{"paper":{"title":"Faster Convolutions: Yates and Strassen Revisited","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Baitian Li, Cornelius Brand, Kevin Pratt, Radu Curticapean","submitted_at":"2025-05-28T14:38:22Z","abstract_excerpt":"Given two vectors $u,v \\in \\mathbb{Q}^D$ over a finite domain $D$ and a function $f : D\\times D\\to D$, the convolution problem asks to compute the vector $w \\in \\mathbb{Q}^D$ whose entries are defined by $w(d) = \\sum_{\\substack{x,y \\in D \\\\ f(x,y)=d}} u(x)v(y).$ In parameterized and exponential-time algorithms, convolutions on product domains are particularly prominent: Here, a finite domain $B$ and a function $h : B \\times B \\to B$ are fixed, and convolution is done over the product domain $D = B^k$, using the function $h^k :D \\times D\\to D$ that applies $h$ coordinate-wise to its input tuple"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.22410","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.22410/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}