Abstract: While score-based diffusion models have achieved remarkable success in high-dimensional generative modeling, some basic theoretical questions have not been precisely resolved. In this talk, we address minimax optimality of density estimation, functional estimation, and hypothesis testing. First, we show diffusion models achieve the optimal density estimation rate over Holder balls. This result is a…

Abstract: Moravec’s Paradox observes that AI systems have struggled far more with learning physical action than symbolic reasoning. Yet just recently, there has been a tremendous increase in the capability of AI-driven robotic systems, reminiscent  of the early acceleration in language modeling capabilities a few years prior.  Using the lens of control-theoretic stability, this talk…

Abstract: Spectral gradient methods, such as the recently proposed Muon optimizer, are a promising alternative to standard gradient descent for training deep neural networks and transformers. Yet, it remains unclear in which regimes these spectral methods are expected to perform better. In this talk, I will present a simple condition that predicts when a spectral update…

Abstract: Flow and diffusion models have become cornerstones of both scientific and industrial generative AI research. These methods work by construction of a dynamics that maps samples from a reference distribution to samples from a target distribution known empirically through data. An open question is how to best control and modify these dynamics so as…