Did you know that AI can, by itself, find ways to multiply matrices faster than the ones we’ve been using for 50 years?

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By Nicolás Moreira

October 14, 2022

DeepMind, a division of Google that develops cutting-edge machine learning tools for solving human challenges, has recently published AlphaTensor, an AI algorithm to find much more efficient ways to multiply matrices. This operation, which might sound a bit nerdy and specific, is actually an essential piece in video games and communication engines, and is certainly quite computationally demanding.

For centuries, mathematicians have invested a lot of time trying to figure out faster ways to multiply matrices. Nevertheless, the existing ways to do so are still slow. As an example, one of these renowned scientists, Volker Strassen, devised an algorithm 50 years ago that accelerated this process for 2×2 matrices. Our current applications, however, are based on matrices with much larger dimensions, which we still don’t know how to multiply efficiently.

Data scientists at DeepMind came to turn that table. They built on top of AlphaZero, a neural network that learns by itself how to play board games like chess and has beaten some of the greatest players in the world. To use it, they mapped the matrix multiplication problem into a single-player game in which the AI had to find by itself small sets of instructions to rapidly obtain accurate matrix multiplications. The search is driven by an iterative process in which the model is rewarded every time its answer is faster and better. Starting from not knowing at all how to multiply matrices, AlphaTensor incrementally improved itself, reaching first the very same set of operations we learned to use in Linear Algebra courses, then reproducing some other ingenious ways designed for specific matrix sizes, and finally producing much better algorithms with fewer steps.

This rewarding strategy is known as reinforcement learning, and is essentially the same thing we do when we train our dogs: an AI agent decides to take actions over a predefined environment, and an interpreter provides it with a reward every time the resulting state is improved. These algorithms have been increasingly used in applications beyond gaming, including autonomous driving, stock trading or even for training robots!

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