ORFE Professors Boris Hanin and Ludovic Tangpi have each received a National Science Foundation CAREER grant which is the “most prestigious award from the NSF in support of early-career faculty who have potential to serve as academic role models in research and education and to lead advances in the mission of their department or organization”. Professor Hanin’s proposal is titled “Random Neural Nets and Random Matrix Products”, and Professor Tangpi’s proposal is titled “A new form of propagation of chaos and its applications to large population games and risk management”.

Professor Hanin describes his 5-year project as follows: We live in an era of big data and cheap computation. Vast stores of information can efficiently be analyzed for underlying patterns by machine learning algorithms, leading to remarkable progress in applications ranging from self-driving cars to automatic drug discovery and machine translation. Underpinning many of these exciting practical developments is a class of computational models called neural networks. Originally developed in the 1940's and 1950's, the neural nets used today are as complex as they are powerful. This grant combines ideas from random matrix theory, stochastic processes, and perturbation theory to develop a range of principled techniques for understanding key aspects of how neural networks work in practice and how to make them better. Specifically, the proposed research seeks to answer questions such as: which network architectures and initialization schemes are numerically stable? which network architectures are capable of learning data-dependent features? why are deeper networks often better in practice?

Professor Tangpi describes his 5-year project as follows: Many examples of interactions around us can be modeled using particles systems. For instance, in financial economics when considering the systemic risk of default by a large number of banks engaged in inter-bank borrowing and lending, in urban planning when modeling commuters trying to find the shortest path while avoiding congestions, or in epidemiology when all members of a society join forces to reduce the spread of a virus. When the size of the population becomes very large, analyzing such systems pose serious analytical and computational challenges, and understanding the infinite population limit of such systems, referred to as propagation of chaos, becomes essential, providing a more tractable microscopic reformulation. This project investigates new aspects of this phenomenon for particle systems with known terminal configurations, and explains the link with active areas of applied mathematics including large population games, optimal transport and financial risk management.