arXiv:2611.04175 · v1

Semidirect sums of tensors and the matrix multiplication exponent

首次提交 2026-11-03 10:06

版本更新 2026-11-03 10:06

雷达观测 2026-11-04 23:40

摘要

This note is an exposition of the recent preprints from OpenAI that establish the bound $ω\leq 9/4$ on the matrix multiplication exponent. We argue that the heart of these preprints is a new technique, which we formulate as the untwisting lemma for semidirect sums of tensors. This gives a generally applicable method for analyzing tensors. We also discuss further consequences of this method, as well as the relation between the OpenAI proof and previous work.

作者备注：31 pages, 1 figure