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Paper:

TR26-298 | 3rd November 2026 02:43

Semidirect sums of tensors and the matrix multiplication exponent

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TR26-298
Authors: Baitian Li
Publication: 4th November 2026 07:50
Downloads: 13
Keywords: 


Abstract:

This note is an exposition of the recent preprints from OpenAI that establish the bound $\omega \leq 9/4$ 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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