Someone found a new algorithm for 4x4 matrix multiplication. .
This will save the industry billions.
Probably an overstatement. See the discussion of the previous AlphaTensor results: Matrix multiply breakthrough, AlphaTensor (could also do for other algorithms): "AlphaTensor discovered algorithms that are more efficient than the state of the art for many matrix sizes."
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Also… are they numerically stable? You not only need to care about performance but also the error growth of the new algorithms, and for Strassen’s it requires modifications to make that work:
AlphaEvolve didn’t have any measure of numerical stability, and lots of these “faster matrix multiplication” algorithms have difficulty in this area. So I would presume AlphaEvolve will have poor error growth behavior without extra changes and corrections, and those of course slow it down.
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