AI provides mathematical breakthrough

Google subsidiary DeepMind Technologies has unveiled AlphaTensor, an AI system designed to independently find novel, efficient and provable algorithms for complex mathematical tasks. The AI has already identified a new algorithm that can perform matrix multiplications faster than before. The team published their findings in a paper at Nature. The team claims a ten- to twenty-fold speedup over previously known standard methods.

AlphaTensor builds on the AI AlphaZero, an AI that is significantly superior to humans at board games such as chess, Go, and shogi. According to its founder Demosthenes "Demis" Hassabi, DeepMind's goal is to develop AI that solves fundamental problems in science. With AlphaTensor, DeepMind achieves another breakthrough. The company had already made breakthroughs with AlphaGo and AlphaFold.

Faster algorithms

The search for faster algorithms for matrix multiplication is not trivial and has been occupying the scientific community for 50 years. In 1969, the mathematician, physicist and philosopher Volker Strassen had found an improved method to multiply matrices faster than the methods known until then.The Strassen algorithm named after him is considered groundbreaking and is still often used in practice today. AlphaTensor is a maximum of 4.2 percent faster compared to the Strassen calculation method when it comes to matrices with 8,192 x 8,192 elements. For 20,480 x 20,480 elements, the new algorithm is 2.6 percent faster. For the multiplication of much smaller matrices, the easily implemented and widely used calculation path will certainly continue to be used.

Finding algorithms as a game

The approach Deepmind used to find a solution is a game: Instead of finding the best paths in a game of chess or Go, the system calculated individual calculation steps in the three-dimensional game Tensorgame. Whenever the software found a shorter path, it was rewarded. The positive feedback was then used for further attempts. In the end, the series of moves resulted in an efficient way for matrix multiplication.