Researchers at London-based DeepMind have shown that artificial intelligence (AI) can find shortcuts in a fundamental type of mathematical calculation, turning the problem into a game and then leveraging the machine-learning techniques used by another of the company's AIs to beat human players at games like Go and chess.
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Artificial intelligence has discovered algorithms that break decades-old records for computational performance, and the team's findings, published October 5 in Nature1, could open new avenues for faster calculations in some fields.
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“It’s very impressive,” says Martina Seidl, a computer scientist at Johannes Kepler University in Linz, Austria. “This work demonstrates the potential of using machine learning to solve difficult mathematical problems.”
Algorithms chasing algorithms
Increasingly, scientists are turning technology back on itself, using machine learning to improve its own algorithms.
The AI developed by DeepMind – called AlphaTensor – was designed to perform a type of calculation called matrix multiplication. This involves multiplying numbers arranged in grids – or arrays – that might represent sets of pixels in images, air conditions in a weather model or the inner workings of an artificial neural network. To multiply two arrays together, a mathematician must multiply individual numbers and add them in specific ways to create a new array. In 1969, mathematician Volker Strassen found a way to multiply a pair of 2×2 arrays using just seven multiplications rather than eight, prompting other researchers to look for more such tricks.
DeepMind’s approach uses a form of machine learning called reinforcement learning, in which an AI “agent” (often a neural network) learns to interact with its environment to achieve a multi-step goal, such as winning a board game. If it does well, the agent is reinforced — its internal parameters are updated to make future success.
AlphaTensor also incorporates a game method called tree search, in which the AI explores the outcomes of branching possibilities while planning its next action. By choosing which paths to prioritize during tree search, it asks a neural network to predict the most promising actions at each step. As the agent continues to learn, it uses the outcomes of its games as feedback to improve the neural network, which further improves the tree search.
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Each game is a single-player puzzle that starts with a 3D tensor – a grid of numbers – correctly filled in. AlphaTensor aims to zero out all numbers in the fewest number of moves, choosing from a collection of allowed moves. Each move represents a calculation that, when reversed, combines entries from the first two tables to create an entry in the output table. The game is difficult because at each step the agent may have to choose from trillions of moves.
Gray Ballard, a computer scientist at Wake Forest University in Winston-Salem, North Carolina, sees potential for future human-computer collaborations.
Information source: nature.com
