元翻转图遇见偶然乘积：新的快速矩阵乘法结果
Meta Flip Graph meets Serendipitous Product: new Fast Matrix Multiplication results
AI总结：
通过结合元翻转图框架与偶然乘积构造，在高达16×16×16的680种矩形格式中改进了206种格式的秩，发现了84种三元方案和23种具有指数ω<log₂7的新方案。
摘要：
本文展示了通过结合元翻转图框架与偶然乘积构造，在小格式快速矩阵乘法方面取得的新结果。该框架已扩展至支持所有维度高达16×16×16的680种矩形格式。与先前的最新技术相比，206种格式的秩得到了改进。对于84种格式，发现了三元方案，而之前仅已知整数或有理系数。此外，发现了23种具有渐近指数ω<log₂7的新方案，使得此类方案总数达到52种。所有研究格式中系数类型的总体分布为：375种三元、18种整数和287种有理。所有代码和发现的方案均以开源形式提供。
英文摘要：
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 207 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
