AlphaTensor: DeepMind’s AI System for Discovering Faster Matrix Multiplication Algorithms

DeepMind has introduced AlphaTensor, an AI system built on the AlphaZero architecture and reinforcement learning, designed to automatically discover efficient matrix multiplication algorithms.

Historically, algorithms for basic operations have evolved from ancient Egyptian methods to modern breakthroughs such as Strassen’s algorithm, which showed that the standard matrix multiplication is not optimal.

AlphaTensor treats the search for faster algorithms as a single‑player game where a three‑dimensional tensor represents the current state of an algorithm; the agent makes moves that modify the tensor, aiming to reduce it to zero, which corresponds to a correct multiplication algorithm.

Training from scratch, AlphaTensor rediscovered known fast algorithms (e.g., Strassen) and uncovered new ones that require fewer scalar multiplications—for example, reducing the count for a 4×5 by 5×5 multiplication from 100 to 76 multiplications.

The system also found algorithms that improve upon Strassen’s method over finite fields and generated thousands of diverse algorithms for various matrix sizes, some of which are optimized for specific hardware such as Nvidia V100 GPUs or Google TPU v2, yielding 10‑20% speedups on large‑scale multiplications.

These results demonstrate that AI‑designed algorithms can surpass human‑crafted ones, offering insights into the richness of the algorithmic space and promising efficiency gains for graphics, communication, neural‑network training, and scientific computing.

DeepMind envisions extending this approach to other fundamental computational problems, using AI to tackle some of the most challenging mathematical and scientific questions.