{"paper":{"title":"Hardness of learning noisy halfspaces using polynomial thresholds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Arnab Bhattacharyya, Rishi Saket, Suprovat Ghoshal","submitted_at":"2017-07-06T13:56:35Z","abstract_excerpt":"We prove the hardness of weakly learning halfspaces in the presence of adversarial noise using polynomial threshold functions (PTFs). In particular, we prove that for any constants $d \\in \\mathbb{Z}^+$ and $\\varepsilon > 0$, it is NP-hard to decide: given a set of $\\{-1,1\\}$-labeled points in $\\mathbb{R}^n$ whether (YES Case) there exists a halfspace that classifies $(1-\\varepsilon)$-fraction of the points correctly, or (NO Case) any degree-$d$ PTF classifies at most $(1/2 + \\varepsilon)$-fraction of the points correctly. This strengthens to all constant degrees the previous NP-hardness of lea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01795","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"}