{"id":7967,"date":"2025-08-17T18:03:18","date_gmt":"2025-08-17T09:03:18","guid":{"rendered":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/?p=7967"},"modified":"2025-09-30T16:00:32","modified_gmt":"2025-09-30T07:00:32","slug":"%e3%83%90%e3%83%83%e3%83%81%e3%82%b5%e3%82%a4%e3%82%ba%e3%81%8c%e5%a4%a7%e3%81%8d%e3%81%84%e3%81%a8%e3%81%aa%e3%81%9c%e6%b1%8e%e5%8c%96%e6%80%a7%e8%83%bd%e3%81%8c%e4%b8%8b%e3%81%8c%e3%82%8b%e3%81%ae","status":"publish","type":"post","link":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/08\/17\/%e3%83%90%e3%83%83%e3%83%81%e3%82%b5%e3%82%a4%e3%82%ba%e3%81%8c%e5%a4%a7%e3%81%8d%e3%81%84%e3%81%a8%e3%81%aa%e3%81%9c%e6%b1%8e%e5%8c%96%e6%80%a7%e8%83%bd%e3%81%8c%e4%b8%8b%e3%81%8c%e3%82%8b%e3%81%ae\/","title":{"rendered":"\u30d0\u30c3\u30c1\u30b5\u30a4\u30ba\u304c\u5927\u304d\u3044\u3068\u306a\u305c\u6c4e\u5316\u6027\u80fd\u304c\u4e0b\u304c\u308b\u306e\u304b\uff1f"},"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\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/08\/17\/%e3%83%90%e3%83%83%e3%83%81%e3%82%b5%e3%82%a4%e3%82%ba%e3%81%8c%e5%a4%a7%e3%81%8d%e3%81%84%e3%81%a8%e3%81%aa%e3%81%9c%e6%b1%8e%e5%8c%96%e6%80%a7%e8%83%bd%e3%81%8c%e4%b8%8b%e3%81%8c%e3%82%8b%e3%81%ae\/#%E6%96%87%E7%8C%AE%E6%83%85%E5%A0%B1\" >\u6587\u732e\u60c5\u5831<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/08\/17\/%e3%83%90%e3%83%83%e3%83%81%e3%82%b5%e3%82%a4%e3%82%ba%e3%81%8c%e5%a4%a7%e3%81%8d%e3%81%84%e3%81%a8%e3%81%aa%e3%81%9c%e6%b1%8e%e5%8c%96%e6%80%a7%e8%83%bd%e3%81%8c%e4%b8%8b%e3%81%8c%e3%82%8b%e3%81%ae\/#%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\/2025\/08\/17\/%e3%83%90%e3%83%83%e3%83%81%e3%82%b5%e3%82%a4%e3%82%ba%e3%81%8c%e5%a4%a7%e3%81%8d%e3%81%84%e3%81%a8%e3%81%aa%e3%81%9c%e6%b1%8e%e5%8c%96%e6%80%a7%e8%83%bd%e3%81%8c%e4%b8%8b%e3%81%8c%e3%82%8b%e3%81%ae\/#%E8%83%8C%E6%99%AF\" >\u80cc\u666f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/08\/17\/%e3%83%90%e3%83%83%e3%83%81%e3%82%b5%e3%82%a4%e3%82%ba%e3%81%8c%e5%a4%a7%e3%81%8d%e3%81%84%e3%81%a8%e3%81%aa%e3%81%9c%e6%b1%8e%e5%8c%96%e6%80%a7%e8%83%bd%e3%81%8c%e4%b8%8b%e3%81%8c%e3%82%8b%e3%81%ae\/#%E6%B1%8E%E5%8C%96%E6%80%A7%E8%83%BD%E4%BD%8E%E4%B8%8B%E3%81%AE%E5%8E%9F%E5%9B%A0\" >\u6c4e\u5316\u6027\u80fd\u4f4e\u4e0b\u306e\u539f\u56e0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/08\/17\/%e3%83%90%e3%83%83%e3%83%81%e3%82%b5%e3%82%a4%e3%82%ba%e3%81%8c%e5%a4%a7%e3%81%8d%e3%81%84%e3%81%a8%e3%81%aa%e3%81%9c%e6%b1%8e%e5%8c%96%e6%80%a7%e8%83%bd%e3%81%8c%e4%b8%8b%e3%81%8c%e3%82%8b%e3%81%ae\/#%E6%95%B0%E5%80%A4%E5%AE%9F%E9%A8%93\" >\u6570\u5024\u5b9f\u9a13<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/08\/17\/%e3%83%90%e3%83%83%e3%83%81%e3%82%b5%e3%82%a4%e3%82%ba%e3%81%8c%e5%a4%a7%e3%81%8d%e3%81%84%e3%81%a8%e3%81%aa%e3%81%9c%e6%b1%8e%e5%8c%96%e6%80%a7%e8%83%bd%e3%81%8c%e4%b8%8b%e3%81%8c%e3%82%8b%e3%81%ae\/#SB%E3%81%A8LB%E3%81%AE%E6%B1%8E%E5%8C%96%E6%80%A7%E8%83%BD%E3%81%AE%E8%A9%95%E4%BE%A1\" >SB\u3068LB\u306e\u6c4e\u5316\u6027\u80fd\u306e\u8a55\u4fa1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/08\/17\/%e3%83%90%e3%83%83%e3%83%81%e3%82%b5%e3%82%a4%e3%82%ba%e3%81%8c%e5%a4%a7%e3%81%8d%e3%81%84%e3%81%a8%e3%81%aa%e3%81%9c%e6%b1%8e%e5%8c%96%e6%80%a7%e8%83%bd%e3%81%8c%e4%b8%8b%e3%81%8c%e3%82%8b%e3%81%ae\/#%E6%90%8D%E5%A4%B1%E9%96%A2%E6%95%B0%E3%81%AE%E6%96%AD%E9%9D%A2%E5%9B%B3\" >\u640d\u5931\u95a2\u6570\u306e\u65ad\u9762\u56f3<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/08\/17\/%e3%83%90%e3%83%83%e3%83%81%e3%82%b5%e3%82%a4%e3%82%ba%e3%81%8c%e5%a4%a7%e3%81%8d%e3%81%84%e3%81%a8%e3%81%aa%e3%81%9c%e6%b1%8e%e5%8c%96%e6%80%a7%e8%83%bd%e3%81%8c%e4%b8%8b%e3%81%8c%e3%82%8b%e3%81%ae\/#%E3%80%8C%E8%B0%B7%E3%81%AE%E9%8B%AD%E3%81%95%E3%80%8D%E6%8C%87%E6%A8%99%E3%81%AE%E5%B0%8E%E5%85%A5\" >\u300c\u8c37\u306e\u92ed\u3055\u300d\u6307\u6a19\u306e\u5c0e\u5165<\/a><\/li><\/ul><\/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\/2025\/08\/17\/%e3%83%90%e3%83%83%e3%83%81%e3%82%b5%e3%82%a4%e3%82%ba%e3%81%8c%e5%a4%a7%e3%81%8d%e3%81%84%e3%81%a8%e3%81%aa%e3%81%9c%e6%b1%8e%e5%8c%96%e6%80%a7%e8%83%bd%e3%81%8c%e4%b8%8b%e3%81%8c%e3%82%8b%e3%81%ae\/#%E3%83%90%E3%83%83%E3%83%81%E3%82%B5%E3%82%A4%E3%82%BA%E3%81%AE%E3%81%97%E3%81%8D%E3%81%84%E5%80%A4%E3%81%A8%E5%8E%9F%E5%9B%A0\" >\u30d0\u30c3\u30c1\u30b5\u30a4\u30ba\u306e\u3057\u304d\u3044\u5024\u3068\u539f\u56e0<\/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\/2025\/08\/17\/%e3%83%90%e3%83%83%e3%83%81%e3%82%b5%e3%82%a4%e3%82%ba%e3%81%8c%e5%a4%a7%e3%81%8d%e3%81%84%e3%81%a8%e3%81%aa%e3%81%9c%e6%b1%8e%e5%8c%96%e6%80%a7%e8%83%bd%e3%81%8c%e4%b8%8b%e3%81%8c%e3%82%8b%e3%81%ae\/#%E8%80%83%E5%AF%9F%E3%83%BB%E7%B5%90%E8%AB%96\" >\u8003\u5bdf\u30fb\u7d50\u8ad6<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/08\/17\/%e3%83%90%e3%83%83%e3%83%81%e3%82%b5%e3%82%a4%e3%82%ba%e3%81%8c%e5%a4%a7%e3%81%8d%e3%81%84%e3%81%a8%e3%81%aa%e3%81%9c%e6%b1%8e%e5%8c%96%e6%80%a7%e8%83%bd%e3%81%8c%e4%b8%8b%e3%81%8c%e3%82%8b%e3%81%ae\/#%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-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2025\/08\/17\/%e3%83%90%e3%83%83%e3%83%81%e3%82%b5%e3%82%a4%e3%82%ba%e3%81%8c%e5%a4%a7%e3%81%8d%e3%81%84%e3%81%a8%e3%81%aa%e3%81%9c%e6%b1%8e%e5%8c%96%e6%80%a7%e8%83%bd%e3%81%8c%e4%b8%8b%e3%81%8c%e3%82%8b%e3%81%ae\/#%E6%9C%AC%E8%A8%98%E4%BA%8B%E3%81%AE%E6%8B%85%E5%BD%93%E8%80%85\" >\u672c\u8a18\u4e8b\u306e\u62c5\u5f53\u8005<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><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><strong>\u30bf\u30a4\u30c8\u30eb<\/strong>: ON LARGE-BATCH TRAINING FOR DEEP LEARNING: GENERALIZATION GAP AND SHARP MINIMA<\/li>\n<li><strong>\u8457\u8005<\/strong>: Keskar, N. S. et al.<\/li>\n<li><strong>\u66f8\u8a8c\u60c5\u5831<\/strong>: arXiv:1609.04836<\/li>\n<li><strong>\u51fa\u7248\u5e74<\/strong>: 2017<\/li>\n<\/ul>\n<h2><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>\u6df1\u5c64\u5b66\u7fd2\u3067\u306f\u8a08\u7b97\u52b9\u7387\u3092\u9ad8\u3081\u308b\u305f\u3081\u306b\u5927\u898f\u6a21\u30d0\u30c3\u30c1\u5b66\u7fd2\uff08LB\uff09\u304c\u76db\u3093\u306b\u4f7f\u308f\u308c\u307e\u3059\u304c\u3001\u7d4c\u9a13\u7684\u306b\u300c\u30c6\u30b9\u30c8\u7cbe\u5ea6\u304c\u4e0b\u304c\u308b\u300d\u3068\u3044\u3046\u554f\u984c\u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002\u672c\u8ad6\u6587\u3067\u306f\u3001\u305d\u306e\u539f\u56e0\u3092\u300c\u640d\u5931\u95a2\u6570\u306e\u8c37\u306e\u5f62\u72b6\u300d\u3068\u3044\u3046\u89b3\u70b9\u304b\u3089\u63a2\u308a\u3001\u6570\u5024\u5b9f\u9a13\u3092\u901a\u3057\u3066LB\u304c\u92ed\u3044\u8c37\u306b\u3001\u5c0f\u898f\u6a21\u30d0\u30c3\u30c1\uff08SB\uff09\u304c\u5e73\u5766\u306a\u8c37\u306b\u53ce\u675f\u3057\u3084\u3059\u3044\u3053\u3068\u3092\u793a\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u4e21\u8005\u306e\u5229\u70b9\u3092\u6d3b\u304b\u3059\u305f\u3081\u306b\u63d0\u6848\u3055\u308c\u305f\u300c\u30a6\u30a9\u30fc\u30e0\u30b9\u30bf\u30fc\u30c8\u300d\u306e\u52b9\u679c\u3092\u7d39\u4ecb\u3057\u3001\u6c4e\u5316\u6027\u80fd\u3092\u3081\u3050\u308b\u65b0\u305f\u306a\u7406\u89e3\u3068\u4eca\u5f8c\u306e\u8ab2\u984c\u306b\u3064\u3044\u3066\u8003\u5bdf\u3057\u307e\u3059\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E8%83%8C%E6%99%AF\"><\/span>\u80cc\u666f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6df1\u5c64\u5b66\u7fd2\u306f\u3001\u640d\u5931\u95a2\u6570 $f(x)$ \u306e\u5024\u3092\u6700\u5c0f\u5316\u3059\u308b\u30d1\u30e9\u30e1\u30fc\u30bf$x$\u3092\u898b\u3064\u3051\u308b\u554f\u984c\u3067\u3059\u3002\u3053\u306e\u6700\u5c0f\u5316\u306e\u305f\u3081\u306b\u3001\u78ba\u7387\u7684\u52fe\u914d\u964d\u4e0b\u6cd5\uff08Stochastic Gradient Descent, SGD\uff09\u304c\u5e83\u304f\u7528\u3044\u3089\u308c\u3066\u3044\u307e\u3059\u3002SGD\u306f\u3001\u5b66\u7fd2\u30c7\u30fc\u30bf\u5168\u4f53\u3067\u306f\u306a\u304f\u3001\u30e9\u30f3\u30c0\u30e0\u306b\u62bd\u51fa\u3057\u305f\u4e00\u90e8\u306e\u5c0f\u3055\u306a\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\uff08\u30df\u30cb\u30d0\u30c3\u30c1\uff09\u3092\u4f7f\u3063\u3066\u52fe\u914d\u3092\u8a08\u7b97\u3057\u3001\u30e2\u30c7\u30eb\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u66f4\u65b0\u3059\u308b\u624b\u6cd5\u3067\u3059\u3002\u5177\u4f53\u7684\u306b\u306f\u3001\u5404\u30b9\u30c6\u30c3\u30d7$k$\u3067\u4ee5\u4e0b\u306e\u66f4\u65b0\u5f0f\u306b\u5f93\u3063\u3066\u30d1\u30e9\u30e1\u30fc\u30bf$x$\u3092\u66f4\u65b0\u3057\u307e\u3059\u3002<\/p>\n<p>$$<br \/>\nx_{k+1} = x_k &#8211; \\alpha_k \\left( \\frac{1}{|B_k|} \\sum_{i \\in B_k} \\nabla f_i(x_k) \\right) \\quad<br \/>\n$$<\/p>\n<p>\u3053\u3053\u3067\u3001\u8a18\u53f7 $\\nabla$ (\u30ca\u30d6\u30e9)\u306f\u52fe\u914d\uff08gradient\uff09\u3092\u610f\u5473\u3057\u3001$\\alpha_k$\u306f\u30b9\u30c6\u30c3\u30d7\u30b5\u30a4\u30ba(\u5b66\u7fd2\u7387)\u3001$i$\u306f\u30c7\u30fc\u30bf\u756a\u53f7\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u52fe\u914d\u6cd5\u3092\u7e70\u308a\u8fd4\u3059\u3053\u3068\u3067\u640d\u5931\u95a2\u6570\u306e\u8c37\u5e95\uff08\u6700\u5c0f\u5024\uff09\u3092\u63a2\u3057\u307e\u3059\u3002\u3057\u304b\u3057\u3001SGD\u306f\u4e00\u3064\u524d\u306e\u66f4\u65b0\u7d50\u679c\u3092\u4f7f\u3063\u3066\u6b21\u306e\u66f4\u65b0\u3092\u884c\u3046\u9010\u6b21\u7684\u306a\u8a08\u7b97\u3067\u3042\u308b\u305f\u3081\u3001\u4e26\u5217\u5316\u306b\u3088\u308b\u5927\u5e45\u306a\u9ad8\u901f\u5316\u304c\u96e3\u3057\u304f\u3001\u7279\u306b\u5927\u898f\u6a21\u306a\u30e2\u30c7\u30eb\u3067\u306f\u5b66\u7fd2\u306b\u975e\u5e38\u306b\u9577\u3044\u6642\u9593\u304c\u304b\u304b\u3063\u3066\u3057\u307e\u3046\u3068\u3044\u3046\u8ab2\u984c\u304c\u3042\u308a\u307e\u3059\u3002\u30d0\u30c3\u30c1\u30b5\u30a4\u30ba\u3092\u5927\u304d\u304f\u3059\u308b\u5927\u898f\u6a21\u30d0\u30c3\u30c1(Large Batch, LB)\u5b66\u7fd2\u3067\u306f\u30011\u30a8\u30dd\u30c3\u30af\u306b\u304a\u3051\u308b\u30d1\u30e9\u30e1\u30fc\u30bf\u66f4\u65b0\u306e\u56de\u6570\u304c\u5c11\u306a\u3044\u305f\u3081\u3001\u5c0f\u898f\u6a21\u30d0\u30c3\u30c1(Small Batch, SB)\u5b66\u7fd2\u3088\u308a\u3082\u6bd4\u8f03\u7684\u8a08\u7b97\u52b9\u7387\u304c\u9ad8\u3044\u3068\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u30d0\u30c3\u30c1\u30b5\u30a4\u30ba\u304c\u5927\u304d\u3044\u3068\u3001\u30e2\u30c7\u30eb\u306e\u6c4e\u5316\u6027\u80fd(\u672a\u77e5\u306e\u30c7\u30fc\u30bf\u306b\u5bfe\u3059\u308b\u6027\u80fd)\u304c\u4f4e\u4e0b\u3057\u3066\u3057\u307e\u3046\u3068\u3044\u3046\u3001\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u306e\u95a2\u4fc2\u304c\u3042\u308b\u3053\u3068\u304c\u7d4c\u9a13\u7684\u306b\u77e5\u3089\u308c\u3066\u3044\u307e\u3057\u305f\u3002\u672c\u8ad6\u6587\u3067\u306f\u3001\u3053\u306e\u300c\u30e9\u30fc\u30b8\u30d0\u30c3\u30c1\u5b66\u7fd2\u306b\u304a\u3051\u308b\u6c4e\u5316\u6027\u80fd\u306e\u4f4e\u4e0b\u300d\u3068\u3044\u3046\u554f\u984c\u306b\u3064\u3044\u3066\u3001\u640d\u5931\u95a2\u6570\u306e\u5e7e\u4f55\u5b66\u7684\u306a\u5f62\u72b6\u3068\u3044\u3046\u89b3\u70b9\u304b\u3089\u305d\u306e\u539f\u56e0\u3092\u89e3\u660e\u3057\u307e\u3059\u3002<\/p>\n<figure style=\"text-align: center;\"><figcaption>\u88681: \u30d0\u30c3\u30c1\u30b5\u30a4\u30ba\u306b\u3088\u308b\u7279\u5fb4<\/figcaption><table border=\"1\" style=\"width: 100%; border-collapse: collapse;\">\n<thead>\n<tr>\n<th style=\"text-align: left;\">\u30d0\u30c3\u30c1\u30b5\u30a4\u30ba<\/th>\n<th style=\"text-align: center;\">\u8a08\u7b97\u52b9\u7387<\/th>\n<th style=\"text-align: center;\">\u6c4e\u5316\u6027\u80fd<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: left;\">\u5927\u898f\u6a21(LB)<\/td>\n<td style=\"text-align: center;\">\u25ef<\/td>\n<td style=\"text-align: center;\">\u2715<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: left;\">\u5c0f\u898f\u6a21(SB)<\/td>\n<td style=\"text-align: center;\">\u25b3<\/td>\n<td style=\"text-align: center;\">\u25ef<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<h2><span class=\"ez-toc-section\" id=\"%E6%B1%8E%E5%8C%96%E6%80%A7%E8%83%BD%E4%BD%8E%E4%B8%8B%E3%81%AE%E5%8E%9F%E5%9B%A0\"><\/span>\u6c4e\u5316\u6027\u80fd\u4f4e\u4e0b\u306e\u539f\u56e0<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5927\u898f\u6a21\u30d0\u30c3\u30c1\u306b\u3088\u308a\u6c4e\u5316\u6027\u80fd\u304c\u4f4e\u4e0b\u3059\u308b\u539f\u56e0\u306f\u3044\u304f\u3064\u304b\u8003\u3048\u3089\u308c\u3066\u304d\u307e\u3057\u305f\u304c\u3001\u672c\u8ad6\u6587\u306e\u8457\u8005\u3089\u306f\u300c\u5927\u898f\u6a21\u30d0\u30c3\u30c1(LB)\u6cd5\u306f\u640d\u5931\u95a2\u6570\u306e\u92ed\u3044\u8c37\u306e\u6700\u5c0f\u89e3(Sharp Minimum)\u306b\u53ce\u675f\u3059\u308b\u50be\u5411\u304c\u3042\u308b\u300d\u3068\u3044\u3046\u8003\u3048\u3092\u652f\u6301\u3057\u3066\u3044\u307e\u3059\u3002\u56f31\u306b\u640d\u5931\u95a2\u6570\u306b\u304a\u3051\u308b\u92ed\u3044\u8c37\u3068\u5e73\u5766\u306a\u8c37\u306e\u6982\u5ff5\u56f3\u3092\u793a\u3057\u307e\u3059\u3002\u56f3\u306e\u3088\u3046\u306b\u3001\u5b66\u7fd2\u30c7\u30fc\u30bf\u3067\u5f97\u3089\u308c\u305f\u95a2\u6570(Training Function)\u3068\u3001\u30c6\u30b9\u30c8\u30c7\u30fc\u30bf\u3067\u5f97\u3089\u308c\u305f\u95a2\u6570(Testing Function)\u306f\u308f\u305a\u304b\u306b\u30ba\u30ec\u3066\u3044\u308b\u3068\u8003\u3048\u3089\u308c\u307e\u3059\u3002\u3082\u3057\u3001\u5b66\u7fd2\u3067\u5f97\u3089\u308c\u305f\u30d1\u30e9\u30e1\u30fc\u30bf\u304cSharp Minimum\u3067\u3042\u308c\u3070\u3001Testing Function\u3067\u8a55\u4fa1\u3057\u305f\u969b\u306b\u8a55\u4fa1\u5024\u304c\u6025\u6fc0\u306b\u60aa\u5316\u3057\u3001\u3053\u308c\u304c\u6c4e\u5316\u6027\u80fd\u306e\u4f4e\u4e0b\u3092\u62db\u304d\u307e\u3059\u3002\u4e00\u65b9\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u304cFlat Minimum\u3067\u3042\u308c\u3070\u3001Testing Function\u3067\u8a55\u4fa1\u3057\u3066\u3082\u8a55\u4fa1\u5024\u306f\u305d\u308c\u307b\u3069\u60aa\u5316\u305b\u305a\u3001\u30c6\u30b9\u30c8\u30c7\u30fc\u30bf\u306b\u5bfe\u3057\u3066\u3082\u7cbe\u5ea6\u306e\u9ad8\u3044\u7d50\u679c\u304c\u5f97\u3089\u308c\u308b\u3068\u8003\u3048\u3089\u308c\u307e\u3059\u3002\u6b21\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001LB\u6cd5\u3067\u5f97\u3089\u308c\u305f\u89e3\u304cSharp Minimum\u3067\u3042\u308b\u3053\u3068\u3092\u6570\u5024\u5b9f\u9a13\u306b\u3088\u308a\u793a\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<div id=\"attachment_7973\" style=\"width: 1376px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-7973\" src=\"\/T-Wave\/wp-content\/uploads\/2025\/08\/fig1.png\" alt=\"\" width=\"1366\" height=\"528\" class=\"size-full wp-image-7973\" \/><p id=\"caption-attachment-7973\" class=\"wp-caption-text\">\u56f31: \u640d\u5931\u95a2\u6570\u306b\u304a\u3051\u308b\u92ed\u3044\u8c37\u3068\u5e73\u5766\u306a\u8c37\u306e\u6982\u5ff5\u56f3 (\u5f15\u7528: https:\/\/arxiv.org\/abs\/1609.04836)<\/p><\/div>\n<h2><span class=\"ez-toc-section\" id=\"%E6%95%B0%E5%80%A4%E5%AE%9F%E9%A8%93\"><\/span>\u6570\u5024\u5b9f\u9a13<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u3053\u3053\u3067\u306f\u3001LB\u6cd5\u3067\u5f97\u3089\u308c\u305f\u89e3\u304cSharp Minimum\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3059\u305f\u3081\u306b\u6570\u5024\u5b9f\u9a13\u3092\u884c\u3044\u307e\u3059\u3002<\/p>\n<h3><span class=\"ez-toc-section\" id=\"SB%E3%81%A8LB%E3%81%AE%E6%B1%8E%E5%8C%96%E6%80%A7%E8%83%BD%E3%81%AE%E8%A9%95%E4%BE%A1\"><\/span>SB\u3068LB\u306e\u6c4e\u5316\u6027\u80fd\u306e\u8a55\u4fa1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u307e\u305a\u3001LB\u6cd5\u306b\u3088\u308a\u6c4e\u5316\u6027\u80fd\u304c\u4f4e\u4e0b\u3059\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3059\u3002\u5b9f\u9a13\u3067\u4f7f\u7528\u3059\u308b\u6df1\u5c64\u5b66\u7fd2\u306e\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306f\u88682\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>\n<figure style=\"text-align: center;\"><figcaption style=\"margin-bottom: 8px;\">\u88682: \u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u69cb\u6210 (\u5f15\u7528: <a href=\"https:\/\/arxiv.org\/abs\/1609.04836\" target=\"_blank\" rel=\"noopener\">https:\/\/arxiv.org\/abs\/1609.04836<\/a>)<\/figcaption><table border=\"1\" style=\"width: 100%; border-collapse: collapse;\">\n<thead>\n<tr>\n<th style=\"text-align: left;\">\u540d\u524d<\/th>\n<th style=\"text-align: left;\">\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u30bf\u30a4\u30d7<\/th>\n<th style=\"text-align: left;\">\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: left;\">$F_1$<\/td>\n<td style=\"text-align: left;\">\u5168\u7d50\u5408<\/td>\n<td style=\"text-align: left;\">MNIST<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: left;\">$F_2$<\/td>\n<td style=\"text-align: left;\">\u5168\u7d50\u5408<\/td>\n<td style=\"text-align: left;\">TIMIT<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: left;\">$C_1$<\/td>\n<td style=\"text-align: left;\">\uff08\u6d45\u3044\uff09\u7573\u307f\u8fbc\u307f<\/td>\n<td style=\"text-align: left;\">CIFAR-10<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: left;\">$C_2$<\/td>\n<td style=\"text-align: left;\">\uff08\u6df1\u3044\uff09\u7573\u307f\u8fbc\u307f<\/td>\n<td style=\"text-align: left;\">CIFAR-10<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: left;\">$C_3$<\/td>\n<td style=\"text-align: left;\">\uff08\u6d45\u3044\uff09\u7573\u307f\u8fbc\u307f<\/td>\n<td style=\"text-align: left;\">CIFAR-100<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: left;\">$C_4$<\/td>\n<td style=\"text-align: left;\">\uff08\u6df1\u3044\uff09\u7573\u307f\u8fbc\u307f<\/td>\n<td style=\"text-align: left;\">CIFAR-100<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p>\u3059\u3079\u3066\u306e\u5b9f\u9a13\u306b\u304a\u3044\u3066\u3001LB\u6cd5\u3067\u306f\u5b66\u7fd2\u30c7\u30fc\u30bf\u306e10%\u3092\u30d0\u30c3\u30c1\u30b5\u30a4\u30ba\u3068\u3057\u3066\u4f7f\u7528\u3057\u3001SB\u6cd5\u3067\u306f256\u500b\u306e\u30c7\u30fc\u30bf\u3092\u30d0\u30c3\u30c1\u30b5\u30a4\u30ba\u3068\u3057\u307e\u3057\u305f\u3002\u4e21\u624b\u6cd5\u3067ADAM(\u52fe\u914d\u6cd5\u306e\u8a08\u7b97\u65b9\u6cd5\u306e\u4e00\u7a2e)\u3092\u4f7f\u7528\u3057\u307e\u3057\u305f\u3002\u3059\u3079\u3066\u306e\u5b9f\u9a13\u3067\u7570\u306a\u308b\u958b\u59cb\u70b9(\u4e00\u69d8\u5206\u5e03\u3067\u30e9\u30f3\u30c0\u30e0)\u304b\u30895\u56de\u5b9f\u65bd\u3057\u3001\u5e73\u5747\u3068\u6a19\u6e96\u504f\u5dee\u3092\u88683\u306b\u793a\u3057\u307e\u3059\u3002\u5b66\u7fd2\u30c7\u30fc\u30bf\u306b\u5bfe\u3059\u308b\u7cbe\u5ea6\u306fSB, LB\u3068\u3082\u306b\u9ad8\u3044\u5024\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u4e00\u65b9\u3001\u30c6\u30b9\u30c8\u30c7\u30fc\u30bf\u306b\u95a2\u3057\u3066\u306fLB\u306fSB\u3088\u308a\u3082\u7cbe\u5ea6\u304c\u4f4e\u304f\u306a\u3063\u3066\u304a\u308a\u3001\u6c4e\u5316\u6027\u80fd\u306e\u4f4e\u4e0b\u304c\u78ba\u8a8d\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306b\u3001\u30c6\u30b9\u30c8\u30c7\u30fc\u30bf\u306b\u5bfe\u3057\u3066\u6975\u7aef\u306b\u6027\u80fd\u304c\u60aa\u5316\u3059\u308b\u3053\u3068\u3092Generalization Gap\u3068\u547c\u3073\u307e\u3059\u3002\u672c\u8ad6\u6587\u306e\u8457\u8005\u3089\u306f\u3001Generalization Gap\u306e\u539f\u56e0\u306f\u904e\u5b66\u7fd2\u306b\u3088\u308b\u3082\u306e\u3067\u306f\u306a\u3044\u3053\u3068\u3092\u5f37\u8abf\u3057\u3066\u3044\u307e\u3059\u3002\u901a\u5e38\u3001\u904e\u5b66\u7fd2\u3067\u306f\u30d4\u30fc\u30af\u306b\u9054\u3057\u305f\u5f8c\u3001\u7cbe\u5ea6\u306f\u6e1b\u5c11\u3057\u3066\u3044\u304d\u307e\u3059\u304c\u3001\u56f32\u306e\u3088\u3046\u306b\u5b66\u7fd2\u6642\u306e\u66f2\u7dda\u306f\u98fd\u548c\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u78ba\u8a8d\u3067\u304d\u307e\u3059\u3002<\/p>\n<figure style=\"text-align: center;\"><figcaption style=\"margin-bottom: 8px;\">\u88683: \u5404\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306b\u304a\u3051\u308b\u5c0f\u898f\u6a21\u30d0\u30c3\u30c1\uff08SB\uff09\u3068\u5927\u898f\u6a21\u30d0\u30c3\u30c1\uff08LB\uff09\u306e\u6027\u80fd<br \/>\n(\u5f15\u7528: <a href=\"https:\/\/arxiv.org\/abs\/1609.04836\" target=\"_blank\" rel=\"noopener\">https:\/\/arxiv.org\/abs\/1609.04836<\/a>)<\/figcaption><table border=\"1\" style=\"width: 100%; border-collapse: collapse;\">\n<thead>\n<tr>\n<th style=\"text-align: left;\">\u540d\u524d<\/th>\n<th style=\"text-align: left;\">\u5b66\u7fd2\u7cbe\u5ea6 (SB)<\/th>\n<th style=\"text-align: left;\">\u5b66\u7fd2\u7cbe\u5ea6 (LB)<\/th>\n<th style=\"text-align: left;\">\u30c6\u30b9\u30c8\u7cbe\u5ea6 (SB)<\/th>\n<th style=\"text-align: left;\">\u30c6\u30b9\u30c8\u7cbe\u5ea6 (LB)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: left;\">$F_1$<\/td>\n<td style=\"text-align: left;\">$99.66\\% \\pm 0.05\\%$<\/td>\n<td style=\"text-align: left;\">$99.92\\% \\pm 0.01\\%$<\/td>\n<td style=\"text-align: left;\">$98.03\\% \\pm 0.07\\%$<\/td>\n<td style=\"text-align: left;\">$97.81\\% \\pm 0.07\\%$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: left;\">$F_2$<\/td>\n<td style=\"text-align: left;\">$99.99\\% \\pm 0.03\\%$<\/td>\n<td style=\"text-align: left;\">$98.35\\% \\pm 2.08\\%$<\/td>\n<td style=\"text-align: left;\">$64.02\\% \\pm 0.2\\%$<\/td>\n<td style=\"text-align: left;\">$59.45\\% \\pm 1.05\\%$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: left;\">$C_1$<\/td>\n<td style=\"text-align: left;\">$99.89\\% \\pm 0.02\\%$<\/td>\n<td style=\"text-align: left;\">$99.66\\% \\pm 0.2\\%$<\/td>\n<td style=\"text-align: left;\">$80.04\\% \\pm 0.12\\%$<\/td>\n<td style=\"text-align: left;\">$77.26\\% \\pm 0.42\\%$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: left;\">$C_2$<\/td>\n<td style=\"text-align: left;\">$99.99\\% \\pm 0.04\\%$<\/td>\n<td style=\"text-align: left;\">$99.99\\% \\pm 0.01\\%$<\/td>\n<td style=\"text-align: left;\">$89.24\\% \\pm 0.12\\%$<\/td>\n<td style=\"text-align: left;\">$87.26\\% \\pm 0.07\\%$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: left;\">$C_3$<\/td>\n<td style=\"text-align: left;\">$99.56\\% \\pm 0.44\\%$<\/td>\n<td style=\"text-align: left;\">$99.88\\% \\pm 0.30\\%$<\/td>\n<td style=\"text-align: left;\">$49.58\\% \\pm 0.39\\%$<\/td>\n<td style=\"text-align: left;\">$46.45\\% \\pm 0.43\\%$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: left;\">$C_4$<\/td>\n<td style=\"text-align: left;\">$99.10\\% \\pm 1.23\\%$<\/td>\n<td style=\"text-align: left;\">$99.57\\% \\pm 1.84\\%$<\/td>\n<td style=\"text-align: left;\">$63.08\\% \\pm 0.5\\%$<\/td>\n<td style=\"text-align: left;\">$57.81\\% \\pm 0.17\\%$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<div id=\"attachment_7972\" style=\"width: 1818px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-7972\" src=\"\/T-Wave\/wp-content\/uploads\/2025\/08\/fig0.png\" alt=\"\" width=\"1808\" height=\"660\" class=\"size-full wp-image-7972\" \/><p id=\"caption-attachment-7972\" class=\"wp-caption-text\">\u56f32: \u5404\u30a8\u30dd\u30c3\u30af\u306b\u304a\u3051\u308bSB\u3068LB\u306e\u5b66\u7fd2\u7cbe\u5ea6 (\u5f15\u7528: https:\/\/arxiv.org\/abs\/1609.04836)<\/p><\/div>\n<h3><span class=\"ez-toc-section\" id=\"%E6%90%8D%E5%A4%B1%E9%96%A2%E6%95%B0%E3%81%AE%E6%96%AD%E9%9D%A2%E5%9B%B3\"><\/span>\u640d\u5931\u95a2\u6570\u306e\u65ad\u9762\u56f3<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u672c\u7ae0\u3067\u306f\u3001\u524d\u7ae0\u3067\u5f97\u3089\u308c\u305f\u89e3\u304c\u3069\u306e\u3088\u3046\u306b\u8c37\u306b\u4f4d\u7f6e\u3057\u3066\u3044\u308b\u306e\u304b\u53ef\u8996\u5316\u3092\u884c\u3044\u307e\u3059\u3002\u3053\u3053\u3067\u3001$x$\u306f\u591a\u6b21\u5143\u3067\u3042\u308b\u305f\u3081\u3001\u305d\u306e\u307e\u307e\u3067\u306f\u53ef\u8996\u5316\u3059\u308b\u3053\u3068\u304c\u56f0\u96e3\u3067\u3059\u3002\u305d\u3053\u3067\u3001SB\u3068LB\u3067\u5f97\u3089\u308c\u305f\u89e3\u3092\u305d\u308c\u305e\u308c$x^{*}_{s}, x^{*}_{l}$\u3068\u3057\u3001$f(\\alpha x^{*}_{l} + ( 1-\\alpha) x^{*}_{s})$\u3092\u30d7\u30ed\u30c3\u30c8\u3059\u308b\u3053\u3068\u3067\u640d\u5931\u95a2\u6570\u306e\u65ad\u9762\u56f3\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u307e\u3059\u3002\u3053\u3053\u3067\u3001$\\alpha \\in [-1, 2]$\u306e\u7bc4\u56f2\u3092\u52d5\u304d\u307e\u3059\u30023\u6b21\u5143\u306e\u4f8b\u3092\u56f33\u306b\u793a\u3057\u307e\u3059\u3002$\\alpha x^{*}_{l} + ( 1-\\alpha) x^{*}_{s}$\u306f\u56f3\u306e\u3001$x^{*}_{s}, x^{*}_{l}$\u3092\u7d50\u3076\u8d64\u7dda\u3067\u8868\u73fe\u3055\u308c\u3066\u304a\u308a\u3001\u3053\u306e\u7dda\u306b\u304a\u3051\u308b\u640d\u5931\u95a2\u6570\u306e\u65ad\u9762\u56f3\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u305f\u306e\u304c\u56f34\u3067\u3059\u3002$\\alpha=1$\u306eLB\u89e3\u306e\u4ed8\u8fd1\u3067\u306f\u78ba\u304b\u306b\u92ed\u3044\u8c37\u306b\u306a\u3063\u3066\u304a\u308a\u3001$\\alpha=0$\u306eSB\u89e3\u306e\u4ed8\u8fd1\u3067\u306f\u5e73\u5766\u306a\u8c37\u306b\u306a\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u78ba\u8a8d\u3067\u304d\u307e\u3059\u3002<\/p>\n<div id=\"attachment_7971\" style=\"width: 375px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-7971\" src=\"\/T-Wave\/wp-content\/uploads\/2025\/08\/example.png\" alt=\"\" width=\"365\" height=\"302\" class=\" wp-image-7971\" \/><p id=\"caption-attachment-7971\" class=\"wp-caption-text\">\u56f33: \u65ad\u9762\u56f3\u306e\u53ef\u8996\u5316\u306e\u6982\u8981<\/p><\/div>\n<div id=\"attachment_7974\" style=\"width: 434px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-7974\" src=\"\/T-Wave\/wp-content\/uploads\/2025\/08\/fig2.png\" alt=\"\" width=\"424\" height=\"320\" class=\" wp-image-7974\" \/><p id=\"caption-attachment-7974\" class=\"wp-caption-text\">\u56f34: \u640d\u5931\u95a2\u6570\u306e\u65ad\u9762\u56f3 (\u5f15\u7528: https:\/\/arxiv.org\/abs\/1609.04836)<\/p><\/div>\n<h3><span class=\"ez-toc-section\" id=\"%E3%80%8C%E8%B0%B7%E3%81%AE%E9%8B%AD%E3%81%95%E3%80%8D%E6%8C%87%E6%A8%99%E3%81%AE%E5%B0%8E%E5%85%A5\"><\/span>\u300c\u8c37\u306e\u92ed\u3055\u300d\u6307\u6a19\u306e\u5c0e\u5165<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u6b21\u306b\u3001\u300c\u8c37\u306e\u92ed\u3055\u300d\u3092\u5b9a\u91cf\u7684\u306b\u8a55\u4fa1\u3059\u308b\u305f\u3081\u306e\u6307\u6a19\u3092\u5c0e\u5165\u3057\u307e\u3059\u3002\u901a\u5e38\u3001\u30d8\u30c3\u30bb\u884c\u5217 $\\nabla ^2 f(x)$\u306e\u56fa\u6709\u5024\u3068\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u3067\u3001$f(x)$\u306e\u66f2\u7387(\u66f2\u304c\u308a\u5177\u5408)\u3092\u8a08\u7b97\u3067\u304d\u308b\u305f\u3081\u3001\u89e3\u304c\u4f4d\u7f6e\u3059\u308b\u8c37\u306e\u5f62\u72b6\u3092\u8a55\u4fa1\u3067\u304d\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u6df1\u5c64\u5b66\u7fd2\u306e\u640d\u5931\u95a2\u6570\u306f\u975e\u51f8\u3067\u3042\u308a\u975e\u5e38\u306b\u9ad8\u6b21\u5143\u3067\u3042\u308b\u305f\u3081\u3001\u30d8\u30c3\u30bb\u884c\u5217\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u56f0\u96e3\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u672c\u8ad6\u6587\u3067\u306f\u300c\u8c37\u306e\u92ed\u3055\u300d\u306b\u95a2\u3059\u308b\u4ee5\u4e0b\u306e\u6307\u6a19\u3092\u63d0\u6848\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<p><strong>\u6307\u6a19:<\/strong><\/p>\n<p>$x \\in \\mathbb{R}^n$\u3001$\\epsilon &gt; 0$\u3001\u304a\u3088\u3073$A \\in \\mathbb{R}^{n \\times p}$\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u3001$x$\u5730\u70b9\u306b\u304a\u3051\u308b$f$\u306e\u92ed\u3055\u3092\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3057\u307e\u3059\uff1a<\/p>\n<p>$$<br \/>\n% \\begin{align*}<br \/>\n\\phi_{x,f}(\\epsilon, A) := \\frac{\\left(\\max_{y \\in \\mathcal{C}_\\epsilon} f(x+Ay)\\right) &#8211; f(x)}{1+f(x)} \\times 100<br \/>\n% \\end{align*}<br \/>\n\\tag{1}<br \/>\n$$<\/p>\n<p>\u3053\u3053\u3067\u3001\u5236\u7d04\u96c6\u5408 $\\mathcal{C}_\\epsilon$ \u306f\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\uff1a<\/p>\n<p>$$<br \/>\n% \\begin{align*}<br \/>\n\\mathcal{C}_\\epsilon = \\{ z \\in \\mathbb{R}^p : -\\epsilon(|(A^+x)_i| + 1) \\le z_i \\le \\epsilon(|(A^+x)_i| + 1) \\quad \\forall i \\in \\{1, 2, \\dots, p\\} \\}<br \/>\n% \\end{align*}<br \/>\n\\tag{2}<br \/>\n$$<\/p>\n<p>\u5404\u5f0f\u306e\u8aac\u660e\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\u3002<\/p>\n<ul>\n<li><strong>\u5f0f(1)<\/strong>: \u3053\u308c\u306f\u3001\u89e3$x$\u304b\u3089\u5c11\u3057\u52d5\u3044\u305f\u3068\u304d\u306b($Ay$\u306e\u5206\u3060\u3051\u52d5\u304f)\u3001\u95a2\u6570\u306e\u5024\u304c\u3069\u308c\u3060\u3051\u6025\u6fc0\u306b\u5897\u52a0\u3059\u308b\u304b\u3092\u8a08\u7b97\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u5024\u304c\u5927\u304d\u3044\u307b\u3069\u300c\u92ed\u3044\u8c37\u300d\u306e\u5e95\u306b\u3044\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002$A$\u306f\u92ed\u3055\u3092\u8a08\u6e2c\u3059\u308b\u65b9\u5411\u3092\u683c\u7d0d\u3057\u305f\u884c\u5217\u3067\u3059\u3002\u5206\u6bcd\u306e+1\u306f$f(x)$\u304c0\u306e\u6642\u3067\u3082\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u3059\u308b\u305f\u3081\u3060\u3068\u8003\u3048\u3089\u308c\u307e\u3059\u3002<\/li>\n<li><strong>\u5f0f(2)<\/strong>: \u3053\u308c\u306f\u3001\u5f0f(1)\u3067\u89e3\u306e\u5468\u308a\u3092\u63a2\u7d22\u3059\u308b\u300c\u7bc4\u56f2\u300d\u3092\u5b9a\u7fa9\u3057\u3066\u3044\u307e\u3059\u3002$p$\u306f\u63a2\u7d22\u3059\u308b\u65b9\u5411\u306e\u6b21\u5143\u6570\u3067\u3059\u3002$\\epsilon$\u304c\u3053\u306e\u7bc4\u56f2\u306e\u5927\u304d\u3055\u3092\u6c7a\u3081\u308b\u30d1\u30e9\u30e1\u30fc\u30bf\u3067\u3001\u5927\u304d\u3044\u307b\u3069\u5e83\u3044\u7bc4\u56f2\u3092\u63a2\u7d22\u3059\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002$A^{+}$\u306f$A$\u306e\u64ec\u4f3c\u9006\u884c\u5217\u3067\u3059($A$\u304c\u6b63\u65b9\u884c\u5217\u3067\u306a\u3044\u305f\u3081)\u3002$A^{+}x$\u3068\u3059\u308b\u3053\u3068\u3067\u9ad8\u6b21\u5143\u3067\u3042\u308b$x$\u3092$p$\u6b21\u5143\u306b\u5c04\u5f71\u3057\u3001\u5404\u65b9\u5411\u3067\u92ed\u3055\u3092\u8a08\u6e2c\u3057\u307e\u3059\u3002(\u3061\u306a\u307f\u306b\u3001\u6b21\u5143\u524a\u6e1b\u3092\u3059\u308b\u3060\u3051\u306a\u3089$A^{+}$\u3067\u3042\u308b\u5fc5\u8981\u306f\u306a\u3044\u3067\u3059\u304c\u3001\u300c$x$\u306e\u5927\u304d\u3055\u306b\u5fdc\u3058\u305f\u63a2\u7d22\u7bc4\u56f2\u300d\u3092\u5b9a\u3081\u308b\u3001\u3068\u3044\u3046\u30b9\u30b1\u30fc\u30ea\u30f3\u30b0\u306e\u5f79\u5272\u3082\u679c\u305f\u3057\u3066\u3044\u307e\u3059\u3002)<\/li>\n<\/ul>\n<p>\u305d\u308c\u3067\u306f\u3001\u3053\u308c\u3089\u306e\u6307\u6a19\u3092\u7528\u3044\u305f\u7d50\u679c\u3092\u88684\u30fb5\u306b\u793a\u3057\u307e\u3059\u3002\u88684\u3067\u306f\u5168\u7a7a\u9593\u306b\u5bfe\u3057\u3066\u8a08\u6e2c(\u3064\u307e\u308a\u3001$A=I_{n}$)\u3092\u884c\u3044\u30012\u3064\u306e\u7570\u306a\u308b\u7bc4\u56f2$\\epsilon$\u306e\u7d50\u679c\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u88685\u3067\u306f\u30e9\u30f3\u30c0\u30e0\u306b100\u65b9\u5411\u3092\u9078\u629e\u3057\u3001\u540c\u69d8\u306e\u8a08\u6e2c\u3092\u884c\u3063\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u30892\u3064\u306e\u7d50\u679c\u304b\u3089\u3001\u30e9\u30f3\u30c0\u30e0\u9078\u629e\u63a2\u7d22\u306e\u5834\u5408\u306b\u6bd4\u3079\u3066\u5168\u7a7a\u9593\u63a2\u7d22\u306e\u65b9\u304cSB\u3068LB\u306e\u5dee\u304c\u5927\u304d\u304f\u3001\u307e\u305f\u3001\u5168\u7a7a\u9593\u63a2\u7d22\u306e\u6a19\u6e96\u504f\u5dee\u3082LB\u304c\u975e\u5e38\u306b\u5927\u304d\u3044\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u92ed\u3044\u8c37\u306b\u4f4d\u7f6e\u3057\u3066\u3044\u308b\u3068\u8003\u3048\u3089\u308c\u3066\u3044\u305fLB\u89e3\u3067\u3059\u304c\u3001\u5468\u8fba\u306e\u307b\u3068\u3093\u3069\u306f\u5e73\u5766\u306a\u8c37\u306b\u306a\u3063\u3066\u304a\u308a\u3001\u308f\u305a\u304b\u306a\u4e00\u90e8\u306e\u6025\u5cfb\u306a\u65b9\u5411\u304c\u3001\u3053\u306e\u6307\u6a19\u3092\u5927\u304d\u304f\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3057\u305f\u3002\u6b21\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u3069\u306e\u7a0b\u5ea6\u306e\u30d0\u30c3\u30c1\u30b5\u30a4\u30ba\u304c\u9069\u5207\u3067\u3042\u308b\u306e\u304b\u306b\u3064\u3044\u3066\u5b9f\u9a13\u3092\u884c\u3044\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u306a\u305cSB\u89e3\u304c\u5e73\u5766\u306b\u8c37\u306b\u843d\u3061\u3084\u3059\u3044\u306e\u304b\u306b\u3064\u3044\u3066\u3082\u8b70\u8ad6\u3057\u307e\u3059\u3002<\/p>\n<table style=\"border: none; width: 100%;\">\n<tbody>\n<tr style=\"border: none;\"><!-- \u88684 --><\/p>\n<td style=\"vertical-align: top; padding-right: 20px; border: none; width: 50%;\">\n<figure style=\"text-align: center;\"><figcaption style=\"margin-bottom: 8px;\">\u88684: \u5168\u7a7a\u9593\u306b\u304a\u3051\u308b\u6700\u5c0f\u5316\u70b9\u306e\u92ed\u3055<br \/>\n(\u5f15\u7528: <a href=\"https:\/\/arxiv.org\/abs\/1609.04836\" target=\"_blank\" rel=\"noopener\">https:\/\/arxiv.org\/abs\/1609.04836<\/a>)<\/figcaption><table border=\"1\" style=\"border-collapse: collapse; width: 100%;\">\n<thead>\n<tr>\n<th><\/th>\n<th colspan=\"2\">\u03b5=10<sup>-3<\/sup><\/th>\n<th colspan=\"2\">\u03b5=5 \u00b7 10<sup>-4<\/sup><\/th>\n<\/tr>\n<tr>\n<th><\/th>\n<th><strong>SB<\/strong><\/th>\n<th><strong>LB<\/strong><\/th>\n<th><strong>SB<\/strong><\/th>\n<th><strong>LB<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>F<sub>1<\/sub><\/td>\n<td>1.23 \u00b1 0.83<\/td>\n<td>205.14 \u00b1 69.52<\/td>\n<td>0.61 \u00b1 0.27<\/td>\n<td>42.90 \u00b1 17.14<\/td>\n<\/tr>\n<tr>\n<td>F<sub>2<\/sub><\/td>\n<td>1.39 \u00b1 0.02<\/td>\n<td>310.64 \u00b1 38.46<\/td>\n<td>0.90 \u00b1 0.05<\/td>\n<td>93.15 \u00b1 6.81<\/td>\n<\/tr>\n<tr>\n<td>C<sub>1<\/sub><\/td>\n<td>28.58 \u00b1 3.13<\/td>\n<td>707.23 \u00b1 43.04<\/td>\n<td>7.08 \u00b1 0.88<\/td>\n<td>227.31 \u00b1 23.23<\/td>\n<\/tr>\n<tr>\n<td>C<sub>2<\/sub><\/td>\n<td>8.68 \u00b1 1.32<\/td>\n<td>925.32 \u00b1 38.29<\/td>\n<td>2.07 \u00b1 0.86<\/td>\n<td>175.31 \u00b1 18.28<\/td>\n<\/tr>\n<tr>\n<td>C<sub>3<\/sub><\/td>\n<td>29.85 \u00b1 5.98<\/td>\n<td>258.75 \u00b1 8.96<\/td>\n<td>8.56 \u00b1 0.99<\/td>\n<td>105.11 \u00b1 13.22<\/td>\n<\/tr>\n<tr>\n<td>C<sub>4<\/sub><\/td>\n<td>12.83 \u00b1 3.84<\/td>\n<td>421.84 \u00b1 36.97<\/td>\n<td>4.07 \u00b1 0.87<\/td>\n<td>109.35 \u00b1 16.57<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<\/td>\n<p><!-- \u88685 --><\/p>\n<td style=\"vertical-align: top; border: none; width: 50%;\">\n<figure style=\"text-align: center;\"><figcaption style=\"margin-bottom: 8px;\">\u88685: 100\u6b21\u5143\u306e\u30e9\u30f3\u30c0\u30e0\u90e8\u5206\u7a7a\u9593\u306b\u304a\u3051\u308b\u6700\u5c0f\u5316\u70b9\u306e\u92ed\u3055<br \/>\n(\u5f15\u7528: <a href=\"https:\/\/arxiv.org\/abs\/1609.04836\" target=\"_blank\" rel=\"noopener\">https:\/\/arxiv.org\/abs\/1609.04836<\/a>)<\/figcaption><table border=\"1\" style=\"border-collapse: collapse; width: 100%;\">\n<thead>\n<tr>\n<th><\/th>\n<th colspan=\"2\">\u03b5=10<sup>-3<\/sup><\/th>\n<th colspan=\"2\">\u03b5=5 \u00b7 10<sup>-4<\/sup><\/th>\n<\/tr>\n<tr>\n<th><\/th>\n<th><strong>SB<\/strong><\/th>\n<th><strong>LB<\/strong><\/th>\n<th><strong>SB<\/strong><\/th>\n<th><strong>LB<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>F<sub>1<\/sub><\/td>\n<td>0.11 \u00b1 0.00<\/td>\n<td>9.22 \u00b1 0.56<\/td>\n<td>0.05 \u00b1 0.00<\/td>\n<td>9.17 \u00b1 0.14<\/td>\n<\/tr>\n<tr>\n<td>F<sub>2<\/sub><\/td>\n<td>0.29 \u00b1 0.02<\/td>\n<td>23.63 \u00b1 0.54<\/td>\n<td>0.05 \u00b1 0.00<\/td>\n<td>6.28 \u00b1 0.19<\/td>\n<\/tr>\n<tr>\n<td>C<sub>1<\/sub><\/td>\n<td>2.18 \u00b1 0.23<\/td>\n<td>137.25 \u00b1 21.60<\/td>\n<td>0.71 \u00b1 0.15<\/td>\n<td>29.50 \u00b1 7.48<\/td>\n<\/tr>\n<tr>\n<td>C<sub>2<\/sub><\/td>\n<td>0.95 \u00b1 0.34<\/td>\n<td>25.09 \u00b1 2.61<\/td>\n<td>0.31 \u00b1 0.08<\/td>\n<td>5.82 \u00b1 0.52<\/td>\n<\/tr>\n<tr>\n<td>C<sub>3<\/sub><\/td>\n<td>17.02 \u00b1 2.20<\/td>\n<td>36.03 \u00b1 31.26<\/td>\n<td>4.03 \u00b1 1.45<\/td>\n<td>86.96 \u00b1 27.39<\/td>\n<\/tr>\n<tr>\n<td>C<sub>4<\/sub><\/td>\n<td>6.05 \u00b1 1.13<\/td>\n<td>72.99 \u00b1 10.96<\/td>\n<td>1.89 \u00b1 0.33<\/td>\n<td>19.85 \u00b1 4.12<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2><span class=\"ez-toc-section\" id=\"%E3%83%90%E3%83%83%E3%83%81%E3%82%B5%E3%82%A4%E3%82%BA%E3%81%AE%E3%81%97%E3%81%8D%E3%81%84%E5%80%A4%E3%81%A8%E5%8E%9F%E5%9B%A0\"><\/span>\u30d0\u30c3\u30c1\u30b5\u30a4\u30ba\u306e\u3057\u304d\u3044\u5024\u3068\u539f\u56e0<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u554f\u984c\u306e\u30d0\u30c3\u30c1\u30b5\u30a4\u30ba\u3092\u5897\u3084\u3059\u3068\u3001\u3042\u308b\u95be\u5024\u304b\u3089\u30e2\u30c7\u30eb\u306e\u54c1\u8cea\u304c\u4f4e\u4e0b\u3059\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002\u56f33\u3067\u306f\u3001\uff12\u3064\u306e\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306b\u3064\u3044\u3066\u3001\u30d0\u30c3\u30c1\u30b5\u30a4\u30ba\u3092\u5897\u3084\u3057\u305f\u3068\u304d\u306e\u30c6\u30b9\u30c8\u7cbe\u5ea6\u3068\u3001\u89e3\u306e\u92ed\u3055\u306b\u3064\u3044\u3066\u30d7\u30ed\u30c3\u30c8\u3057\u3066\u3044\u307e\u3059\u3002$F_{2}$\u3067\u306f\u7d0415000\u3067\u3001$C_{1}$\u3067\u306f\u7d04500\u3067\u6025\u6fc0\u306b\u7cbe\u5ea6\u304c\u6e1b\u5c11\u3057\u3001\u305d\u308c\u3068\u306f\u53cd\u5bfe\u306b\u8c37\u306e\u92ed\u3055\u306f\u4e0a\u6607\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u78ba\u8a8d\u3067\u304d\u307e\u3059\u3002<\/p>\n<div id=\"attachment_7975\" style=\"width: 1604px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-7975\" src=\"\/T-Wave\/wp-content\/uploads\/2025\/08\/fig3.png\" alt=\"\" width=\"1594\" height=\"568\" class=\"size-full wp-image-7975\" \/><p id=\"caption-attachment-7975\" class=\"wp-caption-text\">\u56f35: \u30d0\u30c3\u30c1\u30b5\u30a4\u30ba\u306b\u304a\u3051\u308b\u30c6\u30b9\u30c8\u7cbe\u5ea6\u3068\u8c37\u306e\u92ed\u3055<\/p><\/div>\n<p>\u3053\u3053\u307e\u3067\u306e\u5b9f\u9a13\u304b\u3089\u3001SB\u306b\u3088\u308b\u5b66\u7fd2\u306e\u65b9\u304c\u6c4e\u5316\u6027\u80fd\u304c\u9ad8\u3044\u305f\u3081\u3001LB\u3088\u308a\u3082\u512a\u4f4d\u3060\u3068\u8003\u3048\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002\u3057\u304b\u3057\u3001\u5192\u982d\u3067\u8aac\u660e\u3057\u305f\u3088\u3046\u306b\u3001\u8a08\u7b97\u52b9\u7387\u306e\u9762\u3067\u306fLB\u306e\u65b9\u304c\u512a\u308c\u3066\u3044\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u6b21\u306e\u5b9f\u9a13\u3067\u306f\u6700\u521d\u306e\u6570\u30a8\u30dd\u30c3\u30af\u3092SB\u3067\u5b66\u7fd2\u3057\u3001\u305d\u306e\u5f8cLB\u3067\u5b66\u7fd2\u3092\u884c\u3044\u307e\u3059(\u3053\u308c\u3092\u30a6\u30a9\u30fc\u30e0\u30b9\u30bf\u30fc\u30c8\u3084\u3001\u30d4\u30ae\u30fc\u30d0\u30c3\u30af\u3068\u547c\u3093\u3067\u3044\u307e\u3059)\u3002\u7d50\u679c\u306f\u56f36\u306e\u901a\u308a\u3067\u3059\u3002\u6a2a\u8ef8\u306f\u3001\u6700\u521d\u306eSB\u3067\u5b66\u7fd2\u3057\u305f\u30a8\u30dd\u30c3\u30af\u6570\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u6a2a\u8ef820\u306e\u30e9\u30a4\u30f3\u306f\u3001\u300cSB\u6cd5\u306720\u30a8\u30dd\u30c3\u30af\u5b66\u7fd2\u3055\u305b\u305f\u6642\u70b9\u306e\u30e2\u30c7\u30eb\u300d\u306e\u7d50\u679c\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u9752\u7dda\u306e\u7d50\u679c\u306f\u3001LB\u3092\u5b9f\u884c\u3059\u308b\u524d\u306eSB\u306e\u307f\u306b\u3088\u308b\u5b66\u7fd2\u7d50\u679c\u3067\u3042\u308a\u3001\u30a6\u30a9\u30fc\u30e0\u30b9\u30bf\u30fc\u30c8\u306b\u3088\u308a\u9752\u7dda\u304b\u3089\u8d64\u7dda\u307e\u3067\u7cbe\u5ea6\u304c\u5411\u4e0a\u3057\u305f\u3068\u3044\u3046\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<div id=\"attachment_7976\" style=\"width: 1568px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-7976\" src=\"\/T-Wave\/wp-content\/uploads\/2025\/08\/fig4.png\" alt=\"\" width=\"1558\" height=\"570\" class=\"size-full wp-image-7976\" \/><p id=\"caption-attachment-7976\" class=\"wp-caption-text\">\u56f36: \u30a6\u30a9\u30fc\u30e0\u30b9\u30bf\u30fc\u30c8\u306e\u5b9f\u9a13 (\u5f15\u7528: https:\/\/arxiv.org\/abs\/1609.04836)<\/p><\/div>\n<p>\u3053\u3053\u3067\u3001\u30a6\u30a9\u30fc\u30e0\u30b9\u30bf\u30fc\u30c8\u3067SB\u3092\u6570\u30a8\u30dd\u30c3\u30af\u3057\u304b\u4f7f\u7528\u3057\u306a\u3044\u5834\u5408\u3001LB\u306b\u3088\u3063\u3066\u6c4e\u5316\u6027\u80fd\u306f\u5411\u4e0a\u3057\u306a\u3044\u3053\u3068\u304c\u5206\u304b\u3063\u3066\u3044\u307e\u3059\u3002\u6c4e\u5316\u6027\u80fd\u304c\u5411\u4e0a\u3059\u308b\u306e\u306f\u3001SB\u304c\u63a2\u7d22\u3092\u7d42\u3048\u3066\u5e73\u5766\u306a\u6700\u5c0f\u5316\u70b9\u3092\u767a\u898b\u3057\u305f\u5f8c\u306bLB\u3092\u5b9f\u884c\u3057\u305f\u5834\u5408\u3060\u3068\u8003\u3048\u3089\u308c\u307e\u3059\u3002\u307e\u305f\u3001\u6700\u5c0f\u89e3\u3068SB\u89e3\u3001LB\u89e3\u306e\u8ddd\u96e2\u3092\u8a08\u6e2c\u3059\u308b\u3068\u3001SB\u89e3\u306fLB\u89e3\u3088\u308a3~10\u500d\u9060\u3044\u4f4d\u7f6e\u307e\u3067\u79fb\u52d5\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u5206\u304b\u3063\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u7d50\u679c\u304b\u3089\u3001SB\u3067\u306f\u52fe\u914d\u8a08\u7b97\u306b\u304a\u3044\u3066\u30ce\u30a4\u30ba\u304c\u5927\u304d\u3044\u305f\u3081\u3001\u92ed\u3044\u8c37\u306b\u30cf\u30de\u3089\u305a\u5e83\u7bc4\u56f2\u3092\u63a2\u7d22\u3067\u304d\u3066\u304a\u308a\u3001LB\u3067\u306f\u30ce\u30a4\u30ba\u304c\u5c0f\u3055\u3044\u305f\u3081\u3001\u3059\u3050\u8fd1\u304f\u306e\u92ed\u3044\u8c37\u306b\u53ce\u675f\u3057\u3066\u3057\u307e\u3046\u3068\u8003\u3048\u3089\u308c\u307e\u3059\u3002\u3053\u306e\u8003\u5bdf\u3092\u88cf\u4ed8\u3051\u308b\u305f\u3081\u306e\u7d50\u679c\u304c\u56f37\u3067\u3059\u3002\u6a2a\u8ef8\u304c\u30af\u30ed\u30b9\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u306b\u306a\u3063\u3066\u304a\u308a\u3001\u53f3\u306b\u884c\u304f\u307b\u3069\u5b66\u7fd2\u304c\u9032\u3093\u3067\u3044\u308b\u72b6\u614b\u3092\u8868\u3057\u307e\u3059\u3002(a)(b)\u3068\u3082\u306b\u3001\u5b66\u7fd2\u304c\u9032\u3080\u306b\u3064\u308c\u3001LB\u306f\u3088\u308a\u92ed\u3044\u8c37\u3078\u3001SB\u306f\u3088\u308a\u5e73\u5766\u306a\u8c37\u3078\u79fb\u52d5\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002<\/p>\n<div id=\"attachment_7977\" style=\"width: 1552px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-7977\" src=\"\/T-Wave\/wp-content\/uploads\/2025\/08\/fig5.png\" alt=\"\" width=\"1542\" height=\"570\" class=\"size-full wp-image-7977\" \/><p id=\"caption-attachment-7977\" class=\"wp-caption-text\">\u56f37: \u30af\u30ed\u30b9\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc(\u640d\u5931)\u306b\u5bfe\u3059\u308b\u8c37\u306e\u92ed\u3055 (\u5f15\u7528: https:\/\/arxiv.org\/abs\/1609.04836)<\/p><\/div>\n<h2><span class=\"ez-toc-section\" id=\"%E8%80%83%E5%AF%9F%E3%83%BB%E7%B5%90%E8%AB%96\"><\/span>\u8003\u5bdf\u30fb\u7d50\u8ad6<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u672c\u8ad6\u6587\u3067\u306f\u3001LB\u306b\u3088\u308b\u89e3\u304c\u92ed\u3044\u8c37\u306b\u4f4d\u7f6e\u3059\u308b\u3053\u3068\u3092\u6570\u5024\u5b9f\u9a13\u306b\u3088\u308a\u793a\u3057\u307e\u3057\u305f\u3002\u307e\u305f\u3001\u6700\u521d\u306bSB\u3092\u5b9f\u884c\u3057\u3001\u305d\u306e\u3042\u3068\u306bLB\u3092\u5b9f\u884c\u3059\u308b\u3068\u3044\u3063\u305f\u3001LB\u306e\u8a08\u7b97\u52b9\u7387\u3092\u6d3b\u304b\u3057\u305f\u624b\u6cd5\u306e\u63d0\u6848\u3082\u884c\u3044\u307e\u3057\u305f\u3002\u3057\u304b\u3057\u3001\u73fe\u72b6\u3067\u306f\u4ee5\u4e0b\u306e\u8ab2\u984c\u304c\u5b58\u5728\u3057\u307e\u3059\u3002<\/p>\n<ol type=\"a\">\n<li>LB\u6cd5\u304c\u6df1\u5c64\u5b66\u7fd2\u306e\u5b66\u7fd2\u95a2\u6570\u306e\u92ed\u3044\u6700\u5c0f\u5316\u70b9\u306b\u5178\u578b\u7684\u306b\u53ce\u675f\u3059\u308b\u3053\u3068\u3092\u8a3c\u660e\u3067\u304d\u308b\u304b\uff1f<\/li>\n<li>\u300e\u5e73\u5766\u306a\u6700\u5c0f\u5316\u70b9\u300f\u3068\u300e\u92ed\u3044\u6700\u5c0f\u5316\u70b9\u300f\u306f\u3001\u305d\u308c\u305e\u308c\u3069\u308c\u304f\u3089\u3044\u306e\u5272\u5408\u3067\u5b58\u5728\u3059\u308b\u306e\u304b\uff1f<\/li>\n<li>LB\u6cd5\u306e\u7279\u6027\u306b\u9069\u3057\u305f\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u30a2\u30fc\u30ad\u30c6\u30af\u30c1\u30e3\u3092\u8a2d\u8a08\u3067\u304d\u308b\u304b\uff1f<\/li>\n<li>LB\u6cd5\u304c\u6210\u529f\u3059\u308b\u3088\u3046\u306b\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u3092\u521d\u671f\u5316\u3067\u304d\u308b\u304b\uff1f<\/li>\n<li>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u7684\u307e\u305f\u306f\u6b63\u5247\u5316\u7684\u306a\u624b\u6bb5\u3092\u901a\u3058\u3066\u3001LB\u6cd5\u3092\u92ed\u3044\u6700\u5c0f\u5316\u70b9\u304b\u3089\u9060\u3056\u3051\u308b\u3053\u3068\u306f\u53ef\u80fd\u304b\uff1f<\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"%E3%81%82%E3%81%A8%E3%81%8C%E3%81%8D\"><\/span>\u3042\u3068\u304c\u304d<span 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class=\"ez-toc-section\" id=\"%E6%9C%AC%E8%A8%98%E4%BA%8B%E3%81%AE%E6%8B%85%E5%BD%93%E8%80%85\"><\/span>\u672c\u8a18\u4e8b\u306e\u62c5\u5f53\u8005<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u9e7f\u5185\u601c\u592e<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6df1\u5c64\u5b66\u7fd2\u3067\u306f\u8a08\u7b97\u52b9\u7387\u3092\u9ad8\u3081\u308b\u305f\u3081\u306b\u5927\u898f\u6a21\u30d0\u30c3\u30c1\u5b66\u7fd2\uff08LB\uff09\u304c\u76db\u3093\u306b\u4f7f\u308f\u308c\u307e\u3059\u304c\u3001\u7d4c\u9a13\u7684\u306b\u300c\u30c6\u30b9\u30c8\u7cbe\u5ea6\u304c\u4e0b\u304c\u308b\u300d\u3068\u3044\u3046\u554f\u984c\u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002\u672c\u8a18\u4e8b\u3067\u306f\u3001\u305d\u306e\u539f\u56e0\u3092\u300c\u640d\u5931\u95a2\u6570\u306e\u8c37\u306e\u5f62\u72b6\u300d\u3068\u3044\u3046\u89b3\u70b9\u304b\u3089\u63a2\u308a\u3001\u6570\u5024\u5b9f\u9a13\u3092\u901a\u3057\u3066LB\u304c\u92ed\u3044\u8c37\u306b\u3001\u5c0f\u898f\u6a21\u30d0\u30c3\u30c1\uff08SB\uff09\u304c\u5e73\u5766\u306a\u8c37\u306b\u53ce\u675f\u3057\u3084\u3059\u3044\u3053\u3068\u3092\u793a\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u4e21\u8005\u306e\u5229\u70b9\u3092\u6d3b\u304b\u3059\u305f\u3081\u306b\u63d0\u6848\u3055\u308c\u305f\u300c\u30a6\u30a9\u30fc\u30e0\u30b9\u30bf\u30fc\u30c8\u300d\u306e\u52b9\u679c\u3092\u7d39\u4ecb\u3057\u3001\u6c4e\u5316\u6027\u80fd\u3092\u3081\u3050\u308b\u65b0\u305f\u306a\u7406\u89e3\u3068\u4eca\u5f8c\u306e\u8ab2\u984c\u306b\u3064\u3044\u3066\u8003\u5bdf\u3057\u307e\u3059\u3002<\/p>\n","protected":false},"author":8,"featured_media":8193,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[104],"class_list":["post-7967","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-review","tag-104"],"yoast_head":"<!-- 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