OpenAI 证明矩阵乘法指数 ω≤9/4，新论文梳理其核心引理
Semidirect sums of tensors and the matrix multiplication exponent
OpenAI 这次不是发模型，是证明了矩阵乘法指数降到 9/4，这篇短文帮你拆解它到底用了什么数学技巧。
OpenAI 的预印本给出矩阵乘法指数上界 ω≤9/4 的新证明。这篇 arXiv 文章将该证明的核心提炼为半直和张量的解缠引理（untwisting lemma）。作者把这一方法整理成分析张量的通用工具，并讨论了它与此前进展的关系。
Semidirect sums of tensors and the matrix multiplication exponent
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.
