{"id":7163,"date":"2024-03-19T15:18:08","date_gmt":"2024-03-19T06:18:08","guid":{"rendered":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/?p=7163"},"modified":"2024-03-19T15:18:08","modified_gmt":"2024-03-19T06:18:08","slug":"%e7%84%a1%e9%99%90%e5%b9%85%e3%83%8b%e3%83%a5%e3%83%bc%e3%83%a9%e3%83%ab%e3%83%8d%e3%83%83%e3%83%88%e3%83%af%e3%83%bc%e3%82%af%e3%81%ae%e7%b5%b1%e8%a8%88%e5%8a%9b%e5%ad%a6-%e2%80%95-%e6%b4%bb%e6%80%a7","status":"publish","type":"post","link":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/03\/19\/%e7%84%a1%e9%99%90%e5%b9%85%e3%83%8b%e3%83%a5%e3%83%bc%e3%83%a9%e3%83%ab%e3%83%8d%e3%83%83%e3%83%88%e3%83%af%e3%83%bc%e3%82%af%e3%81%ae%e7%b5%b1%e8%a8%88%e5%8a%9b%e5%ad%a6-%e2%80%95-%e6%b4%bb%e6%80%a7\/","title":{"rendered":"\u7121\u9650\u5e45\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306e\u7d71\u8a08\u529b\u5b66 \u2015 \u6d3b\u6027\u5316\u95a2\u6570\u306e\u89b3\u70b9\u304b\u3089"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-white ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title ez-toc-toggle\" style=\"cursor:pointer\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" 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href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/03\/19\/%e7%84%a1%e9%99%90%e5%b9%85%e3%83%8b%e3%83%a5%e3%83%bc%e3%83%a9%e3%83%ab%e3%83%8d%e3%83%83%e3%83%88%e3%83%af%e3%83%bc%e3%82%af%e3%81%ae%e7%b5%b1%e8%a8%88%e5%8a%9b%e5%ad%a6-%e2%80%95-%e6%b4%bb%e6%80%a7\/#%E6%A6%82%E8%A6%81\" >\u6982\u8981<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/03\/19\/%e7%84%a1%e9%99%90%e5%b9%85%e3%83%8b%e3%83%a5%e3%83%bc%e3%83%a9%e3%83%ab%e3%83%8d%e3%83%83%e3%83%88%e3%83%af%e3%83%bc%e3%82%af%e3%81%ae%e7%b5%b1%e8%a8%88%e5%8a%9b%e5%ad%a6-%e2%80%95-%e6%b4%bb%e6%80%a7\/#%E8%83%8C%E6%99%AF\" >\u80cc\u666f<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/03\/19\/%e7%84%a1%e9%99%90%e5%b9%85%e3%83%8b%e3%83%a5%e3%83%bc%e3%83%a9%e3%83%ab%e3%83%8d%e3%83%83%e3%83%88%e3%83%af%e3%83%bc%e3%82%af%e3%81%ae%e7%b5%b1%e8%a8%88%e5%8a%9b%e5%ad%a6-%e2%80%95-%e6%b4%bb%e6%80%a7\/#%E8%A8%98%E6%86%B6%E5%AE%B9%E9%87%8F%E3%81%AE%E7%B5%B1%E8%A8%88%E5%8A%9B%E5%AD%A6%E7%9A%84%E8%A7%A3%E6%9E%90\" >\u8a18\u61b6\u5bb9\u91cf\u306e\u7d71\u8a08\u529b\u5b66\u7684\u89e3\u6790<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/03\/19\/%e7%84%a1%e9%99%90%e5%b9%85%e3%83%8b%e3%83%a5%e3%83%bc%e3%83%a9%e3%83%ab%e3%83%8d%e3%83%83%e3%83%88%e3%83%af%e3%83%bc%e3%82%af%e3%81%ae%e7%b5%b1%e8%a8%88%e5%8a%9b%e5%ad%a6-%e2%80%95-%e6%b4%bb%e6%80%a7\/#%E6%9C%AC%E7%AF%80%E3%81%AE%E3%81%BE%E3%81%A8%E3%82%81\" >\u672c\u7bc0\u306e\u307e\u3068\u3081<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/03\/19\/%e7%84%a1%e9%99%90%e5%b9%85%e3%83%8b%e3%83%a5%e3%83%bc%e3%83%a9%e3%83%ab%e3%83%8d%e3%83%83%e3%83%88%e3%83%af%e3%83%bc%e3%82%af%e3%81%ae%e7%b5%b1%e8%a8%88%e5%8a%9b%e5%ad%a6-%e2%80%95-%e6%b4%bb%e6%80%a7\/#%E7%84%A1%E9%99%90%E5%B9%85NN%E3%81%A8Gauss%E9%81%8E%E7%A8%8B%E3%81%AE%E5%AF%BE%E5%BF%9C\" >\u7121\u9650\u5e45NN\u3068Gauss\u904e\u7a0b\u306e\u5bfe\u5fdc<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/03\/19\/%e7%84%a1%e9%99%90%e5%b9%85%e3%83%8b%e3%83%a5%e3%83%bc%e3%83%a9%e3%83%ab%e3%83%8d%e3%83%83%e3%83%88%e3%83%af%e3%83%bc%e3%82%af%e3%81%ae%e7%b5%b1%e8%a8%88%e5%8a%9b%e5%ad%a6-%e2%80%95-%e6%b4%bb%e6%80%a7\/#%E6%9C%AC%E7%AF%80%E3%81%AE%E3%81%BE%E3%81%A8%E3%82%81-2\" >\u672c\u7bc0\u306e\u307e\u3068\u3081<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/03\/19\/%e7%84%a1%e9%99%90%e5%b9%85%e3%83%8b%e3%83%a5%e3%83%bc%e3%83%a9%e3%83%ab%e3%83%8d%e3%83%83%e3%83%88%e3%83%af%e3%83%bc%e3%82%af%e3%81%ae%e7%b5%b1%e8%a8%88%e5%8a%9b%e5%ad%a6-%e2%80%95-%e6%b4%bb%e6%80%a7\/#2%E3%81%A4%E3%81%AE%E7%A0%94%E7%A9%B6%E3%81%AE%E5%85%B1%E9%80%9A%E7%82%B9%E3%81%A8%E7%9B%B8%E9%81%95%E7%82%B9\" >2\u3064\u306e\u7814\u7a76\u306e\u5171\u901a\u70b9\u3068\u76f8\u9055\u70b9<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/03\/19\/%e7%84%a1%e9%99%90%e5%b9%85%e3%83%8b%e3%83%a5%e3%83%bc%e3%83%a9%e3%83%ab%e3%83%8d%e3%83%83%e3%83%88%e3%83%af%e3%83%bc%e3%82%af%e3%81%ae%e7%b5%b1%e8%a8%88%e5%8a%9b%e5%ad%a6-%e2%80%95-%e6%b4%bb%e6%80%a7\/#%E7%B5%90%E8%AB%96\" >\u7d50\u8ad6<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/03\/19\/%e7%84%a1%e9%99%90%e5%b9%85%e3%83%8b%e3%83%a5%e3%83%bc%e3%83%a9%e3%83%ab%e3%83%8d%e3%83%83%e3%83%88%e3%83%af%e3%83%bc%e3%82%af%e3%81%ae%e7%b5%b1%e8%a8%88%e5%8a%9b%e5%ad%a6-%e2%80%95-%e6%b4%bb%e6%80%a7\/#%E3%81%82%E3%81%A8%E3%81%8C%E3%81%8D\" >\u3042\u3068\u304c\u304d<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/03\/19\/%e7%84%a1%e9%99%90%e5%b9%85%e3%83%8b%e3%83%a5%e3%83%bc%e3%83%a9%e3%83%ab%e3%83%8d%e3%83%83%e3%83%88%e3%83%af%e3%83%bc%e3%82%af%e3%81%ae%e7%b5%b1%e8%a8%88%e5%8a%9b%e5%ad%a6-%e2%80%95-%e6%b4%bb%e6%80%a7\/#%E5%8F%82%E8%80%83%E6%96%87%E7%8C%AE\" >\u53c2\u8003\u6587\u732e<\/a><\/li><\/ul><\/nav><\/div>\n<h2 id=\"%E6%96%87%E7%8C%AE%E6%83%85%E5%A0%B1\"><span class=\"ez-toc-section\" id=\"%E6%96%87%E7%8C%AE%E6%83%85%E5%A0%B1\"><\/span>\u6587\u732e\u60c5\u5831<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>\u30bf\u30a4\u30c8\u30eb\uff1aOn neural network kernels and the storage capacity problem<\/li>\n<li>\u8457\u8005\uff1aJacob A. Zavatone-Veth, Cengiz Pehlevan<\/li>\n<li>\u66f8\u8a8c\u60c5\u5831\uff1ahttps:\/\/doi.org\/10.1162\/neco_a_01494<\/li>\n<\/ul>\n<h2 id=\"%E6%A6%82%E8%A6%81\"><span class=\"ez-toc-section\" id=\"%E6%A6%82%E8%A6%81\"><\/span>\u6982\u8981<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u672c\u8a18\u4e8b\u3067\u7d39\u4ecb\u3059\u308b\u8ad6\u6587\u306f\uff0c\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\uff08NN\uff09\u306e\u6027\u80fd\u3068\u6d3b\u6027\u5316\u95a2\u6570\u306e\u95a2\u4fc2\u306b\u307e\u3064\u308f\u308b2\u3064\u306e\u7814\u7a76\u306e\u6d41\u308c\u306e\u9593\u306e\u95a2\u9023\u6027\u3092\u6307\u6458\u3059\u308b\u3082\u306e\u3067\u3059\uff0e<\/p>\n<p>1\u3064\u76ee\u306e\u7814\u7a76\u306e\u6d41\u308c\u306f\uff0c<strong>\u8a18\u61b6\u5bb9\u91cf<\/strong>\u306e\u554f\u984c\u306e\u7d71\u8a08\u529b\u5b66\u7684\u89e3\u6790\u3067\u3059\uff0e<br \/>\n\u8a18\u61b6\u5bb9\u91cf\u3068\u306f\uff0c\u4e8c\u5024\u5206\u985e\u30e2\u30c7\u30eb\u304c\u8a18\u61b6\u3067\u304d\u308b\u30e9\u30f3\u30c0\u30e0\u306a\u30c7\u30fc\u30bf\u306e\u6700\u5927\u6570\uff08\u30d1\u30e9\u30e1\u30fc\u30bf\u3042\u305f\u308a\uff09\u3067\u3059\uff0e<br \/>\n\u8a18\u61b6\u5bb9\u91cf\u306f\u30e2\u30c7\u30eb\u306e\u8868\u73fe\u80fd\u529b\u306e\u6307\u6a19\u306e\u4e00\u3064\u3067\u3042\u308a\uff0c\u8a18\u61b6\u5bb9\u91cf\u304c\u5927\u304d\u3044\u307b\u3069\uff0c\u30e2\u30c7\u30eb\u306f\u8907\u96d1\u306a\u95a2\u6570\u3092\u8868\u73fe\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3068\u8a00\u3048\u307e\u3059\uff0e<br \/>\n\u8a18\u61b6\u5bb9\u91cf\u306e\u554f\u984c\u306f\u53e4\u304f\u304b\u3089\u7d71\u8a08\u529b\u5b66\u7684\u624b\u6cd5\u306b\u3088\u308a\u7814\u7a76\u3055\u308c\u3066\u304d\u307e\u3057\u305f\uff0e<br \/>\n\u8fd1\u5e74\u3067\u306f\uff0c\u6d3b\u6027\u5316\u95a2\u6570\u306e\u9078\u629e\u304c2\u5c64NN\u306e\u8a18\u61b6\u5bb9\u91cf\u306b\u4e0e\u3048\u308b\u5f71\u97ff\u3092\u8abf\u3079\u305f\u7814\u7a76 [1] \u304c\u3042\u308a\u307e\u3059\uff0e<\/p>\n<p>2\u3064\u76ee\u306e\u7814\u7a76\u306e\u6d41\u308c\u306f\uff0c\u7121\u9650\u5e45NN\u3068<strong>Gauss\u904e\u7a0b<\/strong>\u3042\u308b\u3044\u306f<strong>\u30ab\u30fc\u30cd\u30eb\u6cd5<\/strong>\u3068\u306e\u95a2\u9023\u306b\u95a2\u3059\u308b\u3082\u306e\u3067\u3059\uff0e<br \/>\n\u6df1\u5c64NN\u306f\u69d8\u3005\u306a\u30bf\u30b9\u30af\u306b\u304a\u3044\u3066\u975e\u5e38\u306b\u9ad8\u3044\u6027\u80fd\u3092\u767a\u63ee\u3059\u308b\u3053\u3068\u304c\u7d4c\u9a13\u7684\u306b\u308f\u304b\u3063\u3066\u3044\u307e\u3059\u304c\uff0c\u305d\u306e\u9ad8\u3044\u6027\u80fd\u3092\u7406\u8ad6\u7684\u306b\u8aac\u660e\u3059\u308b\u3053\u3068\u306f\u307e\u3060\u5b8c\u5168\u306b\u306f\u3067\u304d\u3066\u3044\u307e\u305b\u3093\uff0e<br \/>\n\u7121\u9650\u5e45NN\u3092Gauss\u904e\u7a0b\u3068\u3057\u3066\u7279\u5fb4\u3065\u3051\u308b\u3053\u306e\u7814\u7a76\u306e\u6d41\u308c\u306f\uff0cNN\u306e\u9ad8\u3044\u6027\u80fd\u306b\u5bfe\u3057\u3066\u3088\u308a\u6df1\u3044\u6d1e\u5bdf\u3092\u4e0e\u3048\u308b\u7406\u8ad6\u3068\u3057\u3066\u6ce8\u76ee\u3055\u308c\u3066\u3044\u307e\u3059\uff0e<\/p>\n<p>\u3053\u308c\u3089\u306e\u7814\u7a76\u306f\u72ec\u7acb\u306b\u767a\u5c55\u3057\u3066\u304d\u3066\u304a\u308a\uff0c\u4e21\u8005\u306e\u95a2\u9023\u6027\u306f\u4eca\u307e\u3067\u7279\u306b\u610f\u8b58\u3055\u308c\u3066\u3044\u307e\u305b\u3093\u3067\u3057\u305f\u304c\uff0c\u672c\u8ad6\u6587\u306f\uff0c\u4e21\u8005\u306b\u306f\u6df1\u3044\u3064\u306a\u304c\u308a\u304c\u3042\u308b\u3053\u3068\u3092\u6307\u6458\u3057\u307e\u3059\uff0e\u7121\u9650\u5e452\u5c64NN\u306e\u8a18\u61b6\u5bb9\u91cf\u3092\u4e0e\u3048\u308b\u516c\u5f0f\u3068\uff0c\u7121\u9650\u5e452\u5c64NN\u3092\u30ab\u30fc\u30cd\u30eb\u6cd5\u3068\u3057\u3066\u307f\u305f\u3068\u304d\u306e\u30ab\u30fc\u30cd\u30eb\u306e\u5024\u3092\u4e0e\u3048\u308b\u516c\u5f0f\u306b\u5171\u901a\u3057\u3066\u73fe\u308c\u308b\u91cf\u306b\u6ce8\u76ee\u3059\u308b\u3053\u3068\u3067\uff0c\u8a18\u61b6\u5bb9\u91cf\u306b\u95a2\u3059\u308b\u7d50\u679c\u3092\u30ab\u30fc\u30cd\u30eb\u306e\u6027\u8cea\u3068\u3057\u3066\u76f4\u89b3\u7684\u306b\u7406\u89e3\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u3068\u306a\u308a\u307e\u3057\u305f\uff0e\u307e\u305f\uff0c\u3053\u308c\u3089\u306e\u7570\u306a\u308b\u7814\u7a76\u306e\u6d41\u308c\u306e\u95a2\u9023\u6027\u304c\u308f\u304b\u3063\u305f\u3053\u3068\u3067\uff0c\u7d71\u8a08\u529b\u5b66\u7684\u624b\u6cd5\u306e\uff0cNN\u306e\u7814\u7a76\u306b\u5bfe\u3059\u308b\u5fdc\u7528\u304c\u4fc3\u9032\u3055\u308c\u308b\u3053\u3068\u304c\u671f\u5f85\u3055\u308c\u307e\u3059\uff0e<\/p>\n<h2 id=\"%E8%83%8C%E6%99%AF\"><span class=\"ez-toc-section\" id=\"%E8%83%8C%E6%99%AF\"><\/span>\u80cc\u666f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 id=\"%E8%A8%98%E6%86%B6%E5%AE%B9%E9%87%8F%E3%81%AE%E7%B5%B1%E8%A8%88%E5%8A%9B%E5%AD%A6%E7%9A%84%E8%A7%A3%E6%9E%90\"><span class=\"ez-toc-section\" id=\"%E8%A8%98%E6%86%B6%E5%AE%B9%E9%87%8F%E3%81%AE%E7%B5%B1%E8%A8%88%E5%8A%9B%E5%AD%A6%E7%9A%84%E8%A7%A3%E6%9E%90\"><\/span>\u8a18\u61b6\u5bb9\u91cf\u306e\u7d71\u8a08\u529b\u5b66\u7684\u89e3\u6790<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u8a18\u61b6\u5bb9\u91cf\u306e\u7814\u7a76\u306f1980\u5e74\u4ee3\u306eGardner\u3089\u306e\u7814\u7a76 [2,3] \u306b\u9061\u308a\u307e\u3059\uff0e<br \/>\nGardner\u3089\u306f\uff0c\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u304c\u8a18\u61b6\u3067\u304d\u308b\u30e9\u30f3\u30c0\u30e0\u306a\u30c7\u30fc\u30bf\u306e\u500b\u6570\u3092\u30ec\u30d7\u30ea\u30ab\u6cd5\u306b\u3088\u308a\u8a08\u7b97\u3057\u307e\u3057\u305f\uff0e<br \/>\n\u30ec\u30d7\u30ea\u30ab\u6cd5\u306f\uff0c\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u7406\u8ad6\u3067\u958b\u767a\u3055\u308c\u305f\u624b\u6cd5\u3067\u3042\u308a\uff0c\u5927\u81ea\u7531\u5ea6\u306e\u30e9\u30f3\u30c0\u30e0\u306a\u7cfb\u306e\u632f\u308b\u821e\u3044\u3092\u89e3\u6790\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u5f37\u529b\u306a\u624b\u6cd5\u3067\u3059\uff0e<br \/>\n\u30c7\u30fc\u30bf\u306e\u500b\u6570\u3092$P$\uff0c\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u6570$N$\u3068\u3057\u3066\uff0c$\\alpha\\coloneqq P\/N&lt;2$\u306a\u3089\u9ad8\u3044\u78ba\u7387\u3067\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u306f\u30c7\u30fc\u30bf\u3092\u8a18\u61b6\u3067\u304d\uff0c$\\alpha &gt; 2$\u306a\u3089\u9ad8\u3044\u78ba\u7387\u3067\u30c7\u30fc\u30bf\u3092\u8a18\u61b6\u3067\u304d\u306a\u3044\u3068\u3044\u3046\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3057\u305f\uff0e<br \/>\n\u3088\u3063\u3066\uff0c\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u306e\u8a18\u61b6\u5bb9\u91cf\u306f$\\alpha_c=2$\u3067\u3042\u308b\u3068\u3044\u3046\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3057\u305f\uff0e<br \/>\nGardner\u3089\u306e\u8a08\u7b97\u306f\uff0c\u6771\u5317\u5927\u5b66 \u5927\u95a2\u771f\u4e4b\u6559\u6388\u306eYouTube\u8b1b\u7fa9 [4] \u3067\u7d39\u4ecb\u3055\u308c\u3066\u3044\u307e\u3059\uff0e<\/p>\n<p>\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u306e\u8a18\u61b6\u5bb9\u91cf\u304c$\\alpha_c=2$\u3067\u3042\u308b\u3068\u3044\u3046\u4e8b\u5b9f\u306f\uff0cGardner\u3089\u306e\u89e3\u6790\u4ee5\u524d\u304b\u3089Cover\u306e\u5b9a\u7406 [5] \u3068\u3057\u3066\u77e5\u3089\u308c\u3066\u3044\u307e\u3057\u305f\u304c\uff0cGardner\u3089\u306e\u624b\u6cd5\u306f\uff0c\u30d1\u30fc\u30bb\u30d7\u30c8\u30ed\u30f3\u306b\u9650\u3089\u306a\u3044\u69d8\u3005\u306a\u30e2\u30c7\u30eb\u306b\u5bfe\u3057\u3066\u9069\u7528\u3067\u304d\u308b\u6c4e\u7528\u6027\u3092\u6301\u3063\u3066\u3044\u308b\u3068\u3044\u3046\u70b9\u3067\u512a\u308c\u3066\u3044\u307e\u3059\uff0e<\/p>\n<p>Gardner\u3089\u306e\u67a0\u7d44\u307f\u306b\u5f93\u3063\u3066\uff0c\u30ec\u30d7\u30ea\u30ab\u6cd5\u30672\u5c64NN\u306e\u8a18\u61b6\u5bb9\u91cf\u3092\u8a08\u7b97\u3059\u308b\u7814\u7a76\u304c1990\u5e74\u4ee3\u306b\u76db\u3093\u306b\u884c\u308f\u308c\u307e\u3057\u305f\uff0e<br \/>\n\u6728\u69cb\u9020\u3067\u6d3b\u6027\u5316\u95a2\u6570\u304c\u7b26\u53f7\u95a2\u6570\u306e2\u5c64NN\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3042\u305f\u308a\u306e\u8a18\u61b6\u5bb9\u91cf\u306f\uff0c\u96a0\u308c\u5c64\u306e\u5e45\u3092$K$\u3068\u3057\u3066\uff0c\u7121\u9650\u5e45\u6975\u9650$K\\to\\infty$\u3067\u767a\u6563\u3059\u308b\u3053\u3068\u304c\u660e\u3089\u304b\u3068\u306a\u308a\u307e\u3057\u305f [6,7]\uff0e\u6f38\u8fd1\u7684\u306b\u306f\uff0c$\\alpha_c\\sim\\frac{16}{\\pi}\\sqrt{\\log K}$\u3068\u306a\u308a\u307e\u3059 [8]\uff0e<br \/>\n\u307e\u305f\uff0c\u5168\u7d50\u5408\u3067\u6d3b\u6027\u5316\u95a2\u6570\u304c\u7b26\u53f7\u95a2\u6570\u306e\u5834\u5408\u3082\uff0c$K\\to\\infty$\u3067\u8a18\u61b6\u5bb9\u91cf\u304c\u767a\u6563\u3059\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3057\u305f\uff0e\u6f38\u8fd1\u7684\u306b\u306f$\\alpha_c\\sim\\frac{16}{\\pi-2}\\sqrt{\\log K}$\u3068\u306a\u308a\uff0c\u6728\u69cb\u9020\u306e\u5834\u5408\u3088\u308a\u3082\u30d1\u30e9\u30e1\u30fc\u30bf\u3042\u305f\u308a\u306e\u8a18\u61b6\u5bb9\u91cf\u304c\u5b9a\u6570\u500d\u5927\u304d\u304f\u306a\u3063\u3066\u3044\u307e\u3059 [9]\uff0e<br \/>\n\u3053\u308c\u306f\u6b21\u306e\u3088\u3046\u306b\u76f4\u89b3\u7684\u306b\u8aac\u660e\u3067\u304d\u307e\u3059\uff0e\u7d50\u5408\u304c\u6728\u69cb\u9020\u306e\u5834\u5408\u306f\uff0c\u305d\u308c\u305e\u308c\u306e\u91cd\u307f\u304c\u7570\u306a\u308b\u5165\u529b\u6210\u5206\u306b\u3064\u306a\u304c\u3063\u3066\u3044\u308b\u305f\u3081\uff0c\u305d\u308c\u305e\u308c\u306e\u91cd\u307f\u306f\u81ea\u5206\u304c\u62c5\u5f53\u3057\u3066\u3044\u308b\u5165\u529b\u6210\u5206\u3092\u3059\u3079\u3066\u8a18\u61b6\u3057\u3088\u3046\u3068\u3057\u307e\u3059\uff0e<br \/>\n\u4e00\u65b9\u3067\u5168\u7d50\u5408\u306e\u5834\u5408\u306f\uff0c\u7570\u306a\u308b\u91cd\u307f\u304c\u540c\u3058\u5165\u529b\u6210\u5206\u306b\u3064\u306a\u304c\u3063\u3066\u3044\u308b\u305f\u3081\uff0c\u305d\u308c\u305e\u308c\u306e\u91cd\u307f\u304c\u7570\u306a\u308b\u5165\u529b\u30d1\u30bf\u30fc\u30f3\u3092\u899a\u3048\u308b\u3088\u3046\u306b\u300c\u5206\u696d\u300d\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff0e<br \/>\n\u3053\u308c\u306b\u3088\u3063\u3066\u305d\u308c\u305e\u308c\u306e\u91cd\u307f\u306e\u8ca0\u62c5\u304c\u6e1b\u308a\uff0c\u8a18\u61b6\u5bb9\u91cf\u304c\u5927\u304d\u304f\u306a\u308b\u3068\u8003\u3048\u3089\u308c\u307e\u3059\uff0e<\/p>\n<p><div style=\"width: 459px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" src=\"\/T-Wave\/wp-content\/uploads\/2024\/03\/cm_arch.png\" alt=\"\" width=\"449\" height=\"457\" \/><p class=\"wp-caption-text\">\u56f31\uff1a2\u5c64NN\u306e\u30a2\u30fc\u30ad\u30c6\u30af\u30c1\u30e3\uff0e (a) \u306f\u6728\u69cb\u9020\uff0c (b) \u306f\u5168\u7d50\u5408\uff0e\u56f3\u306f [7] \u3088\u308a<\/p><\/div>\u8fd1\u5e74\uff0c\u7b26\u53f7\u95a2\u6570\u4ee5\u5916\u306e\u6d3b\u6027\u5316\u95a2\u6570\u3092\u7528\u3044\u305f\u5834\u5408\u306b\u3082\u6728\u69cb\u9020\u306e2\u5c64NN\u306e\u8a18\u61b6\u5bb9\u91cf\u304c\u8a08\u7b97\u3055\u308c\u307e\u3057\u305f [10,11]\uff0eReLU\u95a2\u6570\u3084\u30b7\u30b0\u30e2\u30a4\u30c9\u95a2\u6570\u306a\u3069\u306e\uff0c\u5b9f\u7528\u7684\u306b\u7528\u3044\u3089\u308c\u3066\u3044\u308b\u307b\u3068\u3093\u3069\u306e\u6d3b\u6027\u5316\u95a2\u6570\u3067\uff0c\u7121\u9650\u5e45\u6975\u9650$K\\to\\infty$\u3067\u3082\u8a18\u61b6\u5bb9\u91cf\u304c\u6709\u9650\u306e\u5024\u306b\u3068\u3069\u307e\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3057\u305f\uff0e<\/p>\n<p>2\u5c64NN\u306e\u8a18\u61b6\u5bb9\u91cf\u306f\uff0c\u6d3b\u6027\u5316\u95a2\u6570$f$\u304b\u3089\u5b9a\u307e\u308b\u4ee5\u4e0b\u306e\u95a2\u6570\u306e\u632f\u308b\u821e\u3044\u3067\u7279\u5fb4\u3065\u3051\u3089\u308c\u307e\u3059\uff0e<br \/>\n$$<br \/>\nK_f(q) = \\mathbb{E}\\left[ f(x)f(y) \\mid \\begin{pmatrix}x \\ y\\end{pmatrix} \\sim \\mathcal{N}\\left( \\begin{pmatrix}0 \\ 0\\end{pmatrix}, \\begin{pmatrix}1 &amp; q \\ q &amp; 1\\end{pmatrix} \\right) \\right]<br \/>\n\\tag{1}<br \/>\n$$<br \/>\n\u3053\u306e\u5f0f\u306e\u610f\u5473\u306f\u3059\u306a\u308f\u3061\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\uff0e\u5e73\u5747$0$\uff0c\u5206\u6563$1$\uff0c\u5171\u5206\u6563$q$\u3067\u3042\u308b2\u5909\u91cfGauss\u5206\u5e03\u306b\u5f93\u3063\u30662\u3064\u306e\u5b9f\u6570$x,y$\u3092\u30b5\u30f3\u30d7\u30eb\u3057\u307e\u3059\uff0e$q=0$\u306a\u3089\u3070$x,y$\u306f\u72ec\u7acb\u306b\u5024\u3092\u53d6\u308a\u307e\u3059\uff0e$q$\u304c$1$\u306b\u8fd1\u3044\u307b\u3069\uff0c$x,y$\u306f\u8fd1\u3044\u5024\u3092\u53d6\u308a\u307e\u3059\uff0e\u305d\u3057\u3066\uff0c\u30b5\u30f3\u30d7\u30eb\u3055\u308c\u305f$x,y$\u306b\u3064\u3044\u3066\uff0c\u305d\u308c\u3089\u306b$f$\u3092\u9069\u7528\u3057\u305f\u5024\u306e\u7a4d$f(x)f(y)$\u306e\u5e73\u5747\u5024\u304c$K_f(q)$\u3067\u3059\uff0e\u3053\u308c\u306f\u51fa\u529b$f(x),f(y)$\u306e\u985e\u4f3c\u5ea6\u3092\u8868\u3057\u307e\u3059\uff0e<\/p>\n<p>\u76f4\u89b3\u7684\u306b\u306f\uff0c\u4f3c\u3066\u3044\u308b\u3082\u306e\u3092\u533a\u5225\u3059\u308b\u80fd\u529b\u304c\u9ad8\u3044\u307b\u3069\uff0c\u30e2\u30c7\u30eb\u306e\u5206\u985e\u80fd\u529b\u304c\u9ad8\u304f\u306a\u308a\uff0c\u8a18\u61b6\u5bb9\u91cf\u304c\u5927\u304d\u304f\u306a\u308a\u305d\u3046\u3067\u3059\uff0e\u8a00\u3044\u63db\u3048\u308b\u3068\uff0c$q$\u304c$1$\u306b\u8fd1\u3044\u3068\u304d\u306b$K_f(q)$\u306e\u5024\u304c\u5c0f\u3055\u3051\u308c\u3070\uff0c\u6d3b\u6027\u5316\u95a2\u6570$f$\u304c\u4f3c\u3066\u3044\u308b\u5165\u529b\u3092\u5f15\u304d\u96e2\u3059\u80fd\u529b\u304c\u9ad8\u3044\u3068\u8a00\u3048\uff0c\u8a18\u61b6\u5bb9\u91cf\u304c\u5927\u304d\u304f\u306a\u308a\u305d\u3046\u3067\u3059\uff0e<\/p>\n<p>\u3044\u304f\u3064\u304b\u306e\u5177\u4f53\u7684\u306a\u6d3b\u6027\u5316\u95a2\u6570$f$\u306b\u5bfe\u3057\u3066\uff0c$1$\u306b\u8fd1\u3044$q$\u306b\u5bfe\u3059\u308b$K_f(q)$\u306e\u5024\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\uff0e\u4e0b\u56f3\u306f\uff0c$q=0.99$\u306e2\u5909\u91cfGauss\u5206\u5e03\u306b\u5f93\u3063\u3066\u30b5\u30f3\u30d7\u30eb\u3055\u308c\u305f\u5165\u529b$(x,y)$\uff08\u5de6\u4e0a\uff09\u306b\u5bfe\u3057\u3066\uff0c$(f(x),f(y))$\u306e\u6563\u5e03\u56f3\u3092\u8868\u793a\u3057\u305f\u3082\u306e\u3067\u3059\uff0e$f$\u3068\u3057\u3066\u306f\uff0c\u8aa4\u5dee\u95a2\u6570$\\operatorname{erf}\uff0c\\operatorname{ReLU}\uff0c\u7b26\u53f7\u95a2\u6570\\operatorname{sgn}$\u3092\u7528\u3044\u307e\u3057\u305f\uff0e<br \/>\n\u3069\u306e\u6d3b\u6027\u5316\u95a2\u6570\u3092\u7528\u3044\u3066\u3082\uff0c$f$\u3092\u9069\u7528\u3059\u308b\u3053\u3068\u3067\u5165\u529b\u306e\u76f8\u95a2\u304c\u5c11\u3057\u5c0f\u3055\u304f\u306a\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\uff0e$\\operatorname{erf}$\u3068$\\operatorname{ReLU}$\u3092\u6bd4\u8f03\u3059\u308b\u3068\uff0c$\\operatorname{ReLU}$\u306e\u307b\u3046\u304c\u82e5\u5e72$K_f(q)$\u306e\u5024\u304c\u5c0f\u3055\u304f\u306a\u3063\u3066\u3044\u307e\u3059\uff0e<br \/>\n\u307e\u305f\uff0c$\\operatorname{sgn}$\u304c\u6700\u3082\u76f8\u95a2\u3092\u5c0f\u3055\u304f\u3059\u308b\u52b9\u679c\u304c\u5927\u304d\u3044\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\uff0e<\/p>\n<div style=\"width: 999px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" src=\"\/T-Wave\/wp-content\/uploads\/2024\/03\/article_corr.png\" alt=\"\" width=\"989\" height=\"989\" \/><p class=\"wp-caption-text\">\u56f32\uff1a\u3044\u304f\u3064\u304b\u306e\u6d3b\u6027\u5316\u95a2\u6570 $f$ \u306b\u5bfe\u3059\u308b $K_f(q)$ \u306e\u5024 ($q=0.99$)<\/p><\/div>\n<p>\u6b21\u306b\uff0c\u8a18\u61b6\u5bb9\u91cf\u306e\u5024\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\uff0e[1] \u3067\u5831\u544a\u3055\u308c\u3066\u3044\u308b\u30d1\u30e9\u30e1\u30fc\u30bf\u3042\u305f\u308a\u306e\u8a18\u61b6\u5bb9\u91cf$\\alpha_c$\u306e\u5024\u306f\uff0c$f=\\operatorname{ReLU}$\u306b\u5bfe\u3057\u3066$\\alpha_c\\approx 2.934$\uff0c$f=\\operatorname{erf}$\u306b\u5bfe\u3057\u3066$\\alpha_c\\approx 2.451$\u3067\u3059\uff0e\u307e\u305f\uff0c$f=\\operatorname{sgn}$\u306b\u5bfe\u3057\u3066\u306f\uff0c\u3059\u3067\u306b\u8ff0\u3079\u305f\u3088\u3046\u306b\u8a18\u61b6\u5bb9\u91cf\u304c\u767a\u6563\u3059\u308b\u306e\u3067$\\alpha_c=\\infty$\u3067\u3059\uff0e<\/p>\n<p>\u3053\u308c\u3089\u306e\u4f8b\u3067\u306f\uff0c$q$\u304c$1$\u306b\u8fd1\u3044\u3068\u304d\u306b$K_f(q)$\u306e\u5024\u304c\u5c0f\u3055\u3044\u307b\u3069\u8a18\u61b6\u5bb9\u91cf$\\alpha_c$\u304c\u5927\u304d\u3044\u3068\u3044\u3046\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\uff0e\u5b9f\u306f\uff0c\u3053\u306e\u95a2\u4fc2\u306f\u5e38\u306b\u6210\u308a\u7acb\u3061\uff0c\u6728\u69cb\u9020\u306e2\u5c64NN\u306e\u8a18\u61b6\u5bb9\u91cf\u306f$\\frac{d}{dq} K_f(q) \\Big|_{q=1}$\u306b\u6bd4\u4f8b\u3059\u308b\u3053\u3068\u304c\u308f\u304b\u3063\u3066\u3044\u307e\u3059 [1]\uff0e<\/p>\n<h4 id=\"%E6%9C%AC%E7%AF%80%E3%81%AE%E3%81%BE%E3%81%A8%E3%82%81\"><span class=\"ez-toc-section\" id=\"%E6%9C%AC%E7%AF%80%E3%81%AE%E3%81%BE%E3%81%A8%E3%82%81\"><\/span>\u672c\u7bc0\u306e\u307e\u3068\u3081<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>\u672c\u7bc0\u3067\u306f\uff0c2\u5c64NN\u306e\u8a18\u61b6\u5bb9\u91cf\u306e\u7d71\u8a08\u529b\u5b66\u7684\u89e3\u6790\u3068\u3044\u3046\u7814\u7a76\u306e\u6d41\u308c\u306b\u3064\u3044\u3066\u6982\u8aac\u3057\u307e\u3057\u305f\uff0e<br \/>\n\u4e00\u822c\u306e\u6d3b\u6027\u5316\u95a2\u6570\u3092\u6301\u3064\u6728\u69cb\u90202\u5c64NN\u306e\u8a18\u61b6\u5bb9\u91cf\u3092\u89e3\u6790\u3057\u305f\u7814\u7a76\u306b\u3088\u308b\u3068\uff0c\u5f0f(1)\u3067\u5b9a\u307e\u308b\u5024$K_f(q)$\u304c$q=1$\u4ed8\u8fd1\u3067\u5c0f\u3055\u3044\u3068\u304d\u306b\u8a18\u61b6\u5bb9\u91cf\u304c\u5927\u304d\u304f\u306a\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3057\u305f\uff0e\u3053\u308c\u306f\uff0c\u6d3b\u6027\u5316\u95a2\u6570$f$\u304c\u4f3c\u3066\u3044\u308b\u5165\u529b\u3092\u5f15\u304d\u96e2\u3059\u80fd\u529b\u304c\u9ad8\u3044\u307b\u3069\uff0c\u30e2\u30c7\u30eb\u306e\u5206\u985e\u80fd\u529b\u304c\u9ad8\u304f\u306a\u308b\u3068\u3044\u3046\u89e3\u91c8\u304c\u3067\u304d\u308b\u3053\u3068\u3092\u8ff0\u3079\u307e\u3057\u305f\uff0e<\/p>\n<h3 id=\"%E7%84%A1%E9%99%90%E5%B9%85nn%E3%81%A8gauss%E9%81%8E%E7%A8%8B%E3%81%AE%E5%AF%BE%E5%BF%9C\"><span class=\"ez-toc-section\" id=\"%E7%84%A1%E9%99%90%E5%B9%85NN%E3%81%A8Gauss%E9%81%8E%E7%A8%8B%E3%81%AE%E5%AF%BE%E5%BF%9C\"><\/span>\u7121\u9650\u5e45NN\u3068Gauss\u904e\u7a0b\u306e\u5bfe\u5fdc<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u672c\u7bc0\u3067\u306f\u307e\u305aGauss\u904e\u7a0b\u3068\u30ab\u30fc\u30cd\u30eb\u6cd5\u306b\u3064\u3044\u3066\u7c21\u5358\u306b\u8aac\u660e\u3057\uff0c\u6b21\u306b\u7121\u9650\u5e45NN\u3068Gauss\u904e\u7a0b\u306e\u95a2\u4fc2\u306b\u3064\u3044\u3066\u8ff0\u3079\u307e\u3059\uff0e<\/p>\n<p>Gauss\u904e\u7a0b\u3068\u306f\uff0c\u7c21\u5358\u306b\u8a00\u3046\u3068\u7121\u9650\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u3042\u308b\u3044\u306f<strong>\u95a2\u6570<\/strong>\u3092\u30e9\u30f3\u30c0\u30e0\u306b\u30b5\u30f3\u30d7\u30eb\u3067\u304d\u308bGauss\u5206\u5e03\u3067\u3059\uff0e<br \/>\n\u6a5f\u68b0\u5b66\u7fd2\u3067\u3088\u304f\u7528\u3044\u3089\u308c\u308b\uff0c\u4f8b\u3048\u3070Gauss\u5206\u5e03\u3084Poisson\u5206\u5e03\u306a\u3069\u306e\u78ba\u7387\u5206\u5e03\u306f\uff0c\u5b9f\u6570\u3084\u6709\u9650\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u3092\u30b5\u30f3\u30d7\u30eb\u3059\u308b\u78ba\u7387\u5206\u5e03\u3067\u3059\u304c\uff0c\u305d\u308c\u3092\u62e1\u5f35\u3057\u305f\u3082\u306e\u306b\u306a\u308a\u307e\u3059\uff0e<\/p>\n<p>Gauss\u904e\u7a0b\u306e\u6b63\u78ba\u306a\u5b9a\u7fa9\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff0e<br \/>\n\u95a2\u6570$f: \\mathcal{X} \\to \\mathbb{R}$ \u304cGauss\u904e\u7a0b $\\mathcal{GP}(m,K)$ \u306b\u5f93\u3046\u3068\u306f\uff0c\u4efb\u610f\u306e\u6709\u9650\u500b\u306e\u5165\u529b\u306e\u7d44 $\\bm{x}=(x_1,\\dots,x_n)^\\top$ \u306b\u5bfe\u3057\u3066\uff0c\u51fa\u529b$(f(x_1),\\dots,f(x_n))^\\top$\u304c\u591a\u5909\u91cfGauss\u5206\u5e03$\\mathcal{N}(\\bm{m}&#8217;, K&#8217;)$\u306b\u5f93\u3046\u3053\u3068\u3092\u8a00\u3044\u307e\u3059\uff0e<br \/>\n\u3053\u3053\u3067\uff0c\u5e73\u5747\u3092\u4e0e\u3048\u308b\u95a2\u6570$m: \\mathcal{X} \\to \\mathbb{R}$\u3068\u5171\u5206\u6563\u3092\u4e0e\u3048\u308b\u95a2\u6570$K:\\mathcal{X}\\times\\mathcal{X}\\to\\mathbb{R}$\u3092\u7528\u3044\u3066\uff0c\u591a\u5909\u91cfGauss\u5206\u5e03\u306e\u5e73\u5747\u3092$\\bm{m}&#8217;=(m(x_1),\\dots,m(x_n))^\\top$\uff0c\u5171\u5206\u6563\u884c\u5217\u306e\u6210\u5206\u3092$K&#8217;_{ij}=K(x_i,x_j)$\u3068\u5b9a\u3081\u307e\u3059\uff0e<br \/>\n\u95a2\u6570$K$\u306f<strong>\u30ab\u30fc\u30cd\u30eb<\/strong>\u3068\u3082\u547c\u3070\u308c\u307e\u3059\uff0e<br \/>\n$m,K$\u306b\u9078\u3076\u95a2\u6570\u3092\u8272\u3005\u5909\u3048\u308b\u3053\u3068\u3067\uff0c\u3055\u307e\u3056\u307e\u306a\u5f62\u306e\u95a2\u6570\u3092\u8868\u73fe\u3067\u304d\u307e\u3059\uff0e\u4ee5\u4e0b\u306e\u56f33\u3067\u306f\uff0c$\\mathcal{X}=\\mathbb{R},m=0$\u30683\u7a2e\u985e\u306e\u30ab\u30fc\u30cd\u30eb$K$\u306b\u5bfe\u3057\u3066\uff0cGauss\u904e\u7a0b\u304b\u3089\u30b5\u30f3\u30d7\u30eb\u3055\u308c\u305f\u95a2\u6570\u3092\u3044\u304f\u3064\u304b\u8868\u793a\u3057\u3066\u3044\u307e\u3059\uff0e<br \/>\n\u5de6\u306e\u56f3\u306fRBF\u30ab\u30fc\u30cd\u30eb\u3068\u3044\u3046\u30ab\u30fc\u30cd\u30eb\u3092\u7528\u3044\u305f\u3082\u306e\u3067\uff0c\u6ed1\u3089\u304b\u306a\u95a2\u6570\u304c\u5f97\u3089\u308c\u3066\u3044\u307e\u3059\uff0e\u771f\u3093\u4e2d\u306e\u56f3\u3067\u7528\u3044\u305f\u30ab\u30fc\u30cd\u30eb\u3092\u7528\u3044\u308b\u3068\uff0c\u30ae\u30b6\u30ae\u30b6\u3057\u305f\u95a2\u6570\u304c\u5f97\u3089\u308c\u307e\u3059\uff0e\u53f3\u306e\u56f3\u3067\u306f2\u6b21\u306e\u591a\u9805\u5f0f\u30ab\u30fc\u30cd\u30eb\u3092\u7528\u3044\uff0c2\u6b21\u95a2\u6570\u304c\u5f97\u3089\u308c\u3066\u3044\u307e\u3059\uff0e<\/p>\n<div style=\"width: 1210px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" src=\"\/T-Wave\/wp-content\/uploads\/2024\/03\/gp_kernel.png\" alt=\"\" width=\"1200\" height=\"400\" \/><p class=\"wp-caption-text\">\u56f33\uff1a\u3044\u308d\u3044\u308d\u306a\u30ab\u30fc\u30cd\u30eb\u306eGauss\u904e\u7a0b\uff0e\u51fa\u5178 https:\/\/en.wikipedia.org\/wiki\/Gaussian_process<\/p><\/div>\n<p>\u30ab\u30fc\u30cd\u30eb$K$\u306e\u610f\u5473\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\uff0e<br \/>\n$K(x_i,x_j)$\u306f\uff0c\u5165\u529b$x_i,x_j$\u306b\u5bfe\u3059\u308b\u51fa\u529b$f(x_i),f(x_j)$\u306e\u985e\u4f3c\u5ea6\u3092\u6e2c\u3063\u3066\u3044\u308b\u3068\u307f\u306a\u305b\u307e\u3059\uff0e<br \/>\n\u30ab\u30fc\u30cd\u30eb\u306e\u5024\u304c\u5927\u304d\u3044\u307b\u3069\uff0c\u5171\u5206\u6563\u304c\u5927\u304d\u304f\uff0c2\u3064\u306e\u51fa\u529b\u306f\u8fd1\u3044\u5024\u3092\u53d6\u308a\u307e\u3059\uff0e<br \/>\n\u4e00\u65b9\u3067\uff0c\u30ab\u30fc\u30cd\u30eb\u306e\u5024\u304c$0$\u306b\u8fd1\u3044\u307b\u3069\uff0c\u5171\u5206\u6563\u304c$0$\u306b\u8fd1\u304f\u306a\u308a\uff0c2\u3064\u306e\u51fa\u529b\u306f\u3070\u3089\u3070\u3089\u306b\u72ec\u7acb\u306a\u5024\u3092\u53d6\u308a\u307e\u3059\uff0e<\/p>\n<p>Gauss\u904e\u7a0b\u3092\u7528\u3044\u308b\u3068\uff0c\u4e0d\u78ba\u5b9f\u6027\u3092\u8003\u616e\u3057\u305f\u56de\u5e30\u304c\u884c\u3048\u307e\u3059\uff0e<br \/>\n\u6a5f\u68b0\u5b66\u7fd2\u306b\u304a\u3044\u3066\uff0c\u56de\u5e30\u554f\u984c\u306f\uff0c\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8${(\\bm{x}_i,y_i) \\mid i=1,\\dots,N}$\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\uff0c\u3053\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3092\u51fa\u529b\u3059\u308b\u78ba\u7387\u304c\u6700\u3082\u9ad8\u3044\u3088\u3046\u306a\u95a2\u6570\u3092\u898b\u3064\u3051\u308b\u554f\u984c\u3067\u3059\uff0e<br \/>\n\u3059\u306a\u308f\u3061\uff0c\u672a\u77e5\u306e\u95a2\u6570$f$\u3092\u7528\u3044\u3066$y=f(\\bm{x})+\\epsilon$\uff08$\\epsilon$\u306f\u30ce\u30a4\u30ba\uff09\u3068\u3044\u3046\u5f0f\u3067$y$\u304c\u751f\u6210\u3055\u308c\u3066\u3044\u308b\u3068\u3057\u305f\u3068\u304d\u306b\uff0c\u4e0e\u3048\u3089\u308c\u305f\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u304b\u3089$f$\u3092\u63a8\u5b9a\u3059\u308b\u554f\u984c\u3067\u3059\uff0e<br \/>\nGauss\u904e\u7a0b\u3092\u7528\u3044\u305f\u56de\u5e30\u306fGauss\u904e\u7a0b\u56de\u5e30\u3068\u547c\u3070\u308c\u307e\u3059\uff0e<br \/>\nGauss\u904e\u7a0b\u56de\u5e30\u306e\u8aac\u660e\u306f\u672c\u8a18\u4e8b\u3067\u306f\u7701\u7565\u3057\u307e\u3059\uff0e<br \/>\n\u307e\u305f\uff0cGauss\u904e\u7a0b\u56de\u5e30\u306f\uff0c\u5f37\u529b\u306a\u56de\u5e30\u306e\u624b\u6cd5\u3067\u3042\u308b<strong>\u30ab\u30fc\u30cd\u30eb\u6cd5<\/strong>\u3068\u6df1\u3044\u95a2\u4fc2\u306b\u3042\u308a\u307e\u3059\uff0e<br \/>\nGauss\u904e\u7a0b\u306f\u30ab\u30fc\u30cd\u30eb\u6cd5\u3092\u62e1\u5f35\u3057\u3066\u4e0d\u78ba\u5b9f\u6027\u3092\u6271\u3048\u308b\u3088\u3046\u306b\u3057\u305f\u3082\u306e\u3068\u6349\u3048\u3089\u308c\u307e\u3059\uff0e<\/p>\n<p>\u7121\u9650\u5e45NN\u306e\u8a71\u306b\u79fb\u308a\u307e\u3059\uff0e<br \/>\n\u4e00\u822c\u306bNN\u306f\u591a\u6570\u306e\u81ea\u7531\u5ea6\u3092\u542b\u307f\uff0c\u305d\u306e\u6319\u52d5\u3092\u6b63\u78ba\u306b\u6349\u3048\u308b\u3053\u3068\u306f\u975e\u5e38\u306b\u96e3\u3057\u3044\u8ab2\u984c\u3067\u3059\uff0e<br \/>\n\u3057\u304b\u3057\uff0c\u5e45\u3092\u7121\u9650\u306b\u5927\u304d\u304f\u3059\u308b\u6975\u9650\u3067\u306f\uff0c\u69d8\u3005\u306a\u8fd1\u4f3c\u3092\u65bd\u3059\u3053\u3068\u304c\u3067\u304d\uff0c\u7406\u8ad6\u7684\u306b\u6271\u3044\u3084\u3059\u304f\u306a\u308a\u307e\u3059\uff0e<br \/>\n\u8fd1\u5e74\uff0c\u6df1\u5c64NN\u306e\u8907\u96d1\u306a\u6319\u52d5\u3092\u7406\u89e3\u3059\u308b\u305f\u3081\u306e\u7406\u8ad6\u7684\u67a0\u7d44\u3068\u3057\u3066\uff0c\u7121\u9650\u5e45NN\u306e\u89e3\u6790\u304c\u5927\u304d\u306a\u6ce8\u76ee\u3092\u6d74\u3073\u3066\u3044\u307e\u3059\uff0e<\/p>\n<p>\u7121\u9650\u5e45NN\u306e\u8457\u3057\u3044\u6027\u8cea\u306e\u4e00\u3064\u306f\uff0c<strong>\u7121\u9650\u5e45NN\u304cGauss\u904e\u7a0b\u3068\u307f\u306a\u305b\u308b<\/strong>\u3068\u3044\u3046\u70b9\u3067\u3059 [12]\uff0e<br \/>\n2\u5c64\u306eNN\u306b\u5bfe\u3057\u3066\uff0c\u5177\u4f53\u7684\u306b\u6570\u5f0f\u3067\u898b\u3066\u3044\u304d\u307e\u3057\u3087\u3046\uff0e<br \/>\n\u5165\u529b\u6b21\u5143$d$\uff0c\u96a0\u308c\u5c64\u306e\u5e45$N$\uff0c\u6d3b\u6027\u5316\u95a2\u6570$f$\u3092\u6301\u3064\u5168\u7d50\u54082\u5c64NN\u3092\u8003\u3048\u307e\u3059\uff0e<br \/>\n\u91cd\u307f\u3068\u30d0\u30a4\u30a2\u30b9\u306fGauss\u5206\u5e03\u306b\u5f93\u3063\u3066\u72ec\u7acb\u306b\u521d\u671f\u5316\u3057\u307e\u3059\uff0e<br \/>\n\u5165\u529b$\\bm{x}\\in\\mathbb{R}^d$\u306b\u5bfe\u3059\u308b\u51fa\u529b$y(\\bm{x})\\in\\mathbb{R}$\u306f\u4ee5\u4e0b\u306e\u5f0f\u3067\u8868\u3055\u308c\u307e\u3059\uff0e<br \/>\n$$<br \/>\ny(\\bm{x}) = \\sum_{i=1}^N w_i^1 f(z_i(\\bm{x})) + b^1 \\<br \/>\nz_i(\\bm{x}) = \\sum_{j=1}^d w_{ij}^0 x_j + b^0_i<br \/>\n$$<br \/>\n\u91cd\u307f$w_{ij}^0$\u306f\u72ec\u7acb\u306b\u30b5\u30f3\u30d7\u30eb\u3055\u308c\u3066\u3044\u308b\u306e\u3067\uff0c${z_i}_{i=1,\\dots,N}$\u306f\u72ec\u7acb\u306a\u78ba\u7387\u5909\u6570\u3067\u3059\uff0e<br \/>\n$y(\\bm{x})$\u306f\u72ec\u7acb\u306a$N$\u500b\u306e\u78ba\u7387\u5909\u6570\u306e\u548c\u3067\u3042\u308a\uff0c$N\\to\\infty$\u3067\u4e2d\u5fc3\u6975\u9650\u5b9a\u7406\u306b\u3088\u308a$y(\\bm{x})$\u306fGauss\u5206\u5e03\u306b\u5f93\u3044\u307e\u3059\uff0e<br \/>\n\u3059\u306a\u308f\u3061\uff0c\u3069\u306e\u3088\u3046\u306a$\\bm{x}$\u306b\u5bfe\u3057\u3066\u3082\u51fa\u529b\u306fGauss\u5206\u5e03\u306b\u5f93\u3046\u306e\u3067\uff0cNN\u306e\u521d\u671f\u5316\u6642\u306b\u306f\uff0c$y(\\bm{x})$\u306fGauss\u904e\u7a0b\u3067\u3042\u308b\u3068\u8a00\u3048\u307e\u3059\uff0e<br \/>\n3\u5c64\u4ee5\u4e0a\u306e\u6df1\u5c64NN\u3067\u3082\uff0c\u540c\u69d8\u306e\u8b70\u8ad6\u306b\u3088\u308a\u51fa\u529b\u304cGauss\u904e\u7a0b\u306b\u5f93\u3046\u3053\u3068\u304c\u793a\u3055\u308c\u307e\u3059\uff0e<\/p>\n<p>\u3053\u306eNN\u3068Gauss\u904e\u7a0b\u306e\u5bfe\u5fdc\u306f\uff0c<strong>NN-GP\uff08Neural Network-Gaussian Process\uff09\u5bfe\u5fdc<\/strong>\u3068\u547c\u3070\u308c\u307e\u3059\uff0e<br \/>\n\u5c64\u3092\u6df1\u304f\u3059\u308b\u307b\u3069\uff0c\u5bfe\u5fdc\u3059\u308bGauss\u904e\u7a0b\u306e\u30ab\u30fc\u30cd\u30eb\u304c\u8907\u96d1\u306b\u306a\u308b\u305f\u3081\uff0c\u3088\u308a\u8907\u96d1\u306a\u95a2\u6570\u3092\u8868\u73fe\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff0e<br \/>\n\u3053\u306e\u3053\u3068\u3092\u793a\u3057\u305f\u306e\u304c\u4ee5\u4e0b\u306e\u56f3\u3067\u3059\uff0e\u56f34\u306f\uff0c\u5165\u529b\u6b21\u5143\u3068\u51fa\u529b\u6b21\u5143\u304c1\u306eNN\u306e\u91cd\u307f\u3092Gauss\u5206\u5e03\u306b\u5f93\u3063\u3066\u521d\u671f\u5316\u3057\u305f\u3068\u304d\u306e\u5165\u51fa\u529b\u306e\u95a2\u4fc2\u3092\u8868\u3057\u305f\u3082\u306e\u3067\u3059\uff0e\u5c64\u3092\u5897\u3059\u3054\u3068\u306b\uff0c\u5909\u5316\u306b\u5bcc\u3093\u3060\u8907\u96d1\u306a\u95a2\u6570\u304c\u5b9f\u73fe\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\uff0e<\/p>\n<div style=\"width: 858px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" src=\"\/T-Wave\/wp-content\/uploads\/2024\/03\/nngp.png\" alt=\"\" width=\"848\" height=\"624\" \/><p class=\"wp-caption-text\">\u56f34\uff1a2\u5c64\u304b\u30895\u5c64\u306eNN\u306b\u5bfe\u5fdc\u3059\u308bGauss\u904e\u7a0b\u304b\u3089\u306e\u30b5\u30f3\u30d7\u30eb<\/p><\/div>\n<p>\u7121\u9650\u5e452\u5c64NN\u306b\u5bfe\u5fdc\u3059\u308b\u30ab\u30fc\u30cd\u30eb\u3092\u5177\u4f53\u7684\u306b\u6c42\u3081\u3066\u307f\u307e\u3057\u3087\u3046\uff0e<br \/>\n\u7c21\u5358\u306e\u305f\u3081\uff0c\u30d0\u30a4\u30a2\u30b9$b^0,b^1$\u3092\u7121\u8996\u3057\uff0c\u91cd\u307f$w^0,w^1$\u304c\u5f93\u3046Gauss\u5206\u5e03\u306e\u5e73\u5747\u3092$0$\uff0c\u5206\u6563\u3092$1$\u3068\u3057\u307e\u3059\uff0e<br \/>\n\u3059\u308b\u3068\uff0c\u30ab\u30fc\u30cd\u30eb\u306f<br \/>\n$$<br \/>\nK(\\bm{x},\\bm{x}&#8217;)=\\mathbb{E}[y(\\bm{x})y(\\bm{x}&#8217;)]=\\mathbb{E}[f(z_1(\\bm{x}))f(z_1(\\bm{x}&#8217;))]<br \/>\n$$<br \/>\n\u3068\u306a\u308a\u307e\u3059\uff0e<br \/>\n\u3055\u3089\u306b\uff0c$w^0$\u304cGauss\u5206\u5e03\u306b\u5f93\u3046\u3053\u3068\u306b\u3088\u308a\uff0c$z_1(\\bm{x})$\u3082Gauss\u5206\u5e03\u306b\u5f93\u3044\u307e\u3059\uff0e<br \/>\n\u7279\u306b\uff0c$|\\bm{x}|^2=d,q=\\bm{x}^\\top \\bm{x}&#8217;\/d$\u3068\u3059\u308b\u3068\uff0c<br \/>\n$$<br \/>\nK(\\bm{x},\\bm{x}&#8217;)= \\mathbb{E}\\left[ f(z)f(z&#8217;) \\mid \\begin{pmatrix}z \\ z&#8217;\\end{pmatrix} \\sim \\mathcal{N}\\left( \\begin{pmatrix}0 \\ 0\\end{pmatrix}, \\begin{pmatrix}1 &amp; q \\ q &amp; 1\\end{pmatrix} \\right) \\right]<br \/>\n\\tag{2}<br \/>\n$$<br \/>\n\u3068\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff0e<\/p>\n<p>\u3053\u306e\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u7406\u89e3\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff0e$q$\u306f2\u3064\u306e\u5165\u529b$\\bm{x},\\bm{x}&#8217;$\u306e\u985e\u4f3c\u5ea6\u3092\u6e2c\u3063\u3066\u3044\u307e\u3059\uff0e$q$\u304c$1$\u306b\u8fd1\u3044\u307b\u30692\u3064\u306e\u5165\u529b\u306f\u4f3c\u3066\u3044\u307e\u3059\uff0e\u305d\u3057\u3066\uff0c$z_1(\\bm{x}),z_1(\\bm{x}&#8217;)$\u306e\u985e\u4f3c\u5ea6\uff08\u6b63\u78ba\u306b\u306f\uff0c\u7a4d\u306e\u671f\u5f85\u5024\uff09\u3082$q$\u306b\u306a\u308a\u307e\u3059\uff0e<br \/>\n$K(\\bm{x},\\bm{x}&#8217;)$\u306f\uff0c2\u3064\u306e\u5165\u529b$\\bm{x},\\bm{x}&#8217;$\u306b\u5bfe\u3059\u308b\u51fa\u529b$y(\\bm{x}),y(\\bm{x}&#8217;)$\u306e\u5171\u5206\u6563\u3059\u306a\u308f\u3061\u985e\u4f3c\u5ea6\u3067\u3059\uff0e<br \/>\n\u5171\u5206\u6563\u304c\u5c0f\u3055\u3044\u307b\u3069\uff0c\u51fa\u529b\u306f\u3070\u3089\u3070\u3089\u306a\u5024\u3092\u53d6\u308b\u3053\u3068\u3092\u601d\u3044\u51fa\u3057\u307e\u3057\u3087\u3046\uff0e<br \/>\n\u7279\u306b\uff0c$q$\u304c$1$\u306b\u8fd1\u3044\u3068\u304d\u306b\uff0c$K(\\bm{x},\\bm{x}&#8217;)$\u306e\u5024\u304c\u5c0f\u3055\u3051\u308c\u3070\uff0c\u3088\u308a\u5909\u5316\u306b\u5bcc\u3093\u3060\u8907\u96d1\u306a\u95a2\u6570\u3092\u8868\u73fe\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff0e<\/p>\n<h4 id=\"%E6%9C%AC%E7%AF%80%E3%81%AE%E3%81%BE%E3%81%A8%E3%82%81\"><span class=\"ez-toc-section\" id=\"%E6%9C%AC%E7%AF%80%E3%81%AE%E3%81%BE%E3%81%A8%E3%82%81-2\"><\/span>\u672c\u7bc0\u306e\u307e\u3068\u3081<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>\u672c\u7bc0\u3067\u306f\uff0cGauss\u904e\u7a0b\u306b\u3064\u3044\u3066\u7c21\u5358\u306b\u6982\u8981\u3092\u8ff0\u3079\uff0cNN\u304cGauss\u904e\u7a0b\u3068\u307f\u306a\u305b\u308b\u3068\u3044\u3046NN-GP\u5bfe\u5fdc\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3057\u305f\uff0e\u305d\u3057\u3066\uff0c2\u5c64NN\u306b\u5bfe\u5fdc\u3059\u308bGauss\u904e\u7a0b\u306e\u30ab\u30fc\u30cd\u30eb\u306f\u5f0f(2)\u3067\u4e0e\u3048\u3089\u308c\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3057\u305f\uff0e\u6700\u5f8c\u306b\uff0c\u4f3c\u305f\u5165\u529b\u306b\u5bfe\u3059\u308b\u30ab\u30fc\u30cd\u30eb\u306e\u5024\u304c\u5c0f\u3055\u3044\u307b\u3069\uff0cNN\u306f\u6025\u6fc0\u306b\u5909\u5316\u3059\u308b\u8907\u96d1\u306a\u95a2\u6570\u3092\u8868\u73fe\u3067\u304d\u308b\u3053\u3068\u3092\u8aac\u660e\u3057\u307e\u3057\u305f\uff0e<\/p>\n<h2 id=\"2%E3%81%A4%E3%81%AE%E7%A0%94%E7%A9%B6%E3%81%AE%E5%85%B1%E9%80%9A%E7%82%B9%E3%81%A8%E7%9B%B8%E9%81%95%E7%82%B9\"><span class=\"ez-toc-section\" id=\"2%E3%81%A4%E3%81%AE%E7%A0%94%E7%A9%B6%E3%81%AE%E5%85%B1%E9%80%9A%E7%82%B9%E3%81%A8%E7%9B%B8%E9%81%95%E7%82%B9\"><\/span>2\u3064\u306e\u7814\u7a76\u306e\u5171\u901a\u70b9\u3068\u76f8\u9055\u70b9<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8a18\u61b6\u5bb9\u91cf\u306e\u7d71\u8a08\u529b\u5b66\u7684\u89e3\u6790\u3068\uff0cNN-GP\u5bfe\u5fdc\u3068\u3044\u3046\uff0c2\u3064\u306e\u7814\u7a76\u306e\u6d41\u308c\u3092\u7d39\u4ecb\u3057\u307e\u3057\u305f\uff0e<br \/>\n\u3053\u308c\u3089\u306e\u7814\u7a76\u306e\u5171\u901a\u70b9\u306f\u660e\u3089\u304b\u3067\u3057\u3087\u3046\uff0e\u5f0f(1)\u3068\u5f0f(2)\u306f\u5168\u304f\u540c\u3058\u3067\u3042\u308a\uff0c\u3053\u306e\u5024\u3092\u901a\u3057\u3066\u3053\u308c\u3089\u306e\u7814\u7a76\u306e\u9593\u306e\u95a2\u4fc2\u3092\u7406\u89e3\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff0e<\/p>\n<p>2\u5c64NN\u306e\u8a18\u61b6\u5bb9\u91cf\u306e\u7814\u7a76\u3067\u306f\uff0c\u5f0f(1)\u306e$q=1$\u4ed8\u8fd1\u3067\u306e\u5024\u304c\u5c0f\u3055\u3044\u307b\u3069\uff0cNN\u304c\u540c\u3058\u5165\u529b\u3092\u5f15\u304d\u96e2\u3059\u80fd\u529b\u304c\u9ad8\u304f\uff0c\u8a18\u61b6\u5bb9\u91cf\u304c\u5927\u304d\u304f\u306a\u308b\u3068\u3044\u3046\u7d50\u679c\u304c\u5f97\u3089\u308c\u307e\u3057\u305f\uff0e<br \/>\n\u4e00\u65b9\uff0cNN-GP\u5bfe\u5fdc\u306e\u7814\u7a76\u3067\u306f\uff0c\u5f0f(2)\u306e$q=1$\u4ed8\u8fd1\u3067\u306e\u5024\u304c\u5c0f\u3055\u3044\u307b\u3069\uff0c\u4f3c\u305f\u5165\u529b\u306b\u5bfe\u3059\u308b\u5171\u5206\u6563\u3092\u5c0f\u3055\u304f\u3059\u308b\u3053\u3068\u304c\u3067\u304d\uff0c\u3088\u308a\u5909\u5316\u306b\u5bcc\u3093\u3060\u8907\u96d1\u306a\u95a2\u6570\u3092\u8868\u73fe\u3067\u304d\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3057\u305f\uff0e<\/p>\n<p>\u3053\u306e\u3088\u3046\u306b\uff0c\u8a18\u61b6\u5bb9\u91cf\u3068NN\u306e\u8868\u73fe\u529b\u306f\u76f4\u63a5\u3064\u306a\u304c\u3063\u3066\u3044\u308b\u306e\u3067\u3059\uff0e\u3053\u306e\u95a2\u4fc2\u306f\uff0c\u672c\u8a18\u4e8b\u3067\u7d39\u4ecb\u3057\u3066\u3044\u308b\u8ad6\u6587\u306b\u3088\u3063\u3066\u6700\u521d\u306b\u6307\u6458\u3055\u308c\u307e\u3057\u305f\uff0e<\/p>\n<p>\u4e00\u65b9\u3067\uff0c\u3044\u304f\u3064\u304b\u306e\u76f8\u9055\u70b9\u3082\u8ff0\u3079\u3066\u304a\u304f\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\uff0e<br \/>\n\u8a18\u61b6\u5bb9\u91cf\u306e\u7d71\u8a08\u529b\u5b66\u7684\u89e3\u6790\u306f\uff0c2\u5c64\u4ee5\u4e0b\u306e\u30a2\u30fc\u30ad\u30c6\u30af\u30c1\u30e3\u306b\u3068\u3069\u307e\u3063\u3066\u304a\u308a\uff0c3\u5c64\u4ee5\u4e0a\u306e\u89e3\u6790\u306f\u96e3\u3057\u3044\u3068\u3044\u3046\u306e\u304c\u73fe\u72b6\u3067\u3059\uff0e\u307e\u305f\uff0c\u5165\u529b\u6b21\u5143\u3082\u7121\u9650\u5927\u306b\u5927\u304d\u304f\u3059\u308b\u8a2d\u5b9a\u3067\u306e\u307f\u8a08\u7b97\u3055\u308c\u3066\u3044\u307e\u3059\uff0e<br \/>\n\u4ed6\u65b9\uff0cNN-GP\u5bfe\u5fdc\u306f3\u5c64\u4ee5\u4e0a\u306e\u6df1\u5c64NN\u3067\u3082\u6210\u308a\u7acb\u3061\uff0c\u307e\u305f\u5165\u529b\u6b21\u5143\u3082\u6709\u9650\u306b\u3068\u3069\u3081\u305f\u307e\u307e\u89e3\u6790\u304c\u53ef\u80fd\u3067\u3059\uff0eNN-GP\u5bfe\u5fdc\u306e\u8b70\u8ad6\u306e\u307b\u3046\u304c\uff0c\u3088\u308a\u73fe\u5b9f\u306b\u8fd1\u3044\u8a2d\u5b9a\u3092\u6271\u3063\u3066\u3044\u308b\u3068\u8a00\u3048\u307e\u3059\uff0e<\/p>\n<h2 id=\"%E7%B5%90%E8%AB%96\"><span class=\"ez-toc-section\" id=\"%E7%B5%90%E8%AB%96\"><\/span>\u7d50\u8ad6<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u672c\u8a18\u4e8b\u3067\u306f\uff0c\u6a5f\u68b0\u5b66\u7fd2\u30e2\u30c7\u30eb\u306e\u8a18\u61b6\u5bb9\u91cf\u306e\u7d71\u8a08\u529b\u5b66\u7684\u89e3\u6790\u3068\u3044\u3046\u7814\u7a76\u306e\u6d41\u308c\u3068\uff0cNN-GP\u5bfe\u5fdc\u3068\u3044\u3046\u7814\u7a76\u306e\u6d41\u308c\u3092\u8aac\u660e\u3057\u307e\u3057\u305f\uff0e\u305d\u3057\u3066\uff0c\u3053\u308c\u3089\u306e\u7814\u7a76\u3092\u7121\u9650\u5e452\u5c64NN\u306b\u9069\u7528\u3057\u305f\u3068\u304d\u306b\u5171\u901a\u306b\u73fe\u308c\u308b$K_f(q)$\u3068\u3044\u3046\u91cf\u3092\u901a\u3058\u3066\uff0c\u8a18\u61b6\u5bb9\u91cf\u306e\u554f\u984c\u304c\uff0cNN\u3092Gauss\u904e\u7a0b\u3068\u307f\u306a\u3057\u305f\u3068\u304d\u306e\u30ab\u30fc\u30cd\u30eb\u306e\u6319\u52d5\u3068\u3057\u3066\u7406\u89e3\u3067\u304d\u308b\u3053\u3068\u3092\u8aac\u660e\u3057\u307e\u3057\u305f\uff0e<\/p>\n<p>\u3053\u306e\u8ad6\u6587\u3067\u6307\u6458\u3055\u308c\u305f\uff0c\u8a18\u61b6\u5bb9\u91cf\u3068NN-GP\u5bfe\u5fdc\u306e\u95a2\u4fc2\u3092\u304d\u3063\u304b\u3051\u306b\uff0c\u7d71\u8a08\u529b\u5b66\u3068\u6a5f\u68b0\u5b66\u7fd2\u7406\u8ad6\u306e\u9593\u3067\u306e\u77e5\u898b\u3084\u624b\u6cd5\u306e\u5171\u6709\u304c\u9032\u3080\u3053\u3068\u304c\u671f\u5f85\u3055\u308c\u307e\u3059\uff0e<\/p>\n<h2 id=\"%E3%81%82%E3%81%A8%E3%81%8C%E3%81%8D\"><span class=\"ez-toc-section\" id=\"%E3%81%82%E3%81%A8%E3%81%8C%E3%81%8D\"><\/span>\u3042\u3068\u304c\u304d<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4f59\u8ac7\u3068\u3057\u3066\uff0c\u7b46\u8005\u304c\u73fe\u5728\u53d6\u308a\u7d44\u3093\u3067\u3044\u308b\u7814\u7a76\u3092\u7d39\u4ecb\u3057\u307e\u3059\uff0e\u4ee5\u4e0b\u306e\u5185\u5bb9\u306e\u4e00\u90e8\u306f\uff0c\u65e5\u672c\u7269\u7406\u5b66\u4f1a2024\u5e74\u6625\u5b63\u5927\u4f1a\u3067\u300c\u4e00\u822c\u306e\u6d3b\u6027\u5316\u95a2\u6570\u3092\u6301\u3064\u5168\u7d50\u54082\u5c64\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306e\u8a18\u61b6\u5bb9\u91cf\u300d\u3068\u984c\u3057\u3066\u767a\u8868\u3057\u307e\u3057\u305f\uff0e<\/p>\n<p>2\u5c64NN\u306e\u8a18\u61b6\u5bb9\u91cf\u306f\uff0c\u4ee5\u4e0b\u306e3\u3064\u306e\u5834\u5408\u306b\u6c42\u3081\u3089\u308c\u3066\u3044\u308b\u3053\u3068\u3092\u672c\u8a18\u4e8b\u3067\u8aac\u660e\u3057\u307e\u3057\u305f\uff1a<\/p>\n<ul>\n<li>\u6d3b\u6027\u5316\u95a2\u6570\u304c\u7b26\u53f7\u95a2\u6570\u3067\uff0c\u30a2\u30fc\u30ad\u30c6\u30af\u30c1\u30e3\u304c\u6728\u69cb\u9020<\/li>\n<li>\u6d3b\u6027\u5316\u95a2\u6570\u304c\u7b26\u53f7\u95a2\u6570\u3067\uff0c\u30a2\u30fc\u30ad\u30c6\u30af\u30c1\u30e3\u304c\u5168\u7d50\u5408<\/li>\n<li>\u6d3b\u6027\u5316\u95a2\u6570\u304c\u4e00\u822c\u306e\u95a2\u6570\u3067\uff0c\u30a2\u30fc\u30ad\u30c6\u30af\u30c1\u30e3\u304c\u6728\u69cb\u9020<\/li>\n<\/ul>\n<p>\u6b21\u306e\u81ea\u7136\u306a\u30b9\u30c6\u30c3\u30d7\u306f\uff0c\u6d3b\u6027\u5316\u95a2\u6570\u304c\u4e00\u822c\u306e\u95a2\u6570\u3067\uff0c\u30a2\u30fc\u30ad\u30c6\u30af\u30c1\u30e3\u304c\u5168\u7d50\u5408\u306e\u5834\u5408\u306e\u89e3\u6790\u3067\u3059\uff0e<br \/>\n2\u5c64NN\u306e\u4e2d\u3067\u306f\uff0c\u3053\u306e\u8a2d\u5b9a\u304c\u3082\u3063\u3068\u3082\u73fe\u5b9f\u306b\u8fd1\u3044\u3082\u306e\u3067\u3042\u308a\uff0c2\u5c64NN\u306e\u4e2d\u3067\u306f\u5b9f\u7528\u7684\u306a\u7acb\u5834\u304b\u3089\u6700\u3082\u8208\u5473\u306e\u3042\u308b\u3082\u306e\u3067\u3042\u308b\u3068\u7b46\u8005\u306f\u8003\u3048\u307e\u3059\uff0e<br \/>\n\u305d\u3053\u3067\uff0c\u7b46\u8005\u306f\u3053\u306e\u8a2d\u5b9a\u306b\u304a\u3051\u308b\u8a18\u61b6\u5bb9\u91cf\u306e\u8a08\u7b97\u306b\u53d6\u308a\u7d44\u307f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u7d50\u679c\u3092\u5f97\u307e\u3057\u305f\uff0e<\/p>\n<ul>\n<li>\u6728\u69cb\u9020\u306e\u5834\u5408\u3068\u540c\u69d8\u306b\uff0c\u7121\u9650\u5e45\u6975\u9650\u3067\u8a18\u61b6\u5bb9\u91cf\u306f\u6709\u9650\u306b\u3068\u3069\u307e\u308b<\/li>\n<li>\u6d3b\u6027\u5316\u95a2\u6570\u304c\u7b26\u53f7\u95a2\u6570\u3067\u5168\u7d50\u5408\u306e\u5834\u5408\u3068\u540c\u69d8\u306b\uff0c\u91cd\u307f\u304c\u5206\u696d\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u8a18\u61b6\u5bb9\u91cf\u304c\u6728\u69cb\u9020\u306e\u5834\u5408\u3068\u6bd4\u3079\u3066\u5927\u304d\u304f\u306a\u308b<\/li>\n<li>\u8a18\u61b6\u5bb9\u91cf\u306e\u5024\u306f\uff0c$\\frac{\\langle f&#8217;^2 \\rangle &#8211; \\langle f&#8217; \\rangle^2}{\\langle f^2 \\rangle &#8211; \\langle f \\rangle^2 &#8211; \\langle f&#8217; \\rangle^2}$\u3068\u66f8\u3051\u308b\uff0e\u3053\u3053\u3067\uff0c$\\langle \\cdot \\rangle$\u306f\u6a19\u6e96\u6b63\u898f\u5206\u5e03\u306b\u95a2\u3059\u308b\u671f\u5f85\u5024\u3067\u3042\u308b\uff0e\uff08\u6728\u69cb\u9020\u306e\u5834\u5408\u306b\u306f$\\frac{\\langle f&#8217;^2 \\rangle}{\\langle f^2 \\rangle &#8211; \\langle f 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id=\"%E5%8F%82%E8%80%83%E6%96%87%E7%8C%AE\"><span class=\"ez-toc-section\" id=\"%E5%8F%82%E8%80%83%E6%96%87%E7%8C%AE\"><\/span>\u53c2\u8003\u6587\u732e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>[1] Zavatone-Veth, J. A., &amp; Pehlevan, C. (2021). Activation function dependence of the storage capacity of treelike neural networks. Physical Review E, 103(2). https:\/\/doi.org\/10.1103\/PhysRevE.103.L020301<\/li>\n<li>[2] Gardner, E. (1988). The space of interactions in neural network models. Journal of Physics A: General Physics, 21(1). https:\/\/doi.org\/10.1088\/0305-4470\/21\/1\/030<\/li>\n<li>[3] Gardner, E., &amp; Derrida, B. (1988). Optimal storage properties of neural network models. Journal of Physics A: Mathematical and General, 21(1), 271\u2013284. https:\/\/doi.org\/10.1088\/0305-4470\/21\/1\/031<\/li>\n<li>[4] \u5927\u95a2\u771f\u4e4b\u306e\u96d1\u8ac7\u65b9\u7a0b\u5f0f &#8211; \u3053\u308c\u3063\u3066\u4eba\u751f\u5909\u3048\u3061\u3083\u3046\u6388\u696d\u304b\u3082 &#8211; (2021). \u60c5\u5831\u79d1\u5b66\u3068\u3057\u3066\u306e\u6570\u7406\u60c5\u5831\u5b66\u30102021\u5e74\u5ea6\u30fb\u6771\u5317\u5927\u5b66\u3011. https:\/\/www.youtube.com\/playlist?list=PLsBJ3psEqyr8Vo4Ez-xVKkesc8ba9ezu_ (2024\u5e742\u670813\u65e5\u95b2\u89a7)<\/li>\n<li>[5] Cover, T. M. (1965). Geometrical and Statistical Properties of Systems of Linear Inequalities with Applications in Pattern Recognition. In IEEE Transactions on Electronic Computers: Vol. EC-14 (Issue 3). https:\/\/doi.org\/10.1109\/PGEC.1965.264137<\/li>\n<li>[6] Engel, A., K\u00f6hler, H. M., Tschepke, F., Vollmayr, H., &amp; Zippelius, A. (1992). Storage capacity and learning algorithms for two-layer neural networks. Physical Review A, 45(10). https:\/\/doi.org\/10.1103\/PhysRevA.45.7590<\/li>\n<li>[7] Barkai, E., Hansel, D., &amp; Sompolinsky, H. (1992). Broken symmetries in multilayered perceptrons. Physical Review A, 45(6). https:\/\/doi.org\/10.1103\/PhysRevA.45.4146<\/li>\n<li>[8] Monasson, R., &amp; Zecchina, R. (1995). Weight space structure and internal representations: A direct approach to learning and generalization in multilayer neural networks. Physical Review Letters, 75(12). https:\/\/doi.org\/10.1103\/PhysRevLett.75.2432<\/li>\n<li>[9] Xiong, Y., Kwon, C., &amp; Oh, J. H. (1998). The storage capacity of a fully-connected committee machine. Advances in Neural Information Processing Systems.<\/li>\n<li>[10] Baldassi, C., Malatesta, E. M., &amp; Zecchina, R. (2019). Properties of the Geometry of Solutions and Capacity of Multilayer Neural Networks with Rectified Linear Unit Activations. Physical Review Letters, 123(17). https:\/\/doi.org\/10.1103\/PhysRevLett.123.170602<\/li>\n<li>[11] Zavatone-Veth, J. A., &amp; Pehlevan, C. (2021). Activation function dependence of the storage capacity of treelike neural networks. Physical Review E, 103(2). https:\/\/doi.org\/10.1103\/PhysRevE.103.L020301<\/li>\n<li>[12] Lee, J., Bahri, Y., Novak, R., Schoenholz, S. S., Pennington, J., &amp; Sohl-Dickstein, J. (2018). Deep neural networks as Gaussian processes. 6th International Conference on Learning Representations, ICLR 2018 &#8211; Conference Track Proceedings.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\uff08NN\uff09\u306e\u6027\u80fd\u3068\u6d3b\u6027\u5316\u95a2\u6570\u306e\u95a2\u4fc2\u306b\u307e\u3064\u308f\u308b2\u3064\u306e\u7814\u7a76\u306e\u6d41\u308c\u304c\u3042\u308a\u307e\u3059\uff0e1\u3064\u306f\uff0c\u8a18\u61b6\u5bb9\u91cf\u306e\u554f\u984c\u306e\u7d71\u8a08\u529b\u5b66\u7684\u89e3\u6790\u3067\u3059\uff0e\u8a18\u61b6\u5bb9\u91cf\u3068\u306f\uff0c\u4e8c\u5024\u5206\u985e\u30e2\u30c7\u30eb\u304c\u8a18\u61b6\u3067\u304d\u308b\u30e9\u30f3\u30c0\u30e0\u306a\u30c7\u30fc\u30bf\u306e\u6700\u5927\u6570\uff08\u30d1\u30e9\u30e1\u30fc\u30bf\u3042\u305f\u308a\uff09\u3067\uff0c\u30e2\u30c7\u30eb\u306e\u8868\u73fe\u80fd\u529b\u306e\u6307\u6a19\u306e\u4e00\u3064\u3067\u3059\uff0e\u3082\u30461\u3064\u306f\uff0c\u7121\u9650\u5e45NN\u3068Gauss\u904e\u7a0b\u306e\u95a2\u9023\u306b\u95a2\u3059\u308b\u3082\u306e\u3067\u3059\uff0e\u3053\u306e\u7814\u7a76\u306e\u6d41\u308c\u306f\uff0cNN\u306e\u9ad8\u3044\u6027\u80fd\u306b\u5bfe\u3057\u3066\u3088\u308a\u6df1\u3044\u6d1e\u5bdf\u3092\u4e0e\u3048\u308b\u7406\u8ad6\u3068\u3057\u3066\u6ce8\u76ee\u3055\u308c\u3066\u3044\u307e\u3059\uff0e\u3053\u308c\u3089\u306e\u7814\u7a76\u306f\u72ec\u7acb\u306b\u767a\u5c55\u3057\u3066\u304d\u307e\u3057\u305f\u304c\uff0c\u4e21\u8005\u306b\u306f\u6df1\u3044\u3064\u306a\u304c\u308a\u304c\u3042\u308b\u3053\u3068\u3092\u6307\u6458\u3057\u307e\u3059\uff0e<\/p>\n","protected":false},"author":16,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-7163","post","type-post","status-publish","format-standard","hentry","category-review"],"yoast_head":"<!-- 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