{"id":8519,"date":"2026-07-07T15:36:27","date_gmt":"2026-07-07T14:36:27","guid":{"rendered":"https:\/\/sinatootoonian.com\/?post_type=notes&#038;p=8519"},"modified":"2026-07-07T15:36:27","modified_gmt":"2026-07-07T14:36:27","slug":"schemas-for-learning","status":"publish","type":"notes","link":"https:\/\/sinatootoonian.com\/index.php\/notes\/schemas-for-learning\/","title":{"rendered":"Schemas for Learning"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Valentina&#8217;s TNJC on <a href=\"https:\/\/www.biorxiv.org\/content\/10.64898\/2026.05.27.728344v1\" data-type=\"link\" data-id=\"https:\/\/www.biorxiv.org\/content\/10.64898\/2026.05.27.728344v1\">A model of schema learning based on biological dimensionality reduction during sleep<\/a>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"763\" height=\"560\" src=\"https:\/\/sinatootoonian.com\/wp-content\/uploads\/2026\/07\/image-5.png\" alt=\"\" class=\"wp-image-8520\" srcset=\"https:\/\/sinatootoonian.com\/wp-content\/uploads\/2026\/07\/image-5.png 763w, https:\/\/sinatootoonian.com\/wp-content\/uploads\/2026\/07\/image-5-300x220.png 300w\" sizes=\"auto, (max-width: 763px) 100vw, 763px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Main Ideas<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$\\zz$: A fixed, sparse transformation of $\\xx$ through $\\WW_\\text{ZX}$.<\/li>\n\n\n\n<li>Two pathways to compute value:\n<ul class=\"wp-block-list\">\n<li>Direct, rote pathway: $\\WW_\\text{rote} \\zz$<\/li>\n\n\n\n<li>Low-dimensional, schema pathway:\n<ul class=\"wp-block-list\">\n<li>$\\yy = \\WW_\\text{schema} \\zz.$<\/li>\n\n\n\n<li>This is then centered and normalized to $\\tilde \\yy$<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Value computed as the sum: $$ \\vv = \\WW_\\text{rote} \\zz + \\WW_\\text{knowledge} \\tilde \\yy.$$<\/li>\n\n\n\n<li>The benefit of this system is that\n<ul class=\"wp-block-list\">\n<li>It avoids slow learning of new tasks<\/li>\n\n\n\n<li>Can perform transfer learning by aligning schemas<\/li>\n\n\n\n<li>Low-dimensionality of scheme representation also seems to speed up learning.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"featured_media":8520,"template":"","class_list":["post-8519","notes","type-notes","status-publish","has-post-thumbnail","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/sinatootoonian.com\/index.php\/wp-json\/wp\/v2\/notes\/8519","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sinatootoonian.com\/index.php\/wp-json\/wp\/v2\/notes"}],"about":[{"href":"https:\/\/sinatootoonian.com\/index.php\/wp-json\/wp\/v2\/types\/notes"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/sinatootoonian.com\/index.php\/wp-json\/wp\/v2\/media\/8520"}],"wp:attachment":[{"href":"https:\/\/sinatootoonian.com\/index.php\/wp-json\/wp\/v2\/media?parent=8519"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}