Game AI AlphaZero discovered a new way to multiply matrices for the first time in 50 years

Game AI AlphaZero discovered a new way to multiply matrices for the first time in 50 years

The AlphaZero artificial intelligence system developed by DeepMind, originally designed for desktop games, has offered a faster way to multiply matrices, a fundamental mathematical problem for which there have been no new solutions for more than 50 years.

The task of multiplying matrices is at the heart of a range of applications, ranging from putting the image on the screen to modelling complex physics, as well as learning the most artificial intelligence. Optimizing this task would help to simplify many computer operations by reducing costs and saving energy. Despite the widespread proliferation of the task, it is still under-explored.

The matrix is a set of numbers, and the multiplication of matrices is usually a sequenced multiplication of numbers in rows one by number in columns of another. The task seems relatively simple, but it is significantly complicated when trying to find an accelerated method to solve it, and this is an open problem in informatics. It is assumed that the number of available ways of multiplying matrices is larger than the number of atoms in the universe — in some cases, up to 1,033 options.

In order to "interest" the AlphaTensor, a new version of AlphaZero, the task of multiplying the matrices was turned into a kind of desktop game, each action of multiplication compared to the game move, and II received a win award with a minimum number of moves. As a result, AlphaTensor found a new way to multiply the 4×4 matrices more efficiently than the German Volker Strassen suggested in 1969. The basic method is to solve the problem in 64 steps, Strassen has 49 steps, and AlphaTensor is managing 47 steps. In general, IA improved the algorithms for matrices over 70 sizes: at 9×9, the number of steps decreased from 511 to 498, and at 11×11 from 919 to 896. In a number of other cases, AlphaTensor repeated the best known algorithms.

With the results, DeepMind engineers decided to adapt them to the NVIDIA V100 and Google TPU accelerators, which are most commonly used in machine learning.