AlphaTensor: Discovering faster matrix multiplication algorithms with RL

Matej Balog

Improving the efficiency of algorithms for fundamental computational tasks such as matrix multiplication can have widespread impact, as it affects the overall speed of a large amount of computations. Automatic discovery of algorithms using ML offers the prospect of reaching beyond human intuition and outperforming the current best human-designed algorithms. In this talk I’ll present AlphaTensor, our RL agent based on AlphaZero for discovering efficient and provably correct algorithms for the multiplication of arbitrary matrices. AlphaTensor discovered algorithms that outperform the state-of-the-art complexity for many matrix sizes. Particularly relevant is the case of 4?×?4 matrices in a finite field, where AlphaTensor’s algorithm improves on Strassen’s two-level algorithm for the first time since its discovery 50 years ago. I’ll present our problem formulation as a single-player game, the key ingredients that enable tackling such difficult mathematical problems using RL, and the flexibility of the AlphaTensor framework.

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