Matrix multiplication sits beneath scientific computing, graphics, simulation and machine learning. Small improvements to its algorithms can ripple through an extraordinary range of systems.
AlphaTensor learned to play a single-player game: decompose the tensor that represents matrix multiplication using as few operations as possible. It rediscovered known methods and found new ones.
For multiplying 4×4 matrices over a finite field, it improved on a two-level application of Strassen’s algorithm—an advance against a benchmark that had resisted improvement for more than fifty years. The result is especially striking because every proposed algorithm can be checked exactly. This matrix multiplication is executed trillions of times a day to implement large language models (LLM), so this is a case of AI improving AI. Even this two percent improvement can save billions of dollars in AI infrastructure.
AI is not only recognizing patterns in existing knowledge. When answers can be rigorously verified, it can search beyond familiar human strategies and return genuinely new mathematics.
Discovering faster matrix multiplication algorithms with reinforcement learning, 610, 47–53
Nature · 2022
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