300x219.png 300w\" sizes=\"(max-width: 601px) 100vw, 601px\" \/><\/figure><\/div>\n\n\n<p>Hopfield Network\u304c\\(d\\)\u500b\u306e\u30cb\u30e5\u30fc\u30ed\u30f3\u304b\u3089\u69cb\u6210\u3055\u308c\u3066\u3044\u308b\u3068\u3057\u307e\u3059\u3002\u307e\u305f\u3001\\(i\\)\u756a\u76ee\u306e\u30cb\u30e5\u30fc\u30ed\u30f3\u3068\\(j\\)\u756a\u76ee\u306e\u30cb\u30e5\u30fc\u30ed\u30f3\u306e\u91cd\u307f\u3092\\(w_{ij}\\)\u3068\u8868\u3057\u3001\u5168\u3066\u306e\u30cb\u30e5\u30fc\u30ed\u30f3\u9593\u306e\u91cd\u307f\u3092\\(d\\times d\\)\u306e\u884c\u5217\\(\\boldsymbol{W}=(w_{ij})\\)\u3068\u3057\u3066\u8868\u8a18\u3059\u308b\u3053\u3068\u306b\u3057\u307e\u3059\u3002<br>\u203bClassical\u306aHopfield Network\u306f\u3001\u81ea\u5df1\u7d50\u5408\u3092\u6301\u305f\u306a\u3044\u30e2\u30c7\u30eb\u3068\u3057\u3066\u5b9a\u5f0f\u5316\u3055\u308c\u3066\u3044\u307e\u3059\uff08\u3064\u307e\u308a\\(w_{ii}=0\\)\uff09\u3002<\/p>\n\n\n\n<p>\u3042\u308b\u6642\u523b\\(t\\)\u306e\u3042\u308b\u30cb\u30e5\u30fc\u30ed\u30f3\\(i\\)\u306e\u72b6\u614b\uff08\uff1d\u51fa\u529b\uff09\u3092\\(\\xi_i(t)\\)\u3068\u66f8\u304f\u3068\u304d\u3001\u3042\u308b\u30cb\u30e5\u30fc\u30ed\u30f3\u306e\u6b21\u306e\u72b6\u614b\u306f\u4ee5\u4e0b\u306e\u5f0f\u3067\u8868\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$<br>\\xi_i(t+1) = \\text{sgn}\\left(\\sum_{j=1, j\\neq i}^d w_{ij}\\xi_i(t) + b_i\\right)<br>$$<\/p>\n\n\n\n<p>\u3053\u3053\u3067\u3001\\(b\\)\u306f\u30d0\u30a4\u30a2\u30b9\u3067\u3059\u3002\u306a\u305c\u3001\u30cb\u30e5\u30fc\u30ed\u30f3\u306e\u5fdc\u7b54\u3092\u3053\u306e\u3088\u3046\u306b\u8a18\u8ff0\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u306e\u304b\u306b\u3064\u3044\u3066\u7591\u554f\u306b\u601d\u3044\u307e\u3057\u305f\u3089\u3001\u73fe\u5728\u306e\u30cb\u30e5\u30fc\u30ed\u30f3\u30e2\u30c7\u30eb\u306e\u7956\u3068\u3082\u3044\u3048\u308b\u30de\u30ab\u30ed\u30c3\u30af\u30d4\u30c3\u30c4\u30cb\u30e5\u30fc\u30ed\u30f3[4]\u306b\u3064\u3044\u3066\u8abf\u3079\u3066\u307f\u308b\u3068\u3088\u3044\u3067\u3057\u3087\u3046\uff08\u4e0b\u56f3\u306e\u901a\u308a\uff09\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"652\" height=\"412\" src=\"https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2020\/11\/image-23.png\" alt=\"\" class=\"wp-image-2943\" srcset=\"https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2020\/11\/image-23.png 652w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2020\/11\/image-23-300x190.png 300w\" sizes=\"(max-width: 652px) 100vw, 652px\" \/><\/figure><\/div>\n\n\n<p>\u4ee5\u4e0a\u3088\u308a\u3001Hopfield Network\u306e\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306e\u69cb\u9020\u306b\u3064\u3044\u3066\u6982\u8981\u304c\u7406\u89e3\u3067\u304d\u305f\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u5b66\u7fd2\u65b9\u6cd5<\/h3>\n\n\n\n<p>\u3055\u3066\u3001\u6b21\u306b\u60c5\u5831\u3092\u95a2\u9023\u4ed8\u3051\u308b\u4ed5\u7d44\u307f\u3001\u3059\u306a\u308f\u3061\u8a18\u61b6\u3059\u308b\u65b9\u6cd5\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u9023\u60f3\u8a18\u61b6\u306f\u3001\u3042\u308b\u610f\u5473\u3067\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u3092\u6d3b\u7528\u3057\u305f\u30c7\u30fc\u30bf\u30d9\u30fc\u30b9\u306e\u3088\u3046\u306a\u5b58\u5728\u3067\u3059\u3002\u4f8b\u3048\u3070\u3001\u30c7\u30fc\u30bf\u30d9\u30fc\u30b9\u3067\u306f\u4e00\u822c\u7684\u306bSQL\u3068\u547c\u3070\u308c\u308b\u30c7\u30fc\u30bf\u30d9\u30fc\u30b9\u8a00\u8a9e\u304c\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002SQL\u3067\u306f\u3001\u65b0\u3057\u3044\u30c7\u30fc\u30bf\u3092\u8ffd\u52a0\u3059\u308b\u305f\u3081\u306b\"INSERT\"\u6587\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u3053\u306e\u30d7\u30ed\u30bb\u30b9\u306f\u3001Hopfield Network\u306b\u304a\u3051\u308b\"\u5b66\u7fd2\"\u306b\u76f8\u5f53\u3057\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u3053\u3053\u3067\u8a00\u3046\"\u5b66\u7fd2\"\u306f\u3001\u6df1\u5c64\u5b66\u7fd2\u306b\u304a\u3051\u308b\u8aa4\u5dee\u9006\u4f1d\u64ad\u6cd5\u306e\u3088\u3046\u306a\u8907\u96d1\u306a\u30d7\u30ed\u30bb\u30b9\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n\n\n\n<p>\u5177\u4f53\u7684\u306b\u306f\u3001\u8a18\u61b6\u3055\u305b\u305f\u3044\u30c7\u30fc\u30bf\u3092\\(\\{\\boldsymbol{x}_i\\}_{i=1}^N\\)\uff08\\(\\boldsymbol{x}_i\\in\\{-1, 1\\}^d\\)\uff09\u3068\u8868\u73fe\u3057\u305f\u3068\u304d\u3001Hopfield Network\u306e\u91cd\u307f\u884c\u5217\\(\\boldsymbol{W} \\)\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3057\u3066\u5b9a\u7fa9\u3059\u308b\u3060\u3051\u3067\u8a18\u61b6\u3055\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$<br>\\boldsymbol{W} = \\sum_{i=1}^N \\boldsymbol{x}_i\\boldsymbol{x}_i^T<br>$$<\/p>\n\n\n\n<p>\u305f\u3063\u305f\u3053\u308c\u3060\u3051\u306a\u3093\u3067\u3059\u3002\u4e00\u822c\u7684\u306a\u6df1\u5c64\u5b66\u7fd2\u3067\u4f7f\u7528\u3055\u308c\u308b\u8aa4\u5dee\u9006\u4f1d\u64ad\u306e\u3088\u3046\u306a\u8907\u96d1\u306a\u6700\u9069\u5316\u554f\u984c\u3092\u5fc5\u8981\u3068\u305b\u305a\u306b\u5b66\u7fd2\u3092\u884c\u3046\u305f\u3081\u3001\u66f4\u306b\u65b0\u3057\u3044\u30c7\u30fc\u30bf\\(\\boldsymbol{x}_{add}\\)\u3092\u8ffd\u52a0\u3067\u8a18\u61b6\u3055\u305b\u305f\u3044\u5834\u5408\u3067\u3082\u3001\u8ffd\u52a0\u30c7\u30fc\u30bf\u304b\u3089\u8a08\u7b97\u3055\u308c\u308b\u884c\u5217\\(\\boldsymbol{x}_{add}\\boldsymbol{x}_{add}^T\\)\u3092\u65e2\u5b58\u306e\u91cd\u307f\u884c\u5217\u306b\u52a0\u7b97\u3059\u308b\u3060\u3051\u3067\u6e08\u3080\u306e\u3067\u3059\u3002<\/p>\n\n\n\n<p>$$<br>\\boldsymbol{W} \\leftarrow \\boldsymbol{W} + \\boldsymbol{x}_{add}\\boldsymbol{x}_{add}^T<br>$$<br>\u203b\u30c7\u30fc\u30bf\u3092\u5fd8\u308c\u3055\u305b\u305f\u3044\u3068\u304d\u3082\u3001\u8a18\u61b6\u6e08\u307f\u306e\u30d1\u30bf\u30fc\u30f3\u3092\u6e1b\u7b97\u3059\u308b\u3060\u3051\u3067\u6e08\u307f\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u5b66\u7fd2\u65b9\u6cd5\u306f\u3001\u30d8\u30d6\u5247\u3068\u3044\u3046\u539f\u5247\u306b\u57fa\u3065\u3044\u3066\u3044\u307e\u3059\u3002\u30d8\u30d6\u5247\u306f\u3001\u540c\u6642\u306b\u6d3b\u52d5\u3059\u308b\u30cb\u30e5\u30fc\u30ed\u30f3\u9593\u306e\u63a5\u7d9a\u3092\u5f37\u5316\u3057\u3001\u305d\u308c\u4ee5\u5916\u306e\u63a5\u7d9a\u3092\u5f31\u5316\u3059\u308b\u3068\u3044\u3046\u539f\u5247\u3067\u3059\u3002\u884c\u5217\u3067\u8868\u73fe\u3055\u308c\u308b\u3068\u5c11\u3005\u8907\u96d1\u306b\u898b\u3048\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u306e\u3067\u3001\u7279\u5b9a\u306e\u30cb\u30e5\u30fc\u30ed\u30f3\\(i\\)\u3068\\(j\\)\u9593\u306e\u91cd\u307f\u66f4\u65b0\u5f0f\u3060\u3051\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<p>$$<br>w_{ij} \\leftarrow w_{ij} + \\Delta w_{ij}\\ \\ (= w_{ij} + x_ix_j)<br>$$<\/p>\n\n\n\n<p>\u3053\u306e\u5f0f\u306f\u3001\\(i\\)\u3068\\(j\\)\u306e\u4e21\u65b9\u306e\u72b6\u614b\u304c1\u3067\u3042\u308b\u5834\u5408\u306f1\u3092\u52a0\u7b97\u3057\u3001\u4e00\u65b9\u304c1\u3067\u4ed6\u65b9\u304c-1\u3067\u3042\u308b\u5834\u5408\u306f\u91cd\u307f\u304b\u30891\u3092\u6e1b\u7b97\u3059\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306b\u3001Hopfield Network\u306e\u5b66\u7fd2\u6cd5\u306f\u975e\u5e38\u306b\u30b7\u30f3\u30d7\u30eb\u3067\u76f4\u611f\u7684\u3067\u3059\u3002\u6df1\u5c64\u5b66\u7fd2\u3068\u6bd4\u3079\u3066\u3001\u7e70\u308a\u8fd4\u3057\u5b66\u7fd2\u306b\u591a\u304f\u306e\u6642\u9593\u3092\u304b\u3051\u308b\u5fc5\u8981\u304c\u306a\u3044\u3060\u3051\u3067\u306a\u304f\u3001\u65b0\u3057\u3044\u30c7\u30fc\u30bf\u3092\u8ffd\u52a0\u3059\u308b\u969b\u306b\u5168\u3066\u3092\u518d\u5b66\u7fd2\u3059\u308b\u5fc5\u8981\u304c\u306a\u3044\u3068\u3044\u3046\u5229\u70b9\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u70b9\u3067\u3001Hopfield Network\u306f\u975e\u5e38\u306b\u52b9\u7387\u7684\u3067\u3042\u308a\u3001\u65b0\u305f\u306a\u8996\u70b9\u3092\u63d0\u4f9b\u3057\u3066\u304f\u308c\u307e\u3059\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"740\" height=\"118\" src=\"https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2020\/10\/hopfield-1.jpg\" alt=\"\" class=\"wp-image-2390\" srcset=\"https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2020\/10\/hopfield-1.jpg 740w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2020\/10\/hopfield-1-300x48.jpg 300w\" sizes=\"(max-width: 740px) 100vw, 740px\" \/><\/figure><\/div>\n\n\n<h3 class=\"wp-block-heading\">\u60f3\u8d77\u65b9\u6cd5<\/h3>\n\n\n\n<p>\u305d\u308c\u3067\u306f\u3001\u60c5\u5831\u3092\u601d\u3044\u51fa\u3059\u65b9\u6cd5\u3001\u3059\u306a\u308f\u3061\u60f3\u8d77\u65b9\u6cd5\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u307e\u305a\u3001\u6df1\u5c64\u5b66\u7fd2\u3067\u306f\u3001\u8aa4\u5dee\u9006\u4f1d\u64ad\u3092\u542b\u3080\u69d8\u3005\u306a\u624b\u6cd5\u3092\u7528\u3044\u3066\u5b66\u7fd2\u306e\u6700\u9069\u5316\u304c\u884c\u308f\u308c\u3001\u63a8\u8ad6\u30d5\u30a7\u30fc\u30ba\u3067\u306f\u30c7\u30fc\u30bf\u306f\u4e00\u5ea6\u3060\u3051\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306b\u5165\u529b\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u306b\u5bfe\u3057\u3001Hopfield Network\u3067\u306f\u3001\u30c7\u30fc\u30bf\u306e\u683c\u7d0d\u306f\u77ac\u6642\u306b\u884c\u308f\u308c\u307e\u3059\uff08\u65e2\u8ff0\u306e\u901a\u308a\uff09\u304c\u3001\u305d\u306e\u30c7\u30fc\u30bf\u3092\u60f3\u8d77\u3059\u308b\u904e\u7a0b\u306f\u72b6\u614b\u30d9\u30af\u30c8\u30eb\\(\\boldsymbol{\\xi}\\in\\mathbb{R}^d\\)\uff08\u3059\u3079\u3066\u306e\u30cb\u30e5\u30fc\u30ed\u30f3\u306e\u72b6\u614b\u3092\u30d9\u30af\u30c8\u30eb\u306b\u3057\u305f\u3082\u306e\uff09\u306e\u5404\u6210\u5206\u304c\u5909\u5316\u3057\u306a\u304f\u306a\u308b\u3001\u3064\u307e\u308a\\(\\boldsymbol{\\xi}(t+1)=\\boldsymbol{\\xi}(t)\\)\u3068\u306a\u308b\u307e\u3067\u7e70\u308a\u8fd4\u3055\u308c\u307e\u3059\u3002\u3053\u3053\u3067\u5168\u3066\u306e\u30cb\u30e5\u30fc\u30ed\u30f3\u306e\u30d0\u30a4\u30a2\u30b9\u3092\u4e26\u3079\u3066\u30d9\u30af\u30c8\u30eb\u306b\u3057\u305f\u3082\u306e\u3092\\(\\boldsymbol{b}\\in\\mathbb{R}^d\\)\u3068\u3059\u308b\u3068\u3001\u66f4\u65b0\u5f0f\u306f\\(\\boldsymbol{\\xi}(t+1) = \\text{sgn}(\\boldsymbol{W}\\boldsymbol{\\xi}(t) + \\boldsymbol{b})\\)\u3068\u306a\u308a\u307e\u3059\u3002\u3061\u306a\u307f\u306b\u3001\u3053\u306e\u66f4\u65b0\u5f0f\u306f\u4e00\u5ea6\u306e\u8a08\u7b97\u3067\u3001\u5168\u3066\u306e\u30cb\u30e5\u30fc\u30ed\u30f3\u306e\u72b6\u614b\u3092\u66f4\u65b0\uff08\uff1d\u540c\u671f\u66f4\u65b0\uff09\u3057\u307e\u3059\u304c\u3001\u5b9f\u306fHopfield Network\u306f\u3001\u5168\u3066\u306e\u30cb\u30e5\u30fc\u30ed\u30f3\u306e\u72b6\u614b\u3092\u4e00\u62ec\u3067\u66f4\u65b0\u3059\u308b\u540c\u671f\u66f4\u65b0\u3067\u306f\u306a\u304f\u3001\u3042\u308b\u7279\u5b9a\u306e\u6642\u523b\\(t\\)\u3067\u66f4\u65b0\u3055\u308c\u308b\u30cb\u30e5\u30fc\u30ed\u30f3\u306e\u6570\u306b\u5236\u9650\u3092\u8a2d\u3051\u305f\u975e\u540c\u671f\u66f4\u65b0\u304c\u63a1\u7528\u3055\u308c\u3066\u3044\u308b\u306e\u3067\u3001\u66f4\u65b0\u5f0f\u306f\u53b3\u5bc6\u306b\u306f\u7570\u306a\u308a\u3001\u4e00\u822c\u7684\u306b\u306f\u3001\u4e00\u56de\u306e\u66f4\u65b0\u3067\u5909\u5316\u3059\u308b\u30cb\u30e5\u30fc\u30ed\u30f3\u306e\u6570\u306f1\u3064\u306b\u9650\u5b9a\u3055\u308c\u3066\u3044\u307e\u3059\uff08\u3053\u308c\u306f\u6b21\u306b\u8aac\u660e\u3059\u308b\u30a8\u30cd\u30eb\u30ae\u30fc\u95a2\u6570\u306e\u60f3\u8d77\u904e\u7a0b\u306b\u304a\u3051\u308b\u5358\u8abf\u6e1b\u5c11\u3092\u4fdd\u8a3c\u3059\u308b\u305f\u3081\u3067\u3042\u308b\u3068\u8003\u3048\u3089\u308c\u3001\u3042\u307e\u308a\u5927\u304d\u306a\u554f\u984c\u3067\u306f\u306a\u3044\uff09\u3002<\/p>\n\n\n\n<p>\u4e0b\u306e\u56f3\u3092\u898b\u3066\u304f\u3060\u3055\u3044\u3002\u3053\u306e\u56f3\u3067\u306f\u3001\u30ea\u30f3\u30b4\u306e\u753b\u50cf\u3092\u5b66\u7fd2\u6e08\u307f\u306eHopfield Network\u306b\u3001\u534a\u5206\u6b20\u3051\u305f\u30ea\u30f3\u30b4\u306e\u753b\u50cf\u3092\u6642\u523b\\(t=1\\)\u3067\u5165\u529b\u3057\u3001\u305d\u306e\u5f8c\u9806\u6b21\u30cb\u30e5\u30fc\u30ed\u30f3\u306e\u72b6\u614b\u3092\u66f4\u65b0\u3059\u308b\u3053\u3068\u3067\u3001\u60f3\u8d77\u3059\u308b\u904e\u7a0b\u3092\u8996\u899a\u7684\u306b\u8868\u73fe\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u904e\u7a0b\u306b\u3088\u308a\u3001\u6b20\u3051\u3066\u3044\u305f\u30ea\u30f3\u30b4\u306e\u753b\u50cf\u304c\u5f90\u3005\u306b\u660e\u77ad\u306b\u306a\u308a\u3001\u5b66\u7fd2\u6e08\u307f\u306e\u30ea\u30f3\u30b4\u306e\u753b\u50cf\u304c\u6d6e\u304b\u3073\u4e0a\u304c\u3063\u3066\u304d\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306bHopfield Network\u3092\u7528\u3044\u308b\u3068\u3001\u4e00\u90e8\u304b\u3089\u5168\u4f53\u306e\u60c5\u5831\u3092\u60f3\u8d77\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u753b\u50cf\u306e\u60f3\u8d77\u306a\u306e\u3067\u79c1\u305f\u3061\u306b\u3068\u3063\u3066\u30a4\u30e1\u30fc\u30b8\u3057\u3084\u3059\u3044\u3067\u3059\u304c\u3001\u5358\u8a9e\u304b\u3089\u6587\u7ae0\u3092\u60f3\u8d77\u3059\u308b\u5834\u5408\u3067\u3082\u540c\u3058\u3088\u3046\u306b\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" width=\"1024\" height=\"500\" src=\"https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-15-1024x500.png\" alt=\"\" class=\"wp-image-8531\" srcset=\"https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-15-1024x500.png 1024w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-15-300x147.png 300w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-15-768x375.png 768w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-15-1536x751.png 1536w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-15-2048x1001.png 2048w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/div>\n\n\n<h2 class=\"wp-block-heading\">Hopfield Network\u306e\u7279\u5fb4<\/h2>\n\n\n\n<p>\u3053\u3053\u307e\u3067\u793a\u3057\u3066\u304d\u305f\u5185\u5bb9\u3060\u3051\u3067\u9023\u60f3\u8a18\u61b6\u304c\u5b9f\u73fe\u3067\u304d\u3066\u3057\u307e\u3044\u307e\u3059\u3002\u8907\u96d1\u306a\u6700\u9069\u5316\u554f\u984c\u3068\u3057\u3066\u5b9a\u5f0f\u5316\u3059\u308b\u3053\u3068\u306a\u304f\u3001\u5358\u7d14\u306a\u4ed5\u7d44\u307f\u3067\u5b9f\u73fe\u3067\u304d\u308b\u306e\u306f\u3068\u3066\u3082\u51c4\u3044\u3053\u3068\u3060\u3068\u601d\u3044\u307e\u3059\u3002\u3053\u3053\u3067\u306f\u3001Hopfield Network\u306e\u7279\u5fb4\u3068\u3057\u3066\u3001\u30a8\u30cd\u30eb\u30ae\u30fc\u95a2\u6570\u3068\u8a18\u61b6\u5bb9\u91cf\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u30a8\u30cd\u30eb\u30ae\u30fc\u95a2\u6570<\/h3>\n\n\n\n<p>\u5b9f\u306f\u3001Hopfield Network\u306e\u60f3\u8d77\u30d7\u30ed\u30bb\u30b9\u306f\u3001\u3042\u308b\u30a8\u30cd\u30eb\u30ae\u30fc\u95a2\u6570\u306e\u6975\u5c0f\u5024\u3078\u79fb\u52d5\u3059\u308b\u30d7\u30ed\u30bb\u30b9\u3067\u3042\u308b\u3053\u3068\u304c\u5206\u304b\u3063\u3066\u3044\u307e\u3059\u3002\u305d\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u95a2\u6570\u3068\u306f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u73fe\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$<br>E = -\\frac{1}{2}\\boldsymbol{\\xi}^T\\boldsymbol{W}\\boldsymbol{\\xi} - \\boldsymbol{\\xi}^T\\boldsymbol{b}<br>$$<\/p>\n\n\n\n<p>Hopfield Network\u304c\u60f3\u8d77\u3059\u308b\u30d7\u30ed\u30bb\u30b9\u306f\u30a8\u30cd\u30eb\u30ae\u30fc\u95a2\u6570\u4e0a\u306b\u30dc\u30fc\u30eb\u3092\u843d\u3068\u3057\u3001\u305d\u3053\u304b\u3089\u30dc\u30fc\u30eb\u304c\u52fe\u914d\u3092\u6cbf\u3063\u3066\u8ee2\u304c\u308a\u3001\u4e00\u756a\u8fd1\u304f\u306e\u5c40\u6240\u89e3\u3067\u505c\u6b62\u3059\u308b\u69d8\u5b50\u3092\u8003\u3048\u308b\u3068\u7406\u89e3\u3057\u3084\u3059\u3044\u3067\u3059\u3002\u3059\u306a\u308f\u3061\u3001\u8a18\u61b6\u30d1\u30bf\u30fc\u30f3\u306f\u30a8\u30cd\u30eb\u30ae\u30fc\u95a2\u6570\u306e\u5c40\u6240\u89e3\u3068\u306a\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" width=\"1024\" height=\"827\" src=\"https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-12-1024x827.png\" alt=\"\" class=\"wp-image-8521\" srcset=\"https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-12-1024x827.png 1024w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-12-300x242.png 300w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-12-768x620.png 768w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-12.png 1330w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/div>\n\n\n<h3 class=\"wp-block-heading\">\u8a18\u61b6\u5bb9\u91cf<\/h3>\n\n\n\n<p>Hopfield Network\u306b\u8a18\u61b6\u3055\u305b\u308b\u30d1\u30bf\u30fc\u30f3\u6570\u304c\u591a\u304f\u306a\u308b\u3068\u3001\u60f3\u8d77\u3055\u308c\u308b\u30d1\u30bf\u30fc\u30f3\u304c\u5d29\u58ca\u3059\u308b\u306a\u3069\u3001\u6025\u6fc0\u306b\u60f3\u8d77\u3067\u304d\u306a\u304f\u306a\u308b\u8ab2\u984c\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u306e\u8981\u56e0\u306e\uff11\u3064\u306bHopfield Network\u306e\u8a18\u61b6\u5bb9\u91cf\u306e\u554f\u984c\u304c\u3042\u308a\u307e\u3059\u3002\u672c\u8a18\u4e8b\u3067\u8aac\u660e\u3057\u3066\u3044\u308bClassical\u306aHopfield Network\u306e\u8a18\u61b6\u5bb9\u91cf\\(C\\)\u306f\u304a\u3088\u305d\\(0.138d\\)\u3068\u3055\u308c\u3066\u3044\u307e\u3059\uff08\u30e9\u30f3\u30c0\u30e0\u306a\u30c7\u30fc\u30bf\u3092\u8a18\u61b6\u3055\u305b\u308b\u5834\u5408\uff09\u3002<\/p>\n\n\n\n<p>\u8a18\u61b6\u5bb9\u91cf\\(0.138d\\)\u306e\u52b9\u7387\u306e\u60aa\u3055\u3092\u30a4\u30e1\u30fc\u30b8\u3057\u3066\u3044\u305f\u3060\u304f\u305f\u3081\u306b\u4ee5\u4e0b\u306e\u5177\u4f53\u4f8b\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002HD\u30b5\u30a4\u30ba\uff08\\(1920\\times1280\\)\uff09\u306e\u767d\u9ed2\u753b\u50cf\u3092\u8a18\u61b6\uff06\u60f3\u8d77\u3067\u304d\u308bHopfield Network\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u30cb\u30e5\u30fc\u30ed\u30f3\u6570\\(d\\)\u306f\\(1920\\times 1280=2457600\\)\u3067\u3059\u306e\u3067\u3001\u8a18\u61b6\u53ef\u80fd\u306a\u30d1\u30bf\u30fc\u30f3\u6570\u306f\u7d04\\(339148\\)\u3068\u306a\u308a\u307e\u3059\u300234\u4e07\u8fd1\u304f\u306eHD\u767d\u9ed2\u753b\u50cf\u3092\u8a18\u61b6\u3067\u304d\u308b\u306e\u3067\u3042\u308c\u3070\u3001\u4e00\u898b\u51c4\u3044\u3053\u3068\u306b\u611f\u3058\u3066\u3057\u307e\u3044\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u3053\u306e\u30b5\u30a4\u30ba\u306eHopfield Network\u3092\u5b9f\u73fe\u3059\u308b\u3053\u3068\u306f\u30e1\u30e2\u30ea\u30fc\u30b5\u30a4\u30ba\u3084\u8a08\u7b97\u8cc7\u6e90\u7684\u306b\u304b\u306a\u308a\u53b3\u3057\u3044\u3067\u3059\u3002\u305d\u308c\u306f\u3001\\(2457600\\)\u500b\u306e\u30cb\u30e5\u30fc\u30ed\u30f3\u304b\u3089\u69cb\u6210\u3055\u308c\u308bHopfield Network\u306e\u91cd\u307f\u884c\u5217\u306f\u3001\\(2457600\\times 2457600\\)\u306e\u30b5\u30a4\u30ba\u306b\u306a\u308a\u30011\u3064\u306e\u91cd\u307f\u884c\u5217\u306e\u5404\u6210\u5206\u304c4\u30d0\u30a4\u30c8\uff0832bit\uff09\u3060\u3068\u3059\u308b\u3068\u3001\u5fc5\u8981\u306a\u30e1\u30e2\u30ea\u30fc\u5bb9\u91cf\u306f\\(2.4159191\\times 10^{12}Byte \u2252 2416GByte\\)\u3067\u3059\u3002\u305f\u304b\u304cHD\u767d\u9ed2\u753b\u50cf\u3054\u3068\u304d\u3067\u3068\u601d\u3048\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u304c\u3001\u3053\u308c\u3092Hopfield Network\u306b\u4fdd\u5b58\u3059\u308b\u306b\u306f\u60f3\u50cf\u4ee5\u4e0a\u306e\u30e1\u30e2\u30ea\u30fc\u3092\u5fc5\u8981\u3068\u3059\u308b\u306e\u3067\u3059\u3002\u3061\u306a\u307f\u306b\u3001HD\u767d\u9ed2\u753b\u50cf34\u4e07\u679a\u5206\u3092\u753b\u50cf\u30c7\u30fc\u30bf\u3068\u3057\u3066\u4fdd\u5b58\u3059\u308b\u5834\u5408\u3001\\(1920\\times 1280\\times 340000 Bit = 835584000000 Bit = 104448000000 Byte \u2252 104GByte\\)\u306e\u30e1\u30e2\u30ea\u304c\u5fc5\u8981\u3067\u3059\u304c\u3001 Hopfield Network\u306b\u305d\u308c\u3060\u3051\u306e\u30c7\u30fc\u30bf\u3092\u5b66\u7fd2\u3055\u305b\u308b\u306e\u306b\u5fc5\u8981\u306a\u30e1\u30e2\u30ea\u30b5\u30a4\u30ba2416GByte\u306b\u6bd4\u3079\u308c\u3070\u5727\u5012\u7684\u306b\u5c11\u306a\u3044\u3067\u3059\u3002\u3044\u304b\u306b\u52b9\u7387\u304c\u60aa\u3044\u304b\u3092\u3054\u7406\u89e3\u3044\u305f\u3060\u3051\u308b\u306e\u3067\u306f\u306a\u3044\u304b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\\(0.138d\\)\u3068\u3044\u3046\u8a18\u61b6\u5bb9\u91cf\u3092\u6539\u5584\u3059\u308b\u305f\u3081\u306b\u3001\u591a\u304f\u306e\u7814\u7a76\u304c\u306a\u3055\u308c\u3066\u304a\u308a\u3001\u73fe\u5728\u306f\u5927\u5e45\u306b\u6539\u5584\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u306b\u3064\u3044\u3066\u306fModern Hoppfield Network\u306e\u8a18\u4e8b\u3067\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u8ab2\u984c<\/h2>\n\n\n\n<p>\u3053\u3053\u3067\u306f\u3001Classical\u306aHopfield Network\u306e\u8ab2\u984c\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u5148\u307b\u3069\u3001\u8a18\u61b6\u5bb9\u91cf\u306f\u30010.138d\u3067\u3042\u308b\u3053\u3068\u3092\u8aac\u660e\u3057\u307e\u3057\u305f\u3002\u3057\u304b\u3057\u3001\u3053\u308c\u306f\u5fc5\u305a\u3057\u3082\u3001\u305d\u306e\u91cf\u307e\u3067\u5fc5\u305a\u4fdd\u5b58\u53ef\u80fd\u306a\u3053\u3068\u3092\u4fdd\u8a3c\u3059\u308b\u3082\u306e\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u8a18\u61b6\u5bb9\u91cf\u306b\u5168\u304f\u9054\u3057\u3066\u3044\u306a\u304f\u3066\u3082\u3001\u60f3\u8d77\u3067\u304d\u306a\u304f\u306a\u3063\u3066\u3057\u307e\u3046\u554f\u984c\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u3069\u3046\u3044\u3046\u3053\u3068\u3067\u3057\u3087\u3046\u304b\uff1f<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1024\" height=\"454\" src=\"https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-13-1024x454.png\" alt=\"\" class=\"wp-image-8522\" srcset=\"https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-13-1024x454.png 1024w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-13-300x133.png 300w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-13-768x340.png 768w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-13-1536x681.png 1536w, https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/06\/image-13-2048x908.png 2048w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>\u4e0a\u56f3\u306f\u3001\u8a18\u61b6\u30d1\u30bf\u30fc\u30f3\u3092\u5897\u3084\u3059\u3068\u3001\u305d\u306e\u91cd\u307f\u884c\u5217\u3092\u6301\u3064Hopfield Network\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u95a2\u6570\u306b\u6975\u81f4\u304c\u5897\u3048\u308b\u3053\u3068\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002\u8a18\u61b6\u5bb9\u91cf\u304c\u4e00\u676f\u3067\u306a\u304f\u3066\u3082\u3001\u6975\u5c0f\u5024\u304c\u5897\u3048\u308c\u3070\u305d\u306e\u5bc6\u5ea6\u306f\u5fc5\u7136\u7684\u306b\u9ad8\u304f\u306a\u308a\u3001\u8a18\u61b6\u30d1\u30bf\u30fc\u30f3\u306b\u3088\u3063\u3066\u306f\u3001\u3068\u3066\u3082\u8fd1\u3044\u3068\u3053\u308d\u306b\u6975\u5c0f\u5024\u304c\u914d\u7f6e\u3055\u308c\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u3046\u3059\u308b\u3068\u4f55\u304c\u8d77\u3053\u308b\u3067\u3057\u3087\u3046\u304b\uff1f<br>\u6975\u5c0f\u5024\u304c\u8fd1\u304f\u306a\u308b\u3068\u3001\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306f\u6df7\u4e71\u3057\u3084\u3059\u304f\u306a\u308a\u3001\u601d\u3044\u901a\u308a\u306e\u60f3\u8d77\u3092\u3057\u3066\u304f\u308c\u306a\u3044\u3068\u3044\u3046\u72b6\u6cc1\u306b\u306a\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u8a18\u61b6\u30d1\u30bf\u30fc\u30f3\u540c\u58eb\u304c\u5e72\u6e09\u3057\u3066\u3057\u307e\u3063\u3066\u3044\u308b\u72b6\u614b\u3067\u3059\u3002\u3053\u308c\u3092\u30af\u30ed\u30b9\u30c8\u30fc\u30af\u3068\u547c\u3073\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u308c\u3092\u89e3\u6c7a\u3059\u308b\u65b9\u6cd5\u306f\u3001\u591a\u304f\u7814\u7a76\u3055\u308c\u3066\u304a\u308a\u3001\u5225\u306e\u8a18\u4e8b\u3067\u6271\u3046\u4e88\u5b9a\u306eModern Hopfield Network\u3067\u306f\u5927\u304d\u304f\u6539\u5584\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u4eca\u56de\u306e\u8a18\u4e8b\u3067\u306f\u3001Classical Hopfield Network\u306b\u306f\u3053\u306e\u3088\u3046\u306a\u8ab2\u984c\u304c\u6b8b\u3055\u308c\u3066\u3044\u305f\u3068\u3044\u3046\u3053\u3068\u3055\u3048\u3001\u7406\u89e3\u3057\u3066\u3044\u305f\u3060\u3051\u308c\u3070\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u53c2\u8003\u6587\u732e<\/h2>\n\n\n\n<p>[1] Hopfield, John, \"Neural Networks and Physical Systems with Emergent Collective Computational Abilities,\" in Proc. National Academy of Sciences, 1982.<br>[2] Shun-ichi Amari, \"Learning patterns and pattern sequences by Self-Organizing nets of threshold elements,\"&nbsp;<em>IEEE Transactions on Computers<\/em>, 1972.<br>[3] H. K. Sulehria, and Ye Zhang, \"Hopfield neural networks: a survey,\" 2007.<br>[4] W.S. McCulloch, and W. Pitts, \"A logical calculus of the ideas immanent in nervous activity,\" Bulletin of Mathematical Biophysics, 1943.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u8a18\u4e8b\u3067\u306f1982\u5e74\u306b\u63d0\u6848\u3055\u308c\u305fClassical\u306aHopfield Network\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u77e5\u308b\u3053\u3068\u3092\u76ee\u6a19\u306b\u3001\u89e3\u8aac\u3057\u3066\u3044\u304d\u305f\u3044\u3068\u601d\u3044\u307e\u3059\u3002 \u9023\u60f3\u8a18\u61b6\u3068Hopfield Network \u9023\u60f3\u8a18\u61b6\u3068 &#8230; <\/p>\n","protected":false},"author":1,"featured_media":8578,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_vk_print_noindex":"","sitemap_hide":"","_veu_custom_css":"","veu_display_promotion_alert":"","vkexunit_cta_each_option":"","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[170,171],"tags":[],"class_list":["post-8508","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-blog","category-learn"],"veu_head_title_object":{"title":"","add_site_title":""},"jetpack_featured_media_url":"https:\/\/developers.agirobots.com\/jp\/wp-content\/uploads\/2023\/07\/IMG_2652.png","jetpack-related-posts":[],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/developers.agirobots.com\/jp\/wp-json\/wp\/v2\/posts\/8508","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/developers.agirobots.com\/jp\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/developers.agirobots.com\/jp\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/developers.agirobots.com\/jp\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/developers.agirobots.com\/jp\/wp-json\/wp\/v2\/comments?post=8508"}],"version-history":[{"count":53,"href":"https:\/\/developers.agirobots.com\/jp\/wp-json\/wp\/v2\/posts\/8508\/revisions"}],"predecessor-version":[{"id":8577,"href":"https:\/\/developers.agirobots.com\/jp\/wp-json\/wp\/v2\/posts\/8508\/revisions\/8577"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/developers.agirobots.com\/jp\/wp-json\/wp\/v2\/media\/8578"}],"wp:attachment":[{"href":"https:\/\/developers.agirobots.com\/jp\/wp-json\/wp\/v2\/media?parent=8508"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/developers.agirobots.com\/jp\/wp-json\/wp\/v2\/categories?post=8508"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/developers.agirobots.com\/jp\/wp-json\/wp\/v2\/tags?post=8508"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}