Behrooz Tahmasebi Explains Weyl’s Law and Its Relevance to AI
Behrooz Tahmasebi, an MIT PhD student in the Department of Electrical Engineering and Computer Science (EECS), had a lightbulb moment during a mathematics course on differential equations in late 2021. He learned about Weyl’s law and realized it could be useful for a computer science problem he was working on involving artificial intelligence.
Tahmasebi thought about using Weyl’s law to measure the complexity of input data to a neural network and whether it could reduce this complexity by considering the symmetries inherent to the dataset. His advisor, Stefanie Jegelka, thought this was a promising idea. They were able to modify Weyl’s law to factor in symmetry when assessing a dataset’s complexity. Their groundbreaking work on this was presented at the December 2023 conference on Neural Information Processing Systems.
They discovered that by exploiting a dataset’s intrinsic symmetries, they could reduce the complexity of machine learning tasks and the amount of data needed for learning. This could lead to a significant improvement in the efficiency of AI processes.
In their research, they proved two theorems mathematically, one showing that an improvement in sample complexity is possible with the algorithm they provide, and the other demonstrating that this is the best possible gain achievable.
Their formula for predicting the gain from specific symmetries could have broad applications in AI, even for symmetries that are yet to be discovered. According to Haggai Maron, a computer scientist at Technion, their work diverges substantially from previous research and provides a theoretical basis for further developments in Geometric Deep Learning.
Tahmasebi and Jegelka’s work opens up new possibilities for enhancing machine learning through symmetry and has the potential to revolutionize the field of artificial intelligence.