{"id":10200,"date":"2026-02-03T07:02:38","date_gmt":"2026-02-03T07:02:38","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2026\/02\/03\/2602-00387\/"},"modified":"2026-02-03T07:02:38","modified_gmt":"2026-02-03T07:02:38","slug":"2602-00387","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2026\/02\/03\/2602-00387\/","title":{"rendered":"Singular Bayesian Neural Networks"},"content":{"rendered":"

Singular Bayesian Neural Networks
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arXiv:2602.00387v1 Announce Type: new
\nAbstract: Bayesian neural networks promise calibrated uncertainty but require $O(mn)$ parameters for standard mean-field Gaussian posteriors. We argue this cost is often unnecessary, particularly when weight matrices exhibit fast singular value decay. By parameterizing weights as $W = AB^{top}$ with $A in mathbb{R}^{m times r}$, $B in mathbb{R}^{n times r}$, we induce a posterior that is singular with respect to the Lebesgue measure, concentrating on the rank-$r$ manifold. This singularity captures structured weight correlations through shared latent factors, geometrically distinct from mean-field’s independence assumption. We derive PAC-Bayes generalization bounds whose complexity term scales as $sqrt{r(m+n)}$ instead of $sqrt{m n}$, and prove loss bounds that decompose the error into optimization and rank-induced bias using the Eckart-Young-Mirsky theorem. We further adapt recent Gaussian complexity bounds for low-rank deterministic networks to Bayesian predictive means. Empirically, across MLPs, LSTMs, and Transformers on standard benchmarks, our method achieves predictive performance competitive with 5-member Deep Ensembles while using up to $15times$ fewer parameters. Furthermore, it substantially improves OOD detection and often improves calibration relative to mean-field and perturbation baselines.<\/div>\n

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\n Mame Diarra Toure, David A. Stephens
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Singular Bayesian Neural Networks arXiv:2602.00387v1 Announce Type: new Abstract: Bayesian neural networks promise calibrated uncertainty but require $O(mn)$ parameters for standard mean-field Gaussian posteriors. We argue this cost is often unnecessary, particularly when weight matrices exhibit fast singular value decay. By parameterizing weights as $W = AB^{top}$ with $A in mathbb{R}^{m times r}$, $B in […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,181,112],"tags":[557,491,1436],"class_list":["post-10200","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-ap","category-stat-ml","tag-bayesian","tag-networks","tag-singular"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/10200"}],"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=10200"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/10200\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=10200"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=10200"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=10200"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}