DeepMind, Google’s artificial intelligence division, has discovered a faster way to do matrix multiplication, a central problem in computing that affects thousands of everyday tasks and whose previous record dates back 50 years.

DeepMind is always looking for new challenges, and after defeating the Go world champion, it plays checkers, chess, poker, or defeats human players in the multiplayer mode of the real-time strategy video game. Starcraft II wants to showcase its capabilities in other computationally intensive aspects.

For this, they used the board game AlphaZero with the intention of solving a basic mathematical program in computer science. The new challenge was matrix multiplication, a key type of computation at the heart of many applications, from displaying images on a screen to simulating complex physics. It is also fundamental to machine learning itself.

DeepMind and the ABCs of computing

Multiplying two matrices usually involves multiplying the rows of one by the columns of the other. Basic problem solving techniques are taught in high school. “It’s like the ABCs of computing”say the DeepMind AI for Science team.

But things get complicated when you try to find a faster method. “No one knows the best algorithm to solve this.” It is one of the biggest open problems in computing., clarify. This is because there are more ways to multiply two matrices than there are atoms in the universe (10 to 33). “The number of possible actions is almost infinite”says Thomas Hubert, an engineer at DeepMind.

To improve the calculation, the researchers used a new version of AlphaZero, a game that DeepMind used against people at Go or against chess grandmasters. To work with fields, they created a three-dimensional board game called TensorGame. The board simulates a multiplication problem, and each move represents the next step in solving the problem. The series of moves made in the game represents the algorithm and the reward is to win the game in the fewest number of moves possible.

The main result is that AlphaTensor has discovered a faster way to multiply two four-by-four matrices than the method proposed in 1969 by the German mathematician Volker Strassen. no one has been able to improve since then. If the basic high school method is 64 steps and the math method is 49, AlphaTensor found a way to do it in 47 steps.

A surprising result, they describe from the mathematical community. “Matrix multiplication is used everywhere in engineering and computer science. Anything you want to solve numerically, you usually use arrays», they explain. We will see its practical applications, but it is said to speed up this calculation it can have a huge impact on thousands of computing jobs daily, which reduces costs and saves energy.