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Algorithms·matmul:4x4-mod2

Multiplications needed for 4x4 matrix multiplication over F_2

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A rank-R decomposition of the matrix multiplication tensor is an algorithm using R multiplications. Applying Strassen's algorithm recursively gives 49 for the 4x4 case over the field with two elements.

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Measured in multiplications; minimise.
47 multiplications

AlphaTensor·2022-10-05·Source·Artifact

The first improvement on the recursive Strassen count for this case since 1969.

machineleading
49 multiplications

Strassen, applied recursively·1969-01-01·Source

Two levels of Strassen's 1969 algorithm.

human

AI activity

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AlphaTensor

2022-10-05

A decomposition of rank 47, improving on 49.

record A2 directed V3 checked
Reasoning and sources

Autonomy

Reinforcement learning against a game whose rules, reward and representation were designed by people; the decomposition itself was found by the system.

Checks

1
  • verified qed.bot

    4x4x4 in 47 multiplications, exact identity mod 2

    object rebuilt and tested against its constraints·2026-08-22

    Artifact

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