How to solve a Rubik’s Cube in as few moves as possible

Wednesday, November 23, 2022 • 11:00 EST

Except that for a Rubik’s Cube, the number of possible moves at each step is 18; for matrix multiplication, even in relatively simple cases, every step can present more than 1012 options. Last month, a team at the artificial intelligence company DeepMind showed how to tackle the problem from a new direction, reporting in a paper in Nature that they’d successfully trained a neural network to discover new fast algorithms for matrix multiplication. The standard recipe for multiplying two n-by-n matrices requires n3 multiplication operations, so a 2-by-2 matrix, for example, requires eight multiplications. But he and other matrix multiplication specialists also emphasized that such AI assistance will complement rather than replace existing methods — at least in the near term. It was as if the AI had found an unknown strategy for solving a monstrously complex Rubik’s Cube. But not everyone in the matrix multiplication community was so impressed. Matrix multiplication is one of the most fundamental and ubiquitous operations in all of mathematics. And the steps it took to get there can be translated back into steps of the corresponding matrix multiplication algorithm. ( Continue reading.

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