An anonymous reader quotes a report from MIT Technology Review: DeepMind has used its board-game playing AI AlphaZero to discover a faster way to solve a fundamental math problem in computer science, beating a record that has stood for more than 50 years. A year after it took biologists by surprise, AlphaFold has changed how researchers work and set DeepMind on a new course. The problem, matrix multiplication, is a crucial type of calculation at the heart of many different applications, from displaying images on a screen to simulating complex physics. It is also fundamental to machine learning itself. Speeding up this calculation could have a big impact on thousands of everyday computer tasks, cutting costs and saving energy. Despite the calculation's ubiquity, it is still not well understood. A matrix is simply a grid of numbers, representing anything you want. Multiplying two matrices together typically involves multiplying the rows of one with the columns of the other. The basic technique for solving the problem is taught in high school. But things get complicated when you try to find a faster method. This is because there are more ways to multiply two matrices together than there are atoms in the universe (10 to the power of 33, for some of the cases the researchers looked at).
The trick was to turn the problem into a kind of three-dimensional board game, called TensorGame. The board represents the multiplication problem to be solved, and each move represents the next step in solving that problem. The series of moves made in a game therefore represents an algorithm. The researchers trained a new version of AlphaZero, called AlphaTensor, to play this game. Instead of learning the best series of moves to make in Go or chess, AlphaTensor learned the best series of steps to make when multiplying matrices. It was rewarded for winning the game in as few moves as possible. [...] The researchers describe their work in a paper published in Nature today. The headline result is that AlphaTensor discovered a way to multiply together two four-by-four matrices that is faster than a method devised in 1969 by the German mathematician Volker Strassen, which nobody had been able to improve on since. The basic high school method takes 64 steps; Strassen's takes 49 steps. AlphaTensor found a way to do it in 47 steps.
"Overall, AlphaTensor beat the best existing algorithms for more than 70 different sizes of matrix," concludes the report. "It reduced the number of steps needed to multiply two nine-by-nine matrices from 511 to 498, and the number required for multiplying two 11-by-11 matrices from 919 to 896. In many other cases, AlphaTensor rediscovered the best existing algorithm."
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