{"paper":{"title":"A Two Pronged Progress in Structured Dense Matrix Multiplication","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Albert Gu, Atri Rudra, Christopher De Sa, Christopher R\\'e, Rohan Puttagunta","submitted_at":"2016-11-04T23:33:41Z","abstract_excerpt":"Matrix-vector multiplication is one of the most fundamental computing primitives. Given a matrix $A\\in\\mathbb{F}^{N\\times N}$ and a vector $b$, it is known that in the worst case $\\Theta(N^2)$ operations over $\\mathbb{F}$ are needed to compute $Ab$. A broad question is to identify classes of structured dense matrices that can be represented with $O(N)$ parameters, and for which matrix-vector multiplication can be performed sub-quadratically. One such class of structured matrices is the orthogonal polynomial transforms, whose rows correspond to a family of orthogonal polynomials. Other well kno"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01569","kind":"arxiv","version":3},"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"}