{"paper":{"title":"Algorithms and Barriers in the Symmetric Binary Perceptron Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math-ph","math.MP","math.PR"],"primary_cat":"cs.CC","authors_text":"Changji Xu, David Gamarnik, Eren C. K{\\i}z{\\i}lda\\u{g}, Will Perkins","submitted_at":"2022-03-29T15:29:49Z","abstract_excerpt":"The symmetric binary perceptron ($\\texttt{SBP}$) exhibits a dramatic statistical-to-computational gap: the densities at which known efficient algorithms find solutions are far below the threshold for the existence of solutions. Furthermore, the $\\texttt{SBP}$ exhibits a striking structural property: at all positive constraint densities almost all of its solutions are 'totally frozen' singletons separated by large Hamming distance \\cite{perkins2021frozen,abbe2021proof}. This suggests that finding a solution to the $\\texttt{SBP}$ may be computationally intractable. At the same time, the $\\texttt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.15667","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2203.15667/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}