A Matrix Multiplication Permutation Law More Suitable for Computers

Matrix multiplication, as the core fundamental operation of AI, has always been a bottleneck in its development due to its high computational complexity. In the 50 years since the Strassen algorithm was proposed, the academic community has been using the laser method under the Coppersmith Winograd tensor decomposition theory framework. The laser method has approached its theoretical limit, and in order to further improve, it is necessary to improve on the original method of the laser method. This study proposes a breakthrough solution, which involves replacing the positions of the elements in the second half of the A and B matrices in advance, recombining the matrices, and then multiplying them together. It has discovered a faster matrix multiplication algorithm, marking the first time we have found a new method outside of the laser method. This will become a new direction for studying fast matrix multiplication.