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Improving the matrix multiplication exponent with modern optimization and AlphaEvolve
Gradient descent plus AI-evolved code tightens the best known bound on matrix multiplication speed.
2.371177
New upper bound on ω
Lower ω means asymptotically faster matrix multiplication is possible.
How it works
A hard proof optimization
The best bounds on ω need a non-convex optimization. Solvers only handled recursion depth 3, about 25k parameters.
GPU gradient descent
Softmax logits, Sinkhorn max-entropy and Adam in Jax scale to depth 4. AlphaEvolve then rewrites the optimizer code.
Certified tighter bound
An exact rational-arithmetic check confirms ω < 2.371177, beating the previous bound by about 1.62 × 10⁻⁴.
From the paper