{"paper":{"title":"Degree-$d$ Chow Parameters Robustly Determine Degree-$d$ PTFs (and Algorithmic Applications)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS","stat.ML"],"primary_cat":"cs.LG","authors_text":"Daniel M. Kane, Ilias Diakonikolas","submitted_at":"2018-11-07T17:59:16Z","abstract_excerpt":"The degree-$d$ Chow parameters of a Boolean function $f: \\{-1,1\\}^n \\to \\mathbb{R}$ are its degree at most $d$ Fourier coefficients. It is well-known that degree-$d$ Chow parameters uniquely characterize degree-$d$ polynomial threshold functions (PTFs) within the space of all bounded functions. In this paper, we prove a robust version of this theorem: For $f$ any Boolean degree-$d$ PTF and $g$ any bounded function, if the degree-$d$ Chow parameters of $f$ are close to the degree-$d$ Chow parameters of $g$ in $\\ell_2$-norm, then $f$ is close to $g$ in $\\ell_1$-distance. Notably, our bound relat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03491","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"}