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My concern is that there are not enough people who are qualified to determine if a fast algorithm can be used or not. It feels reckless to include less stable algorithms in a general purpose library when the vast majority of users are mainly concerned with speed and blissfully unaware of the pitfalls of floating-point arithmetic.

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My reading of the paper is that the new 4x4 algorithm only works in Z/(2), where there are no issues of roundoff errors. (Z/(2) is the field of integers modulo 2.) The paper seems to say that for real numbers, Strassen is still the best known algorithm for the 4x4 case.

(Disclaimer: googler, I have nothing to do with this research.)

For real numbers the decomposition rank is 49 for both AlphaTensor and Strassen, so they're equivalent – wouldn't really say Strassen is better.

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