DeepMind uses matrix math to automate discovery of better matrix math techniques

Google-owned DeepMind has applied reinforced learning techniques to the multiplication of mathematical matrices, beating some human-made algorithms that have lasted 50 years and working toward improvements in computer science.

Founded in London in 2010, DeepMind has become famous for beating the world champion at board game Go with its AlphaGo AI and taking on the mind-bogglingly complex challenge of protein folding with AlphaFold.

In a wheels-within-wheels move, it has since set its sights on mathematical problems themselves.

A successful project has been to automate the discovery of algorithms which act as shortcuts when multiplying matrices - the cause of headaches for many a teenage math student.

For years, mathematicians have been applying algorithms to these complex array multiplications, some of which are used in computer science.

DeepMind researcher Alhussein Fawzi and his colleagues used deep reinforcement to rediscover earlier algorithms and find new ones. The technique created a system, dubbed AlphaTensor, which plays a game in which the goal is to find the best approach to multiplying two matrices. If the AI agent does well, it is reinforced to make future success more likely.

We note that this AI agent was likely using matrix math in its learning process and in inference; matrix operations to find faster ways to do matrix operations.

In this case, the agent takes on puzzles in the form of a 3D tensor or a grid of numbers, which it must complete in the fewest moves. Each step represents a move in solving the matrix-based puzzle, which might contain trillions of possible moves.

Fawzi told a press briefing this week that mapping out the space of algorithmic discovery was tough work, although navigating it was even more difficult. Nonetheless, the resulting research developed new algorithms for problems which have not been improved on in more than 50 years of human research, he said.

The researchers claim the technique could benefit computational tasks that use multiplication algorithms as well as demonstrate how reinforcement learning can be used to find new and unexpected solutions to known problems, while also noting some limitations. For example, predefined components are necessary to avoid the system missing a subset of efficient algorithms.

Skeptics may point to the application of AlphaFold, which promised breakthroughs in drug discovery via AI-supported protein research. Although the model has predicted nearly all known protein structures discovered, its ability to help scientists discover new drugs remains unproven. ®

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