Abstract: Estimating the score function—or other population-density-dependent functions —is a fundamental component of most generative models. However, such function estimation is computationally and statistically challenging. Can we avoid function estimation for data generation? We propose an estimation-free generative method: A set of points whose locations are deterministically updated with (inverse) gradient descent can transport a uniform distribution to arbitrary data distribution, in the mean field regime, without function estimation, training neural networks, and even noise injection. The proposed method is built upon recent advances in the physics of interacting particles. Leveraging recent advances in mathematical physics, we prove that the proposed method samples from the true underlying data distribution in the asymptotic regime.

Bio:  I am an Assistant Professor of Computer Science at the University of Virginia. My research focuses on the theoretical foundations of machine learning, with an emphasis on theoretical analysis for explainability and reliability of generative AI using tools from probability theory, applied mathematics, and mathematical physics. Prior to joining UVA, I was a FODSI postdoctoral researcher, hosted by MIT and Boston University. Before that, I served as a postdoctoral researcher at Princeton University as well as INRIA Paris. I completed my PhD in computer science at ETH Zurich in 2020. I had the privilege of being advised early in my research training by Professors Francis Bach and Thomas Hofmann.