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AlphaEvolve: 48 multiplications for 4×4 complex matrices

The AlphaEvolve report gives a 48-scalar-multiplication algorithm for multiplying 4×4 matrices over the complex numbers.

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Sources for this record

What was already known

Two levels of Strassen’s algorithm use 49 multiplications in this setting.

What changed and why it matters

A fixed-dimension improvement in complex arithmetic.

The AI contribution

Gemini-generated changes guide an evolutionary search for tensor decompositions.

Limitations

This does not establish a new asymptotic exponent or universal hardware speedup. It is not the same field as AlphaTensor’s F₂ result. AIProofWatch has not checked the decomposition.

Verification evidence

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

Author claim

Algorithm reported in §3.1; no independent check recorded here.

Correction and publication history

2026-10-11 · correction

Public discussion revealed that the novelty comparison needed the bilinear tensor-rank model. Clarify the baseline; retain notable importance. Non-notifying correction.

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