{"id":7404,"date":"2025-10-07T07:02:44","date_gmt":"2025-10-07T07:02:44","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/10\/07\/2510-03809\/"},"modified":"2025-10-07T07:02:44","modified_gmt":"2025-10-07T07:02:44","slug":"2510-03809","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/10\/07\/2510-03809\/","title":{"rendered":"Spectral Thresholds for Identifiability and Stability:Finite-Sample Phase Transitions in High-Dimensional Learning"},"content":{"rendered":"

Spectral Thresholds for Identifiability and Stability:Finite-Sample Phase Transitions in High-Dimensional Learning
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arXiv:2510.03809v1 Announce Type: new
\nAbstract: In high-dimensional learning, models remain stable until they collapse abruptly once the sample size falls below a critical level. This instability is not algorithm-specific but a geometric mechanism: when the weakest Fisher eigendirection falls beneath sample-level fluctuations, identifiability fails. Our Fisher Threshold Theorem formalizes this by proving that stability requires the minimal Fisher eigenvalue to exceed an explicit $O(sqrt{d\/n})$ bound. Unlike prior asymptotic or model-specific criteria, this threshold is finite-sample and necessary, marking a sharp phase transition between reliable concentration and inevitable failure. To make the principle constructive, we introduce the Fisher floor, a verifiable spectral regularization robust to smoothing and preconditioning. Synthetic experiments on Gaussian mixtures and logistic models confirm the predicted transition, consistent with $d\/n$ scaling. Statistically, the threshold sharpens classical eigenvalue conditions into a non-asymptotic law; learning-theoretically, it defines a spectral sample-complexity frontier, bridging theory with diagnostics for robust high-dimensional inference.<\/div>\n

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\n William Hao-Cheng Huang
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Spectral Thresholds for Identifiability and Stability:Finite-Sample Phase Transitions in High-Dimensional Learning arXiv:2510.03809v1 Announce Type: new Abstract: In high-dimensional learning, models remain stable until they collapse abruptly once the sample size falls below a critical level. This instability is not algorithm-specific but a geometric mechanism: when the weakest Fisher eigendirection falls beneath sample-level fluctuations, identifiability fails. […]<\/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":[332,31,634],"class_list":["post-7404","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-ml","tag-high","tag-sample","tag-spectral"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/7404"}],"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=7404"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/7404\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=7404"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=7404"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=7404"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}