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AlphaTensor: a 47-multiplication algorithm over F₂

The authors report an algorithm multiplying 4×4 matrices over the two-element field using 47 scalar multiplications, compared with 49 from two levels of Strassen’s algorithm.

Sources for this record

What was already known

Two levels of Strassen’s method use 49 scalar multiplications for this setting.

What changed and why it matters

A concrete improvement to a long-studied small-matrix computation, discovered through reinforcement learning.

The AI contribution

AlphaTensor uses reinforcement learning to search for tensor decompositions representing algorithms.

Limitations

This claim is specific to arithmetic over F₂ and fixed dimensions. It is not a new bound on the general asymptotic exponent, nor a universal wall-clock speedup.

Verification evidence

Evidence labels show what supports the claim. Importance rates its impact if correct.

Author claim

Claim reported by the authors.

Accessible artifact / proof

Authors’ public code and supporting material; not independently reproduced here.

Peer review

Published in Nature; peer review does not establish infallibility.

Correction and publication history