Researchers at DeepMind have shown that AI can find shortcuts in a fundamental type of mathematical calculation
The AI that DeepMind developed — called AlphaTensor — was designed to perform a type of calculation called matrix multiplication. This involves multiplying numbers arranged in grids — or matrices — that might represent sets of pixels in images, air conditions in a weather model or the internal workings of an artificial neural network. To multiply two matrices together, the mathematician must multiply individual numbers and add them in specific ways to produce a new matrix.
Each game is a one-player puzzle that starts with a 3D tensor — a grid of numbers — filled in correctly. AlphaTensor aims to get all the numbers to zero in the fewest steps, selecting from a collection of allowable moves. Each move represents a calculation that, when inverted, combines entries from the first two matrices to create an entry in the output matrix. The game is difficult, because at each step the agent might need to select from trillions of moves.
“It has got this amazing intuition by playing these games,” said Pushmeet Kohli, a computer scientist at DeepMind, during the press briefing. Fawzi tellsthat “AlphaTensor embeds no human intuition about matrix multiplication”, so “the agent in some sense needs to build its own knowledge about the problem from scratch”.The researchers tackled larger matrix multiplications by creating a meta-algorithm that first breaks problems down into smaller ones.
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