# More Asymmetry Yields Faster Matrix Multiplication

arXiv: https://arxiv.org/abs/2404.16349 · HTML: https://mlsanity.com/paper/2404.16349/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Apr 2024.

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## Abstract (arXiv)

We present a new improvement on the laser method for designing fast matrix multiplication algorithms. The new method further develops the recent advances by [Duan, Wu, Zhou FOCS 2023] and [Vassilevska Williams, Xu, Xu, Zhou SODA 2024]. Surprisingly the new improvement is achieved by incorporating more asymmetry in the analysis, circumventing a fundamental tool of prior work that requires two of the three dimensions to be treated identically. Together with recent advances in numerical optimization [Dupont et al. arXiv:2608.16884], the method yields a new bound on the square matrix multiplication exponent ω<2.371177, improved from the previous bound of ω<2.371552. We also improve the bounds of the exponents for multiplying rectangular matrices of various shapes.