Extension of AlphaZero to Mathematics Unlocks New Possibilities
Algorithms have been an essential tool for mathematicians for centuries. From the algorithms created by the ancient Egyptians and Greek mathematicians to the new algorithms developed during the Islamic Golden Age, these computational methods have played a crucial role in solving equations and performing various mathematical operations. Despite their importance, the process of discovering new algorithms has always been challenging and limited to human reasoning abilities.
In a groundbreaking development, DeepMind introduces AlphaTensor, the first artificial intelligence system designed to discover novel and efficient algorithms for fundamental mathematical tasks. Published in Nature, this research sheds light on a longstanding question in mathematics about finding the fastest way to multiply matrices.
Matrix multiplication may seem like a simple operation, but it has a significant impact on the digital world and modern computing. It is used in image processing, speech recognition, simulations, data compression, and more. Companies invest substantial resources into developing hardware that can efficiently perform matrix multiplication. Therefore, even small improvements in this process can have wide-ranging effects.
For many years, mathematicians believed that the standard matrix multiplication algorithm was the most efficient one possible. However, in 1969, German mathematician Volker Strassen proved that better algorithms exist. His discovery, which involved combining matrix entries in a specific way, revolutionized the field. But the challenge remained for larger matrices, and it was unclear how efficiently one could multiply 3×3 matrices.
Using modern AI techniques, DeepMind’s AlphaTensor explored the automatic discovery of new matrix multiplication algorithms. The AI system surpassed human-designed algorithms and achieved greater efficiency for various matrix sizes. This breakthrough represents a significant advancement in algorithmic discovery.
The process of automating algorithmic discovery involved transforming the search for efficient matrix multiplication algorithms into a single-player game. AlphaTensor was trained using reinforcement learning, gradually improving its performance to outperform historical algorithms. It even discovered faster algorithms than those previously known.
AlphaTensor’s algorithms not only improved on Strassen’s algorithm for multiplying small matrices but also found a variety of state-of-the-art algorithms with different mathematical and practical properties. The system’s flexibility allowed it to optimize algorithms for specific hardware, making matrix multiplication faster.
This research has implications beyond the field of mathematics. It can guide further research in complexity theory and help determine the fastest algorithms for computational problems. Moreover, AlphaTensor’s algorithms can significantly enhance computational tasks in computer graphics, digital communications, neural network training, and scientific computing by making them more efficient. The system’s ability to optimize for different objectives opens doors to new applications, such as energy usage and numerical stability.
While this study focuses on matrix multiplication, it serves as inspiration for using AI in algorithmic discovery for other fundamental computational tasks. The possibilities are endless, and AI has the potential to enhance our understanding and solve complex problems in various fields.