Post #3030771

@highergeometer@mathstodon.xyz I checked with one of the authors of the paper. There is indeed an oversimplification in how the results were presented. AlphaEvolve improved the ability to decompose the tensor corresponding to 4 x 4 complex matrix multiplication, giving a rank 48 decomposition instead of the previous record of 49. This also gives a way to express 4 x 4 complex matrix multiplication using only 48 scalar multiplications; however not every such expression arises from a tensor decomposition, which is what one needs if one is to iterate the operation in the style of Strassen to speed up the multiplication of very large matrices. So instead of AlphaEvolve being the first to multiply 4 x 4 matrices using 48 multiplications, they should have wrote they are the first to find a tensor decomposition of 4 x 4 matrix multiplication that uses 48 multiplications, which is a slightly different statement.