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October 7, 2022

If you just want the executive summary, here it is: these are definitely interesting algorithms from an arithmetic complexity theory standpoint – especially for the case of 4×4 matrices over finite fields, where (to the best of my knowledge) Strassen’s algorithm from 1969 was still the reigning champion. These algorithms are also practically relevant, meaning that not only do they have better asymptotic lower bounds than Strassen’s algorithm, they are still algorithms you might actually use in practice, unlike essentially everything else that has been written on the topic in the last 50 years: these algorithms are correct, and will in principle win over Strassen’s algorithm with large enough matrices, but that cut-off is well beyond the sizes that anyone is actually doing computations with. — On AlphaTensor’s new matrix multiplication algorithms