More Asymmetry Yields Faster Matrix Multiplication
<|reference_start|>More Asymmetry Yields Faster Matrix Multiplication: 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. The method yields a new bound on the square matrix multiplication exponent $$\omega<2.371339,$$ improved from the previous bound of $\omega<2.371552$. We also improve the bounds of the exponents for multiplying rectangular matrices of various shapes.<|reference_end|>
@article{alman2024more,
    title={More Asymmetry Yields Faster Matrix Multiplication},
    author={Josh Alman, Ran Duan, Virginia Vassilevska Williams, Yinzhan Xu,
  Zixuan Xu, Renfei Zhou},
    journal={arXiv preprint arXiv:2404.16349},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.16349},
    primaryClass={cs.DS cs.CC}
}