{"id":9274,"date":"2025-12-22T07:02:49","date_gmt":"2025-12-22T07:02:49","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/12\/22\/2512-17426\/"},"modified":"2025-12-22T07:02:49","modified_gmt":"2025-12-22T07:02:49","slug":"2512-17426","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/12\/22\/2512-17426\/","title":{"rendered":"Perfect reconstruction of sparse signals using nonconvexity control and one-step RSB message passing"},"content":{"rendered":"

Perfect reconstruction of sparse signals using nonconvexity control and one-step RSB message passing
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arXiv:2512.17426v1 Announce Type: new
\nAbstract: We consider sparse signal reconstruction via minimization of the smoothly clipped absolute deviation (SCAD) penalty, and develop one-step replica-symmetry-breaking (1RSB) extensions of approximate message passing (AMP), termed 1RSB-AMP. Starting from the 1RSB formulation of belief propagation, we derive explicit update rules of 1RSB-AMP together with the corresponding state evolution (1RSB-SE) equations. A detailed comparison shows that 1RSB-AMP and 1RSB-SE agree remarkably well at the macroscopic level, even in parameter regions where replica-symmetric (RS) AMP, termed RS-AMP, diverges and where the 1RSB description itself is not expected to be thermodynamically exact. Fixed-point analysis of 1RSB-SE reveals a phase diagram consisting of success, failure, and diverging phases, as in the RS case. However, the diverging-region boundary now depends on the Parisi parameter due to the 1RSB ansatz, and we propose a new criterion — minimizing the size of the diverging region — rather than the conventional zero-complexity condition, to determine its value. Combining this criterion with the nonconvexity-control (NCC) protocol proposed in a previous RS study improves the algorithmic limit of perfect reconstruction compared with RS-AMP. Numerical solutions of 1RSB-SE and experiments with 1RSB-AMP confirm that this improved limit is achieved in practice, though the gain is modest and remains slightly inferior to the Bayes-optimal threshold. We also report the behavior of thermodynamic quantities — overlaps, free entropy, complexity, and the non-self-averaging susceptibility — that characterize the 1RSB phase in this problem.<\/div>\n

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\n Xiaosi Gu, Ayaka Sakata, Tomoyuki Obuchi
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Perfect reconstruction of sparse signals using nonconvexity control and one-step RSB message passing arXiv:2512.17426v1 Announce Type: new Abstract: We consider sparse signal reconstruction via minimization of the smoothly clipped absolute deviation (SCAD) penalty, and develop one-step replica-symmetry-breaking (1RSB) extensions of approximate message passing (AMP), termed 1RSB-AMP. Starting from the 1RSB formulation of belief propagation, we […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,1878,113,112],"tags":[4475,4476,4474],"class_list":["post-9274","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cond-mat-dis-nn","category-cs-lg","category-stat-ml","tag-amp","tag-rs","tag-rsb"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/9274"}],"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=9274"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/9274\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=9274"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=9274"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=9274"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}