Algorithms have helped mathematicians perform basic operations for thousands of years. For example, the ancient Egyptians created an algorithm to multiply two numbers without requiring a multiplication table, and Greek mathematician Euclid described an algorithm to compute the greater common divisor, which is still in use today.  

In a recent DeepMind paper published in Nature, they introduced the first AI system for discovering novel, efficient and provably correct algorithms for fundamental tasks such as matrix multiplication. This sheds light on a 50-year-old open question in mathematics about finding the fastest way to multiply two matrices.

DeepMind's paper is a stepping stone to advancing science and unlocking the most fundamental problems using AI. They stated that AlphaTensor builds upon AlphaZero, an agent that has shown superhuman performance in board games like chess, Go, and shogi. This work shows the journey of AlphaZero, from playing games to tackling unsolved mathematical problems for the first time.   

Incredible results 

The result of the research is said to be ‘incredible’, as per the feedback received from the tech world. For the first time, one of the primary and fundamental algorithms of computing has been made more efficient. Moreover, this discovery was not due to human intuition but algorithms. 

Authors claim that even faster algorithms can be found. Therefore, we can certify that this discovery is only the beginning. More efficient algorithms will make computation wise, allowing for larger models and thus in a kind of positive loop. In addition, reducing the computational cost will enable others who do not have state-of-the-art infrastructure to use models with many parameters.  

Impact on future research   

DeepMind researchers expects AlphaTensor to create a significant impact on future research. From a mathematical point of view, the results can guide further research in complexity theory. It aims to determine the fastest algorithms for solving computational problems. For example, AlphaTensor aids in advancing our understanding of the richness of matrix multiplication algorithms. Studying this space may unlock new results for helping determine the asymptotic complexity of matrix multiplication, one of the most fundamental open problems in computer science.  

Matrix multiplications are the central component in several computational tasks. Mentioned following are some of the spaces where AlphaTensor will widely contribute: 

• Digital communications 
• Neural network training  
• Scientific computing 
• Spanning computer graphics 

The flexibility of the algorithms could make computations in these fields significantly more structured. The flexibility of AlphaTensor to consider any objective could spur new applications for designing algorithms that optimize metrics such as energy usage and numerical stability. It will help prevent minor rounding errors from snowballing as an algorithm works.  

The researchers also say that we can use their method to solve simple math problems, like figuring out other ways to measure rank and NP-hard matrix factorization problems.  

From the research, it is also evident that AlphaZero is a robust algorithm that can be extended well beyond the domain of traditional games to help solve problems in mathematics. DeepMind also looks forward to building upon its research and applying AI to help society solve some of the most critical challenges in mathematics and across the sciences.