Meta Flip Graph meets Serendipitous Product: new Fast Matrix Multiplication results

Abstract: This paper presents new results for fast matrix multiplication in small formats obtained by combining the meta flip graph framework with the serendipitous product construction. The framework has been extended to support all 680 rectangular formats with dimensions up to $16 \times 16 \times 16$. Compared to the previous state of the art, ranks are improved for 206 formats. For 84 formats, ternary schemes are found where previously only integer or rational coefficients were known. Additionally, 23 new schemes with asymptotic exponent $ω< \log_2 7$ are discovered, bringing the total number of such schemes to 52. The overall distribution of coefficient types across all investigated formats is 375 ternary, 18 integer, and 287 rational. All code and discovered schemes are available as open source.