pretty much all progress in theoretical matmul comes from approximate decomposition tools, so results happen only when error is small enough to get fixed easily

pretty much all progress in theoretical matmul comes from approximate decomposition tools, so results happen only when error is small enough to get fixed easily - on large multiplications on the small side even optimal (3x3)(3x3) matmul is unknown more precisely than "between 19 and 23" - with only tiny progress lately in ruling out some symmetrical solutions (https://arxiv.org/html/2402.01011v1 https://arxiv.org/html/2402.01011v1)