On October 5, 2022, DeepMind announced AlphaTensor, a system that used deep reinforcement learning to discover new algorithms for multiplying matrices. Matrix multiplication is one of the most common operations in computing, underlying everything from graphics to neural network training, so faster algorithms have broad practical value. The work was published the same day in Nature as “Discovering faster matrix multiplication algorithms with reinforcement learning.”
AlphaTensor reframed the search for an algorithm as a single-player game built on the same AlphaZero foundations DeepMind used for chess and Go. The agent played in a space of tensor decompositions, where each valid decomposition corresponds to a provably correct multiplication algorithm and fewer steps means a faster algorithm.
The system found algorithms that improved on the long-standing state of the art. For multiplying a 4x5 matrix by a 5x5 matrix, AlphaTensor found a method using 76 scalar multiplications, against 80 for the previous best and 100 for the standard schoolbook approach. DeepMind reported that AlphaTensor improved on Strassen’s two-level algorithm in a finite field for the first time since Strassen published it in 1969, roughly fifty years earlier. The system also surfaced thousands of distinct correct algorithms per matrix size, showing the space was far richer than mathematicians had assumed.
AlphaTensor is an early example of AI used not to approximate an answer but to discover an exact, verifiable mathematical object that humans had missed. It sits alongside FunSearch and AlphaEvolve in DeepMind’s line of systems aimed at algorithmic and mathematical discovery.