The DeepMind lab used AI AlphaZero to solve a fundamental problem in computer science and beat a record set more than 50 years ago. Technology Review reports.
Matrix multiplication is a fundamental type of computation underpinning a range of applications, from rendering images on a screen to modelling complex physical processes.
Despite its widespread use, the method is still not fully understood. A matrix is a grid of numbers that can represent almost anything. The basic technique for multiplying two such objects is taught in high school.
However, the challenge grows when attempting to find faster methods. Scientists say there are more ways to multiply two matrices than there are atoms in the universe.
“The number of possible actions is almost infinite,” said DeepMind engineer Thomas Hubert.
The researchers’ approach is to cast the task as a kind of tabletop game called TensorGame. The board represents the multiplication problem, and each move is aimed at solving it. In this way, the sequence of actions toward the final goal constitutes an algorithm.
Researchers then trained a new version of AlphaZero, named AlphaTensor, to play this game. Similar to chess or Go, the AI studied the best sequences of moves for multiplying matrices. AlphaTensor was rewarded for victory with the minimal number of moves.
“We turned this into a game — our favourite kind of framework,” said Hubert.
The main result is speeding up the solution. For example, the standard 4-by-4 matrix multiplication consists of 64 steps. The fastest method known in 1969 was discovered by German mathematician Volker Strassen: it consists of 49 moves. AlphaTensor did it in 47 moves.
According to the researchers, the DeepMind system outperforms the best existing algorithms for more than 70 different matrix sizes. They were impressed by the number of different correct algorithms found by AlphaTensor for each task.
“It is remarkable that there are at least 14,000 ways to multiply four-by-four matrices,” says Hussein Fauzi, a research scientist at DeepMind.
After identifying the fastest algorithms in theory, the team used AlphaTensor to search for algorithms on Nvidia V100 GPUs and Google TPU. According to the test results, the program found solutions 10-20% faster than standard methods on similar chips.
According to the researchers, this also has fundamental implications for machine learning itself. The acceleration of computation could have a large impact on thousands of everyday computing tasks, reducing costs and saving energy.
In the future, DeepMind plans to use AlphaTensor to discover other types of algorithms.
In July, the AI lab said that AlphaFold predicted the structures of more than 200 million proteins. This accounts for nearly all known protein structures identified in plants, bacteria and animals.
In May, DeepMind unveiled a visual-language model with 80 billion parameters.
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