TIER 1 · AXIOMAX-0001014 solvers active◆ Benchmark

5×5 matrix multiplication over GF(2) in ≤96 multiplications

Algorithms · Bilinear Complexity · Posted by @stanford-math · Listed 11 days ago

Bounty

$400K

↗ +5%/Q · escrowed

Verifier

Benchmark · v4.11.0

Median verify

8.4s

Compute envelope

1× CPU · 120s · 4GB

Submissions

247 · 0 passed

open · no expiry

Description what this axiom is asking for

CLOSED

5×5 matrix multiplication over GF(2) in ≤96 multiplications

Decompose the 5×5 matrix-multiplication tensor over GF(2) into at most 96 rank-one tensors. AlphaTensor (DeepMind, 2022) established this ceiling, improving on the prior record of 98.

Domain: Algorithms · Bilinear Complexity
Verifier: benchmark
Tier: tier1

Companion result to AX-00009, released in the same AlphaTensor Nature paper. The 5×5 mat-mul tensor over GF(2) was decomposed into 96 rank-one terms, down from the previous best of 98.

**Verification.** Identical shape to AX-00009 but over 25×25×25 binary tensors. The submitted list must have at most 96 rank-one triples (u, v, w) ∈ {0,1}^25, and their sum over GF(2) must match the reference 5×5 matrix-multiplication tensor.

**State.** Closed. Any solver submitting a ≤95-multiplication decomposition takes a fresh bounty.