Collaborative Research: MFAI: Mathematical Frontiers of Generative AI

Frontier AI models have pushed the boundaries of machine learning and artificial intelligence research and sparked transformative technological innovation in many US industries. These large-scale AI models are able to process and generate text, image, audio, and video, and currently require massive amounts of data and computing. This Mathematical Foundations of Artificial Intelligence (MFAI) project aims to uncover the mathematical principles that explain when and why these highly advanced AI models are so effective, and to overcome the fundamental limits of brute-force scale presently employed to surpass human expert intelligence in benchmarks. The project looks to advance the capabilities of AI models to conduct inference in new situations in which there is no training data, and to perform complex reasoning and problem-solving tasks. This research seeks to ensure that the US remains the global leader in AI, advancing economic prosperity, national security, and global competitiveness. This project aims to rigorously characterize the mathematical frontiers of generative AI models, including state-of-the-art large language models (LLMs), by developing new theoretical frameworks and modeling principles rooted in machine learning, probability theory, variational analysis, mathematical statistics, and information theory. The research will investigate how frontier AI models achieve remarkable performance despite fundamental theoretical barriers and will identify the key mathematical quantities that drive their generalization abilities. The project looks to develop new mathematical analyses of diffusion-based generative AI models, design novel data strategies for AI models used towards zero-shot inference, and discover scaling laws enabling models to achieve compute-optimal accuracy tradeoffs for inference and generation. This award is jointly funded by the Directorate for Mathematics and Physical Sciences, Division Of Mathematical Sciences; Directorate for Engineering, Division of Civil, Mechanical, & Manufacturing Innovation, and Directorate for Computer & Information Science & Engineering, Division of Computing and Communication Foundations and Division of Information & Intelligent Systems. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.