Agent search drops matrix multiplication exponent below 2.7 at ~500M matrix size
IgorCarron · x · 2026-10-18
Antoine Tilloy shared an upper-bound curve from his agent-driven search for matrix multiplication algorithms: the earliest size where the exponent drops below 2.7 is around 500 million (possibly a record, though agents may have missed better results).
Igor Carron argues engineering is where this new era will yield the most breakthroughs. Matmul is deeply pursued by hardware makers themselves, so external breakthroughs there are unlikely—but large gains remain for specific matrix classes (certain sparsity patterns). He draws an analogy to FFT, whose implementations long ago split into size-dependent algorithms (radix, Bluestein, Rader), as shown in a VkFFT vs cuFFT bandwidth benchmark; FFT itself likely still has some alpha left.
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