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The possible moves are fixed and correspond to algorithmic instructions. The player tries to modify the tensor so that the entries in it are 'zeroed out'. In the game, the 'board' is a three-dimensional tensor (number range) that records how far an algorithm is from the correct result in each case. The team had translated the problem of finding useful algorithms for matrix multiplication into a single-player game. Correspondence between the arithmetic operations (b) and the factors (c) is shown in colour. The stacked factors U, V and W (green, purple, yellow) result in a rank-7 decomposition of the tensor. The tensor indicates which entries are to be read from the input matrices and where the result is to be written. Entries equal to 1 are purple, 0 entries are semi-transparent. Tensor for matrix multiplication and algorithms: here multiplication of 2 x 2 matrices. The Strassen algorithm named after him is considered groundbreaking and is still often used in practice today. The search for faster algorithms to multiply two matrices is not trivial and has been occupying experts for about 50 years: In 1969, the mathematician, physicist and philosopher Volker Strassen found an improved method to multiply matrices of size two faster than the standard methods known until then. With AlphaTensor, DeepMind is apparently achieving another breakthrough, namely making progress in open questions of mathematics tangible through artificial intelligence (AI). Hassabis states that his company's goal is to develop AI that solves fundamental problems in science. Founded by British AI researcher, neuroscientist and computer game developer Demosthenes 'Demis' Hassabis, the company had already set milestones with AlphaGo and AlphaFold. The team gives the factor as a ten to twenty percent acceleration compared to previous standard methods.ĪlphaTensor builds on AlphaZero, an AI agent that proved superior to human players in board games such as Chess, Go and Shogi. AlphaTensor has already identified a new algorithm with which matrix multiplications can be carried out faster than before, as the research team explains in a paper published in the magazine Nature. With AlphaTensor, DeepMind Technologies has presented an AI system that is supposed to independently find novel, efficient and provably correct algorithms for complex mathematical tasks. ( Diesen Beitrag gibt es auch auf Deutsch.)

To the sources: DeepMind, Nature and beyond 'Using optimisations that would be difficult for humans'Īutomatic design of algorithms: not entirely new Implications for computer science and engineering

AlphaTensor: AI system speeds up matrix multiplication with new algorithmįinding algorithms: Tensor game for the AI agent

Signals and systems anand kumar pdf download