{"paper":{"title":"Detection in the stochastic block model with multiple clusters: proof of the achievability conjectures, acyclic BP, and the information-computation gap","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.IT","cs.LG","cs.SI","math.IT"],"primary_cat":"math.PR","authors_text":"Colin Sandon, Emmanuel Abbe","submitted_at":"2015-12-30T19:49:28Z","abstract_excerpt":"In a paper that initiated the modern study of the stochastic block model, Decelle et al., backed by Mossel et al., made the following conjecture: Denote by $k$ the number of balanced communities, $a/n$ the probability of connecting inside communities and $b/n$ across, and set $\\mathrm{SNR}=(a-b)^2/(k(a+(k-1)b)$; for any $k \\geq 2$, it is possible to detect communities efficiently whenever $\\mathrm{SNR}>1$ (the KS threshold), whereas for $k\\geq 4$, it is possible to detect communities information-theoretically for some $\\mathrm{SNR}<1$. Massouli\\'e, Mossel et al.\\ and Bordenave et al.\\ succeede"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09080","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}