{"id":2436,"date":"2022-08-30T11:08:53","date_gmt":"2022-08-30T02:08:53","guid":{"rendered":"https:\/\/hayashiyus.jp\/?p=2436"},"modified":"2023-04-24T01:57:38","modified_gmt":"2023-04-23T16:57:38","slug":"%e8%87%aa%e7%94%b1%e3%82%a8%e3%83%8d%e3%83%ab%e3%82%ae%e3%83%bc%e5%8e%9f%e7%90%86%e3%81%ae%e5%a4%9a%e9%9d%a2%e6%80%a7%e3%81%a8%e3%81%9d%e3%81%ae%e7%89%a9%e7%90%86%e7%9a%84%e8%a7%a3%e9%87%88%e3%81%ab","status":"publish","type":"post","link":"https:\/\/hayashiyus.jp\/?p=2436","title":{"rendered":"\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc\u539f\u7406\u306e\u591a\u9762\u6027\u3068\u305d\u306e\u7269\u7406\u7684\u89e3\u91c8\u306b\u3064\u3044\u3066"},"content":{"rendered":"\r\n

\r\n\u80fd\u52d5\u7684\u63a8\u8ad6\u3092\u81ea\u7136\u306b\u5c0e\u304f\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\uff08\u6b63\u6e96\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\uff09\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f\uff0c\u78ef\u6751\u62d3\u4e5f\u30fb\u30ab\u30fc\u30eb\u30fb\u30d5\u30ea\u30b9\u30c8\u30f3\u300c\u30b3\u30b9\u30c8\u95a2\u6570\u306e\u6027\u8cea\u3092\u660e\u3089\u304b\u306b\u3059\u308b\u305f\u3081\u306e\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u306e\u30ea\u30d0\u30fc\u30b9\u30a8\u30f3\u30b8\u30cb\u30a2\u30ea\u30f3\u30b0<\/a> (2020)\u300d\u306b\u3088\u3063\u3066\u521d\u3081\u3066\u79d1\u5b66\u306e\u8868\u821e\u53f0\u306b\u5f15\u304d\u63da\u3052\u3089\u308c\u305f\uff0e\u305d\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f \"f(x_{t})=\operatorname{sig}^{-1}\left(x_{t}\right)\" \u3068\u3057\u305f\u3068\u304d<\/p>\r\n

(1) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u3068\u3057\u3066\u4e0e\u3048\u3089\u308c\u308b\uff0e\u305f\u3060\u3057\uff0c\"x_{t}\" \u306f\u6642\u523b \"t\" \u306b\u304a\u3051\u308b\u6b63\u6e96\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u306e\u4e2d\u9593\u5c64\u306e\u72b6\u614b\uff0c\"\dot{x}_{t}\" \u306f\u305d\u306e\u6642\u9593\u5fae\u5206 \"\frac{d x_{t}}{d t}\" \u3092\u8868\u3057\u3066\u3044\u308b\uff0e\u3053\u306e\u6b63\u6e96\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u306f\uff0c\u904b\u52d5\u65b9\u7a0b\u5f0f(1)\u5f0f\u304b\u3089\u5c0e\u304b\u308c\u308b\u30b3\u30b9\u30c8\u95a2\u6570 \"\textcolor{red}{L}\" \u304c\u80fd\u52d5\u7684\u63a8\u8ad6\u3092\u884c\u3046\u30a8\u30fc\u30b8\u30a7\u30f3\u30c8\u306e\u5909\u5206\u30d9\u30a4\u30ba\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc \"\textcolor{red}{F}\" \u3068\u53b3\u5bc6\u306a\u5bfe\u5fdc\u95a2\u4fc2\u3092\u6301\u3064<\/font>\uff0c\u3068\u3044\u3046\u3042\u308b\u7a2e\u306e\u6df1\u9060\u3055\u3092\u611f\u3058\u3055\u305b\u308b\u5370\u8c61\u7684\u306a\u6027\u8cea\u3092\u5099\u3048\u3066\u3044\u308b\uff0e<\/p>\r\n

\"\"<\/center>\r\n

\u3064\u307e\u308a\uff0c\u4e0a\u306e\u5bfe\u5fdc\u95a2\u4fc2\u306b\u5f93\u3048\u3070\uff0c\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u304c\u6de1\u3005\u3068\u884c\u3063\u3066\u3044\u308b\u6700\u9069\u5316\u306e\u30d7\u30ed\u30bb\u30b9\u3092\u3044\u3064\u3067\u3082\u80fd\u52d5\u7684\u63a8\u8ad6\u306e\u30d7\u30ed\u30bb\u30b9\u306b\u8aad\u307f\u66ff\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff0e\u8133\u5185\u306b\u6b63\u6e96\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u3068\u540c\u578b\u306e\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u304c\u3042\u308c\u3070\uff0c\u305d\u306e\u6700\u9069\u5316\u30d7\u30ed\u30bb\u30b9\u3092\u74b0\u5883\u3068\u76f8\u4e92\u4f5c\u7528\u3057\u306a\u304c\u3089\u80fd\u52d5\u7684\u63a8\u8ad6\u3092\u884c\u3046\u30a8\u30fc\u30b8\u30a7\u30f3\u30c8\u306e\u30d9\u30a4\u30ba\u6700\u9069\u5316\u306e\u30d7\u30ed\u30bb\u30b9\u3068\u540c\u4e00\u8996\u3067\u304d\u308b\uff0e\u3053\u3046\u3057\u305f\u69cb\u9020\u304c\u5b58\u5728\u3057\u3046\u308b\u3053\u3068\u3092\u793a\u3057\u305f\u70b9\u3067\u5192\u982d\u306e\u8ad6\u6587\u306f\u7d20\u6674\u3089\u3057\u3044\uff0e\u3057\u304b\u3057\uff0c\u540c\u8ad6\u6587\u306f\u30b3\u30b9\u30c8\u95a2\u6570\u306e\u7269\u7406\u7684\u306a\u610f\u5473\u307e\u3067\u306f\u660e\u3089\u304b\u306b\u3057\u3066\u304f\u308c\u306a\u3044\uff0e\u901a\u5e38\u306e\u96fb\u6c17\u56de\u8def\u304c\u7d71\u8a08\u529b\u5b66\u306e\u8a00\u8449\u306b\u3088\u3063\u3066\u7406\u89e3\u3055\u308c\u308b\u3088\u3046\u306b\uff0c1\u30641\u3064\u306e\u30cb\u30e5\u30fc\u30ed\u30f3\u3092\u96fb\u6c17\u56de\u8def\u3068\u307f\u306a\u3057\uff0c\u305d\u306e\u96fb\u6c17\u56de\u8def\u3092\u9023\u7d50\u3055\u305b\u305f\u6b63\u6e96\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u3082\u307e\u305f\u7d71\u8a08\u529b\u5b66\u306e\u8a00\u8449\u306b\u3088\u3063\u3066\u7406\u89e3\u3067\u304d\u308b\u306f\u305a\u3060\uff0e\u3053\u306e\u89b3\u70b9\u306b\u7acb\u3066\u3070\uff0c\u30b3\u30b9\u30c8\u95a2\u6570\u306f\u4f55\u3089\u304b\u306e\u5f62\u3067\u7d71\u8a08\u529b\u5b66\u306b\u767b\u5834\u3059\u308b\u7269\u7406\u91cf\u3068\u95a2\u4fc2\u3057\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\uff0e\u305d\u3053\u3067\u3053\u306e\u30ce\u30fc\u30c8\u3067\u306f\uff0c\u30b3\u30b9\u30c8\u95a2\u6570\u3068\u7269\u7406\u91cf\u306e\u9593\u306b\u3042\u308b\u306f\u305a\u306e\u30df\u30c3\u30b7\u30f3\u30b0\u30d4\u30fc\u30b9\u306e\u8ffd\u8de1\u3092\u8a66\u307f\u308b\uff0e<\/p>\r\n\r\n\r\n\r\n

\uff11. \u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc\u539f\u7406\u306e\u591a\u9762\u6027<\/h4>\r\n\r\n\r\n
\r\n

\uff11\u2212\uff11. \u7528\u8a9e\u306e\u78ba\u8a8d<\/h4>\r\n

<\/p>\r\n

<\/p>\r\n

\u307e\u305a\u6b63\u6e96\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u306e\u57fa\u672c\u7684\u306a\u6027\u8cea\u306b\u3064\u3044\u3066\u78ba\u8a8d\u3057\u3066\u304a\u3053\u3046\uff0e\u306f\u3058\u3081\u306b\u30ce\u30fc\u30c8\u5192\u982d\u306b\u767b\u5834\u3057\u305f(1)\u5f0f\u3092\uff0c\"A_{t}=W_{1} o_{t}+K_{1} x_{t-1}+\phi_{1},\ B_{t}=W_{0} o_{t}+K_{0} x_{t-1}+\phi_{0}\" \u3068\u3057\u3066<\/p>\r\n

(2) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u306e\u3088\u3046\u306b\u66f8\u304d\u76f4\u3057\u3066\u307f\u3088\u3046\uff0e\u3053\u3053\u306b\u767b\u5834\u3059\u308b \"\operatorname{sig}\left(x\right),\ \operatorname{sig}^{-1}\left(x\right)\" \u306f\u30b7\u30b0\u30e2\u30a4\u30c9\u95a2\u6570\u3068\u305d\u306e\u9006\u95a2\u6570\u3092\u8868\u3057\u3066\u3044\u3066\uff0c\u30b7\u30b0\u30e2\u30a4\u30c9\u95a2\u6570<\/a>\u3068\u547c\u3070\u308c\u308b\u95a2\u6570\u306e\u30b0\u30eb\u30fc\u30d7\u306b\u5c5e\u3057\u3066\u3044\u308c\u3070\u5177\u4f53\u7684\u306a\u95a2\u6570\u5f62\u306b\u3088\u3089\u305a\u306b\u540c\u69d8\u306e\u8b70\u8ad6\u3092\u5c55\u958b\u3067\u304d\u308b\uff0e\u304c\uff0c\u4ee5\u4e0b\u3067\u306f\uff0c\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u95a2\u6570\u3068\u305d\u306e\u9006\u95a2\u6570\u3067\u3042\u308b\u30ed\u30b8\u30c3\u30c8\u95a2\u6570\u3092\u4f7f\u3063\u3066\u8b70\u8ad6\u3092\u9032\u3081\u3066\u3044\u304f\u3053\u3068\u306b\u3059\u308b\uff08\u5f93\u3063\u3066 \"x_{t}\" \u306f \"0 \leq x_{t} \leq 1\" \u306e\u7bc4\u56f2\u3092\u52d5\u304f\u5909\u6570\u306b\u306a\u308b\uff09\uff0e<\/p>\r\n

(3) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle <\/p><\/p>\r\n

\u3053\u306e\u3068\u304d\u6b63\u6e96\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u306e\u30b3\u30b9\u30c8\u95a2\u6570 \"L=\int \frac{\partial L}{\partial x} d x\" \u306f\u4ee5\u4e0b\u306b\u306a\u308b\uff0e<\/p>\r\n

(4) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle <\/p><\/p>\r\n

\u305f\u3060\u3057\uff0c\u6700\u5f8c\u306e\u7b49\u53f7\u306e\u5c0e\u51fa\u306b\u306f(3)\u5f0f\u3092\u4f7f\u3063\u305f\uff0e\u3053\u306e\u30b3\u30b9\u30c8\u95a2\u6570 \"L\" \u306f\u80fd\u52d5\u7684\u63a8\u8ad6\u3092\u884c\u3046\u30a8\u30fc\u30b8\u30a7\u30f3\u30c8\u306e\u5909\u5206\u30d9\u30a4\u30ba\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc \"F\" \u3068\u53b3\u5bc6\u306a\u5bfe\u5fdc\u95a2\u4fc2\u3092\u6301\u3064\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u308b\uff0e<\/p>\r\n

(5) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle <\/p><\/p>\r\n

\"\"<\/center>\r\n

\u3053\u3053\u3067\u8b70\u8ad6\u306e\u898b\u901a\u3057\u3092\u3088\u304f\u3059\u308b\u305f\u3081\u306b \"A_{t}=B_{t}=0\" \u3068\u3057\u3066\u6700\u3082\u5358\u7d14\u5316\u3055\u308c\u305f\u6b63\u6e96\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8<\/p>\r\n

(6) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle <\/p><\/p>\r\n

\u3092\u8003\u3048\u308b\u3053\u3068\u306b\u3057\u3088\u3046\uff0e\u3053\u306e\u3068\u304d\u30b3\u30b9\u30c8\u95a2\u6570 \"L\" \u306f<\/p>\r\n

(7) <\/span>   <\/span>\"\begin{align*}<\/p><\/p>\r\n

\u3068\u306a\u308a\uff0c\u30b7\u30e3\u30ce\u30f3\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc \"I=-\sum_{i} p_{i}\ln{p_{i}}\" \u306e\u7b26\u53f7\u3092\u9006\u5411\u304d\u306b\u3057\u305f\u3082\u306e\u3068\u4e00\u81f4\u3059\u308b\uff0e\u826f\u3044\u30bf\u30a4\u30df\u30f3\u30b0\u306a\u306e\u3067\uff0c\u3053\u3053\u3067\u30b7\u30e3\u30ce\u30f3\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u3068\u7269\u7406\u91cf\u306e\u95a2\u4fc2\u306b\u3064\u3044\u3066\u78ba\u8a8d\u3057\u3066\u304a\u3053\u3046\uff0e\u30d8\u30eb\u30e0\u30db\u30eb\u30c4\u306e\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc \"F\" \uff0c\u5185\u90e8\u30a8\u30cd\u30eb\u30ae\u30fc \"E\" \uff0c\u30ae\u30d6\u30ba\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc \"S=k_{\mathrm{B}} I\" \u306f\u7cfb\u306e\u5206\u914d\u95a2\u6570 \"Z=\operatorname{Tr}\ \exp \left(-\beta H\right)\" \u3068\u9006\u6e29\u5ea6 \"\beta=\frac{1}{k_{\mathrm{B}}T}\" \u3092\u4f7f\u3063\u3066\u6b21\u306e\u3088\u3046\u306b\u66f8\u304d\u8868\u305b\u308b\uff08\u306a\u304a\uff0c\u4ee5\u4e0b\u3067\u306f\u5358\u4f4d\u7cfb \"k_{\mathrm{B}}=1\" \u3092\u3068\u308a\u30b7\u30e3\u30ce\u30f3\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u3068\u30ae\u30d6\u30ba\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u3092\u533a\u5225\u305b\u305a\u306b\u8b70\u8ad6\u3059\u308b\uff09\uff0e<\/p>\r\n

(8) <\/span>   <\/span>\"\begin{align*}<\/p><\/p>\r\n

\u3088\u3063\u3066\u6700\u3082\u5358\u7d14\u5316\u3055\u308c\u305f\u6b63\u6e96\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8(6)\u5f0f\u306e\u5834\u5408\uff0c\u30b3\u30b9\u30c8\u95a2\u6570 \"L\" \u3068\u30ae\u30d6\u30ba\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc \"S\" \u306f<\/p>\r\n

(9) <\/span>   <\/span>\"\begin{eqnarray*} & \displaystyle<\/p><\/p>\r\n

\u306e\u5bfe\u5fdc\u95a2\u4fc2\u3092\u6301\u3064\u3053\u3068\u304c\u308f\u304b\u3063\u305f\uff0e<\/p>\r\n<\/div>\r\n\r\n

\r\n

\uff11\u2212\uff12. \u30db\u30c3\u30d7\u30d5\u30a3\u30fc\u30eb\u30c9\u6a21\u578b<\/h4>\r\n

<\/p>\r\n

<\/p>\r\n

\u3053\u308c\u3067\u7528\u8a9e\u306e\u78ba\u8a8d\u304c\u3067\u304d\u305f\u306e\u3067\uff0c\u3044\u3088\u3044\u3088\u672c\u984c\u306b\u5165\u3063\u3066\u3044\u3053\u3046\uff0e\u6b63\u6e96\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u306e\u30b3\u30b9\u30c8\u95a2\u6570\u3068\u7269\u7406\u91cf\u306e\u95a2\u4fc2\u3092\u8abf\u3079\u308b\u305f\u3081\u306b\uff0c\u6b63\u6e96\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u3092\u7269\u7406\u7cfb\u306e\u30e2\u30c7\u30eb\u306b\u7ffb\u8a33\u3059\u308b\u3053\u3068\u3092\u8003\u3048\u3066\u3044\u304f\uff0e\"\mu\" \u756a\u76ee\u306e\u5165\u529b \"\left\{o^{\mu}\right\}^{\mu=1,\ldots, p}\" \u306b\u5bfe\u5fdc\u3059\u308b\"i\" \u756a\u76ee\u306e\u30cb\u30e5\u30fc\u30ed\u30f3\u306e\u8208\u596e\u30d1\u30bf\u30fc\u30f3\uff08\u6559\u5e2b\u30e9\u30d9\u30eb\uff09\"\left\{\xi_{i}^{\mu}\right\}^{\mu=1,\ldots, p}_{i=1,\ldots, N}\" \u3068\u5b9f\u969b\u306e\u767a\u706b\u72b6\u614b \"\left\{S_{i}\right\}_{i=1,\ldots, N}\" \u3092\u8003\u3048\u3066\uff0c\u3069\u3061\u3089\u3082\u30a4\u30b8\u30f3\u30b0\u5909\u6570 \"\left(\pm1\right)\" \u3092\u3068\u308b\u3068\u3059\u308b\uff0e\u305d\u3057\u3066\u5404\u30cb\u30e5\u30fc\u30ed\u30f3\u306e\u767a\u706b\u72b6\u614b\u304c\u5165\u529b\u306b\u5bfe\u5fdc\u3059\u308b\u8208\u596e\u30d1\u30bf\u30fc\u30f3\u3092\u518d\u73fe\u3067\u304d\u305f\u3068\u304d\u60f3\u8d77\uff08\u9023\u60f3\u8a18\u61b6\uff09\u306b\u6210\u529f\u3057\u305f\u3068\u307f\u306a\u3059\uff0e\u3053\u306e\u3088\u3046\u306a\u30e9\u30f3\u30c0\u30e0\u306a\u30a4\u30b8\u30f3\u30b0\u6a21\u578b\u3092\u7528\u3044\u305f\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u306e\u30e2\u30c7\u30eb\u3092\u30db\u30c3\u30d7\u30d5\u30a3\u30fc\u30eb\u30c9\u6a21\u578b\u3068\u547c\u3073\uff0c\u6b63\u6e96\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u3068\u540c\u69d8\u306b\u30d8\u30c3\u30d6\u5247 \"J_{i j}=\frac{1}{N} \sum_{\mu=1}^{p} \xi_{i}^{\mu} \xi_{j}^{\mu}\" \u306b\u57fa\u3065\u3044\u3066\u30b7\u30ca\u30d7\u30b9\u52a0\u91cd \"J_{i j}\" \u3092\u66f4\u65b0\u3057\u3066\u3044\u304f\u30e2\u30c7\u30eb\u306b\u306a\u3063\u3066\u3044\u308b\uff08\u4f8b\u3048\u3070\uff0c\u3053\u306e\u30db\u30c3\u30d7\u30d5\u30a3\u30fc\u30eb\u30c9\u6a21\u578b\u306b\u300e\u30b6\u30fb\u30b7\u30f3\u30d7\u30bd\u30f3\u30ba<\/a>\u300f\u306e\u767b\u5834\u4eba\u7269\u306e\u753b\u50cf\u3092\u8a18\u61b6\u3055\u305b\uff0c\u4e00\u90e8\u304c\u6b20\u640d\u3057\u305f\u753b\u50cf\u304b\u3089\u5143\u306e\u767b\u5834\u4eba\u7269\u3092\u60f3\u8d77\u3055\u305b\u308b\u3068\u3044\u3063\u305f\u30bf\u30b9\u30af<\/a>\u3092\u89e3\u304b\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff09\uff0e<\/p>\r\n

\"\"<\/center>\r\n

\u3053\u306e\u30db\u30c3\u30d7\u30d5\u30a3\u30fc\u30eb\u30c9\u6a21\u578b\u306e\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3 \"H\" \u3068\u5206\u914d\u95a2\u6570 \"Z\" \u306f\u305d\u308c\u305e\u308c<\/p>\r\n

(10) <\/span>   <\/span>\"\begin{align*}<\/p><\/p>\r\n

\u3068\u66f8\u3051\u308b\uff0e\u305f\u3060\u3057\uff0c\u5206\u914d\u95a2\u6570 \"Z\" \u306e1\u884c\u76ee\u304b\u30892\u884c\u76ee\u306e\u7b49\u53f7\u306b\u304b\u3051\u3066\u30ac\u30a6\u30b9\u7a4d\u5206\u306e\u516c\u5f0f<\/p>\r\n

(11) <\/span>   <\/span>\"\begin{align*}<\/p><\/p>\r\n

\u3092\u4f7f\u3063\u305f\uff0e\u3053\u3053\u30672\u884c\u76ee\u306e\u7b49\u53f7\u4ee5\u964d\u306b\u8868\u308c\u308b\u5909\u6570 \"m^{\mu}\" \u3092\u79e9\u5e8f\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u547c\u3073\uff0c\u5404\u30cb\u30e5\u30fc\u30ed\u30f3\u306e\u767a\u706b\u72b6\u614b\u304c\u5165\u529b\u306b\u5bfe\u5fdc\u3059\u308b\u8208\u596e\u30d1\u30bf\u30fc\u30f3\u3068\u5e73\u5747\u7684\u306b\u3069\u308c\u3060\u3051\u8fd1\u3044\u304b\u3092\u8868\u3059\u6307\u6a19\u306b\u306a\u3063\u3066\u3044\u308b\uff0e<\/p>\r\n

(12) <\/span>   <\/span>\"\begin{align*}<\/p><\/p>\r\n

\u3053\u306e\u3088\u3046\u306a\u8a2d\u5b9a\u306e\u3082\u3068\u3067\u30cb\u30e5\u30fc\u30ed\u30f3\u306e\u6570 \"N\" \u304c\u975e\u5e38\u306b\u5927\u304d\u306a\u5024\u3092\u3068\u308b\u72b6\u6cc1\u3092\u8003\u3048\u308b\u305f\u3081\u306b\u71b1\u529b\u5b66\u7684\u6975\u9650 \"N \rightarrow \infty\" \u3092\u3068\u308b\u3068\uff0c\u30db\u30c3\u30d7\u30d5\u30a3\u30fc\u30eb\u30c9\u6a21\u578b\u306e\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc \"F\" \u306f\u30e9\u30d7\u30e9\u30b9\u306e\u65b9\u6cd5<\/p>\r\n

(13) <\/span>   <\/span>\"\begin{align*}<\/p><\/p>\r\n

\u306b\u3088\u308a<\/p>\r\n

(14) <\/span>   <\/span>\"\begin{align*}<\/p><\/p>\r\n

\u3068\u66f8\u304d\u8868\u305b\u308b\uff0e\u3053\u3053\u3067\u30cb\u30e5\u30fc\u30ed\u30f31\u3064\u5f53\u305f\u308a\u306e\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc \"f=\frac{F}{N}\" \u3092\u8003\u3048\u308b\u3068<\/p>\r\n

(15) <\/span>   <\/span>\"\begin{align*}<\/p><\/p>\r\n

\u307e\u305f\uff0c\u3053\u306e\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc \"f\" \u3092\u6700\u5c0f\u306b\u3059\u308b\u79e9\u5e8f\u30d1\u30e9\u30e1\u30fc\u30bf \"\boldsymbol{m}\" \u306f<\/p>\r\n

(16) <\/span>   <\/span>\"\begin{align*}<\/p><\/p>\r\n

\u3067\u4e0e\u3048\u3089\u308c\u308b\uff0e\u3055\u3089\u306b \"N\" \u304c\u5341\u5206\u5927\u304d\u306a\u6975\u9650\u3067\u306f\u8208\u596e\u30d1\u30bf\u30fc\u30f3\u6bce\u306e\u5e73\u5747\u306f\u30cb\u30e5\u30fc\u30ed\u30f3\u6bce\u306e\u914d\u4f4d\u5e73\u5747 \"[\cdots]\" \u306b\u7f6e\u304d\u63db\u3048\u3089\u308c<\/p>\r\n

(17) <\/span>   <\/span>\"\begin{align*}<\/p><\/p>\r\n

\u3068\u306a\u308b\u306e\u3067\uff0c\u8208\u596e\u30d1\u30bf\u30fc\u30f3\u304c1\u3064\u3057\u304b\u306a\u3044\u5834\u5408\u3092\u8003\u3048\u308b\u3068 \"m_{1}=m,\ m_{2}=\cdots=m_{p}=0\" \u3068\u306a\u3063\u3066(17)\u5f0f\u306f<\/p>\r\n

(18) <\/span>   <\/span>\"\begin{align*}<\/p><\/p>\r\n

\u3068\u306a\u308b\u3053\u3068\u304c\u308f\u304b\u308b\uff0e\u3053\u306e\u3068\u304d\u30cb\u30e5\u30fc\u30ed\u30f31\u3064\u5f53\u305f\u308a\u306e\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc \"f=\frac{F}{N}\" \uff0c\u30cb\u30e5\u30fc\u30ed\u30f31\u3064\u5f53\u305f\u308a\u306e\u5185\u90e8\u30a8\u30cd\u30eb\u30ae\u30fc \"\epsilon=\frac{E}{N}\" \uff0c\u30cb\u30e5\u30fc\u30ed\u30f31\u3064\u5f53\u305f\u308a\u306e\u30ae\u30d6\u30ba\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc \"s=\frac{S}{N}\" \u306f\u305d\u308c\u305e\u308c<\/p>\r\n

(19) <\/span>   <\/span>\"\begin{align*}<\/p><\/p>\r\n

\u3053\u3053\u3067\u30cb\u30e5\u30fc\u30ed\u30f3\u306e\u767a\u706b\u72b6\u614b \"\left\{S_{i}\right\}_{i=1,\ldots, N}\" \u304c\u30a4\u30b8\u30f3\u30b0\u5909\u6570 \"\left(\pm1\right)\" \u3067\u306f\u306a\u304f \"0 \leq S_{i} \leq 1\" \u306e\u7bc4\u56f2\u3092\u52d5\u304f\u3088\u3046\u306b\u5024\u57df\u3092\u3068\u308a\u306a\u304a\u3059\u5909\u63db\u3092\u8003\u3048\u308b\u3068<\/p>\r\n

(20) <\/span>   <\/span>\"\begin{align*}<\/p><\/p>\r\n

\u3068\u306a\u308b\u306e\u3067\uff0c\"f\left(x_{t}\right)=2\beta m\" \u306e\u5bfe\u5fdc\u95a2\u4fc2\u3092\u4eee\u5b9a\u3059\u308c\u3070 \"L=-s\" \u304c\u5c0e\u304b\u308c\u308b\uff0e<\/p>\r\n

(21) <\/span>   <\/span>\"\begin{align*}<\/p><\/p>\r\n

\u3053\u306e\u30db\u30c3\u30d7\u30d5\u30a3\u30fc\u30eb\u30c9\u6a21\u578b\u306f \"T \rightarrow 0\"\uff08\"\beta \rightarrow \infty\"\uff09\u306e\u4f4e\u6e29\u6975\u9650\u3067\u79e9\u5e8f\u30d1\u30e9\u30e1\u30fc\u30bf \"m\" \u304c \"m=\pm 1\" \u306e\u3069\u3061\u3089\u304b\u306b\u51cd\u308a\u3064\u304d\uff0c\u5165\u529b\u306b\u5bfe\u5fdc\u3059\u308b\u8208\u596e\u30d1\u30bf\u30fc\u30f3\u3092\u6b63\u78ba\u306b\u518d\u73fe\u3059\u308b\uff08\u60f3\u8d77\u306b\u6210\u529f\u3059\u308b\uff09\u5b89\u5b9a\u72b6\u614b\u3068\u306a\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u308b\uff0e<\/p>\r\n

\"\"<\/center>\r\n

\u3055\u3089\u306b\u3053\u306e\u4f4e\u6e29\u6975\u9650\u3067\u306f \"-s \approx \beta f\" \u3082\u6210\u308a\u7acb\u3064\u306e\u3067\uff0c\u30db\u30c3\u30d7\u30d5\u30a3\u30fc\u30eb\u30c9\u6a21\u578b\u3068\u3044\u3046\u7269\u7406\u7cfb\u306e\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc \"\textcolor{red}{f}\" \u304c\u6b63\u6e96\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u306e\u30b3\u30b9\u30c8\u95a2\u6570 \"\textcolor{red}{L}\" \u3068\u5bfe\u5fdc\u95a2\u4fc2\u3092\u6301\u3064\u3053\u3068\u304c\u308f\u304b\u308b<\/font>\uff0e\u3053\u3046\u3057\u3066\u6b63\u6e96\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u306e\u30b3\u30b9\u30c8\u95a2\u6570 \"L\" \uff0c\u80fd\u52d5\u7684\u63a8\u8ad6\u3092\u884c\u3046\u30a8\u30fc\u30b8\u30a7\u30f3\u30c8\u306e\u5909\u5206\u30d9\u30a4\u30ba\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc \"F\" \u3092\uff0c\u7269\u7406\u7cfb\u306e\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc \"f\" \u306b\u8aad\u307f\u66ff\u3048\u3089\u308c\u308b\u3053\u3068\u304c\u660e\u3089\u304b\u306b\u306a\u3063\u305f\uff0e<\/p>\r\n

(22) <\/span>   <\/span>\"\begin{align*}<\/p><\/p>\r\n

\u3068\u3053\u308d\u3067\u6700\u3082\u5358\u7d14\u5316\u3055\u308c\u305f\u6b63\u6e96\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8(6)\u5f0f\u3092\u5c0e\u5165\u3059\u308b\u969b\uff0c\"A_{t}=B_{t}=0\" \u3092\u4eee\u5b9a\u3057\u305f\uff0e\u5b9f\u306f\u305d\u306e\u80cc\u666f\u306b\u306f \"\dot{x}(t)=0\"\uff0c\u3059\u306a\u308f\u3061<\/p>\r\n

(23) <\/span>   <\/span>\"\begin{align*}<\/p><\/p>\r\n

\u3068\u3044\u3046\u95a2\u4fc2\u5f0f\u304c\u4eee\u5b9a\u3055\u308c\u3066\u3044\u305f\uff0e\u3064\u307e\u308a\uff0c\"A_{t}=B_{t}=0\" \u3092\u4eee\u5b9a\u3059\u308b\u3053\u3068\u306b\u306f\u6b63\u6e96\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u306e\u4e2d\u9593\u5c64\u3078\u306e\u5165\u529b \"A_{t}-B_{t}\" \u3092\u4e00\u5b9a\u5024\u306b\u56fa\u5b9a\u3059\u308b\u3068\u3044\u3046\u610f\u5473\u304c\u3042\u3063\u305f\uff0e\u5165\u529b\u304c\u4e00\u5b9a\u5024\u306b\u56fa\u5b9a\u3055\u308c\u305f\u3068\u3044\u3046\u3053\u3068\u306f\uff0c\u5165\u529b\u304c1\u7a2e\u985e\u306b\u9650\u5b9a\u3055\u308c\u305f\u3068\u8a00\u3044\u63db\u3048\u3066\u3082\u826f\u3044\uff0e\u305d\u306e\u305f\u3081\u4e2d\u9593\u5c64\u306e\u8208\u596e\u30d1\u30bf\u30fc\u30f3\u30821\u7a2e\u985e\u306b\u9650\u5b9a\u3055\u308c\u308b<\/font>\uff0e\u3053\u3046\u3057\u3066(22)\u5f0f\u3092\u5c0e\u304f\u307e\u3067\u306b\u5c0e\u5165\u3055\u308c\u305f\u69d8\u3005\u306a\u4eee\u5b9a\uff08\u71b1\u529b\u5b66\u7684\u6975\u9650 \"N \rightarrow \infty\" \uff0c\u8208\u596e\u30d1\u30bf\u30fc\u30f3\u306e\u6570\u30921\u3064\u306b\u9650\u5b9a \"\boldsymbol{m} = \left(m, 0,0, \ldots\right)\" \uff0c\u4f4e\u6e29\u6975\u9650 \"\beta \rightarrow \infty\" \uff09\u306b\u305d\u308c\u305e\u308c\u7269\u7406\u7684\u306a\u59a5\u5f53\u6027\u304c\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u3063\u305f\uff0e<\/p>\r\n

(24) <\/span>   <\/span>\"\begin{align*}<\/p><\/p>\r\n<\/div>\r\n\r\n

\u53c2\u8003\u6587\u732e<\/h4>\r\n

<\/p>\r\n

<\/p>\r\n

    \r\n\t
  1. Takuya Isomura, Karl Friston; Reverse-Engineering Neural Networks to Characterize Their Cost Functions<\/a>.\u00a0Neural Comput 2020; 32 (11): 2085\u20132121.<\/li>\r\n\t
  2. Takuya Isomura, Hideaki Shimazaki and Karl Friston; Canonical neural networks perform active inference<\/a>.\u00a0Commun Biol 2022; 5, 55.<\/li>\r\n\t
  3. Takuya Isomura; Active inference leads to Bayesian neurophysiology<\/a>.\u00a0Neurosci Res 2022, 175, pp. 38-45.<\/li>\r\n\t
  4. Hidetoshi Nishimori;\u00a0Statistical Physics of Spin Glasses and Information Processing: an Introduction<\/a>. Oxford University Press 2001.<\/li>\r\n\t
  5. Haiping Huang; Statistical Mechanics of Neural Networks<\/a>. Springer 2021.<\/li>\r\n\t
  6. Hubert Ramsauer,\u00a0Bernhard Sch\u00e4fl,\u00a0Johannes Lehner,\u00a0Philipp Seidl,\u00a0Michael Widrich,\u00a0Thomas Adler,\u00a0Lukas Gruber,\u00a0Markus Holzleitner,\u00a0Milena Pavlovi\u0107,\u00a0Geir Kjetil Sandve,\u00a0Victor Greiff,\u00a0David Kreil,\u00a0Michael Kopp,\u00a0G\u00fcnter Klambauer,\u00a0Johannes Brandstetter,\u00a0Sepp Hochreiter; Hopfield Networks is All You Need<\/a>. International Conference on Learning Representations (ICLR) 2021.<\/li>\r\n<\/ol>","protected":false},"excerpt":{"rendered":"

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