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arXiv · 2611.04175

Semidirect sums of tensors and the matrix multiplication exponent

Baitian Li
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Abstract

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.

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Baitian Li. 2026-11-03. Semidirect sums of tensors and the matrix multiplication exponent. https://arxiv.org/abs/2611.04175

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