{"paper":{"title":"Average-Case Lower Bounds and Satisfiability Algorithms for Small Threshold Circuits","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Rahul Santhanam, Ruiwen Chen, Srikanth Srinivasan","submitted_at":"2018-06-16T20:32:51Z","abstract_excerpt":"$ \\newcommand{\\cclass}[1]{{\\normalfont\\textsf{##1}}} $We show average-case lower bounds for explicit Boolean functions against bounded-depth threshold circuits with a superlinear number of wires. We show that for each integer $d > 1$, there is a constant $\\varepsilon_d > 0$ such that the Parity function on $n$ bits has correlation at most $n^{-\\varepsilon_d}$ with depth-$d$ threshold circuits which have at most $n^{1+\\varepsilon_d}$ wires, and the Generalized Andreev function on $n$ bits has correlation at most $\\exp(-{n^{\\varepsilon_d}})$ with depth-$d$ threshold circuits which have at most $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06290","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":""},"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"}