{"paper":{"title":"Decision Trees, Protocols, and the Fourier Entropy-Influence Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Andrew Wan, Chenggang Wu, John Wright","submitted_at":"2013-12-11T00:15:28Z","abstract_excerpt":"Given $f:\\{-1, 1\\}^n \\rightarrow \\{-1, 1\\}$, define the \\emph{spectral distribution} of $f$ to be the distribution on subsets of $[n]$ in which the set $S$ is sampled with probability $\\widehat{f}(S)^2$. Then the Fourier Entropy-Influence (FEI) conjecture of Friedgut and Kalai (1996) states that there is some absolute constant $C$ such that $\\operatorname{H}[\\widehat{f}^2] \\leq C\\cdot\\operatorname{Inf}[f]$. Here, $\\operatorname{H}[\\widehat{f}^2]$ denotes the Shannon entropy of $f$'s spectral distribution, and $\\operatorname{Inf}[f]$ is the total influence of $f$. This conjecture is one of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3003","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"}