{"id":9883,"date":"2026-01-21T07:03:14","date_gmt":"2026-01-21T07:03:14","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2026\/01\/21\/2601-12587\/"},"modified":"2026-01-21T07:03:14","modified_gmt":"2026-01-21T07:03:14","slug":"2601-12587","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2026\/01\/21\/2601-12587\/","title":{"rendered":"A Theory of Diversity for Random Matrices with Applications to In-Context Learning of Schr&#8221;odinger Equations"},"content":{"rendered":"\n<div>A Theory of Diversity for Random Matrices with Applications to In-Context Learning of Schr&#8221;odinger Equations<\/div>\n<p> \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2601.12587v1 Announce Type: new<br \/>\nAbstract: We address the following question: given a collection ${mathbf{A}^{(1)}, dots, mathbf{A}^{(N)}}$ of independent $d times d$ random matrices drawn from a common distribution $mathbb{P}$, what is the probability that the centralizer of ${mathbf{A}^{(1)}, dots, mathbf{A}^{(N)}}$ is trivial? We provide lower bounds on this probability in terms of the sample size $N$ and the dimension $d$ for several families of random matrices which arise from the discretization of linear Schr&#8221;odinger operators with random potentials. When combined with recent work on machine learning theory, our results provide guarantees on the generalization ability of transformer-based neural networks for in-context learning of Schr&#8221;odinger equations.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Frank Cole, Yulong Lu, Shaurya Sehgal<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2601.12587\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A Theory of Diversity for Random Matrices with Applications to In-Context Learning of Schr&#8221;odinger Equations arXiv:2601.12587v1 Announce Type: new Abstract: We address the following question: given a collection ${mathbf{A}^{(1)}, dots, mathbf{A}^{(N)}}$ of independent $d times d$ random matrices drawn from a common distribution $mathbb{P}$, what is the probability that the centralizer of ${mathbf{A}^{(1)}, dots, mathbf{A}^{(N)}}$ [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,112],"tags":[199,915,902],"class_list":["post-9883","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-ml","tag-learning","tag-matrices","tag-random"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/9883"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=9883"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/9883\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=9883"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=9883"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=9883"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}