Alphabet Inc.’s DeepMind unit today detailed AlphaTensor, an artificial intelligence system capable of discovering new algorithms that can be used to solve mathematical problems.

DeepMind researchers have used AlphaTensor to develop a new way of performing matrix multiplications. A matrix multiplication is a type of calculation that AI applications and certain other programs use extensively while processing data. According to DeepMind, AlphaTensor has found a method of carrying out matrix multiplications faster than was possible until now. 

AlphaTensor is based on an AI system dubbed AlphaZero that DeepMind first debuted in 2018. AlphaZero is designed to play board games such as chess, Go and shogi. DeepMind has made a series of upgrades to the AI system that enable it to tackle complex mathematical problems. 

Matrix multiplications, the calculations that DeepMind sped up using its newly debuted AlphaTensor system, are a type of mathematical operation that involves matrices. A matrix is a collection of numbers arranged in rows and columns similarly to a spreadsheet. A matrix multiplication is a calculation that uses two matrices to generate a third matrix.

Mathematicians carried out matrix multiplications in one specific way for centuries until the 1960s, when a new, faster method of performing such calculations was discovered. However, that faster method can only be applied to certain types of matrix multiplications involving relatively few numbers. Moreover, “larger versions of this problem have remained unsolved,” DeepMind researchers detailed in a blog post today.

According to DeepMind, its AlphaTensor system has discovered an improved version of the faster matrix multiplication method. Moreover, the AI generated thousands of entirely new algorithms for performing matrix multiplications. Some of those algorithms are optimized to run on specific types of hardware such as Nvidia Corp. graphics cards.

To build AlphaTensor, DeepMind researchers developed a new approach to algorithm discovery. 

The researchers turned the task of discovering new matrix multiplication algorithms into a game dubbed TensorGame. To win the game, an AI system must complete a complex mathematical operation as a tensor decomposition. Completing the tensor decomposition not only allows the AI system to win the game, but also generates a new matrix multiplication algorithm in the process.

DeepMind equipped AlphaTensor with a neural network architecture specifically optimized for algorithm discovery. Then, the Alphabet unit trained the AI system using a method known as reinforcement learning. The method involves improving a neural network’s accuracy through trial and error by having it repeatedly perform a certain task.

Using AlphaTensor, DeepMind managed to discover a more efficient version of one of the fastest known algorithms for solving matrix multiplications. “For example, if the traditional algorithm taught in school multiplies a 4×5 by 5×5 matrix using 100 multiplications, and this number was reduced to 80 with human ingenuity, AlphaTensor has found algorithms that do the same operation using just 76 multiplications,” DeepMind researchers detailed.

AlphaTensor also discovered thousands of new matrix multiplication algorithms. As part of the project, DeepMind customized AlphaTensor to develop algorithms that are optimized to run on specific chips such as Nvidia’s V100 graphics card and TPU v2, an AI chip developed by Google LLC. Those algorithms run up to 20% faster than existing matrix multiplication methods, according to the Alphabet unit. 

“Because matrix multiplication is a core component in many computational tasks, spanning computer graphics, digital communications, neural network training, and scientific computing, AlphaTensor-discovered algorithms could make computations in these fields significantly more efficient,” DeepMind’s researchers explained. “AlphaTensor’s flexibility to consider any kind of objective could also spur new applications for designing algorithms that optimise metrics such as energy usage.”

Image: DeepMind