2023/12/26 by Qiang Fu, Fu, Qiang, Ashia Wilson +1 · 1 citation
Physics and Astronomy · Computer Science · Mathematics · #Model Reduction and Neural Networks #Adversarial Robustness in Machine Learning #Markov Chains and Monte Carlo Methods
paper · pdf · doi:10.48550/arxiv.2312.16360
We propose a new method called the N-particle underdamped Langevin algorithm for optimizing a special class of non-linear functionals defined over the space of probability measures. Examples of problems with this formulation include training mean-field neural networks, maximum mean discrepancy minimization and kernel Stein discrepancy minimization. Our algorithm is based on a novel spacetime discretization of the mean-field underdamped Langevin dynamics, for which we provide a new, fast mixing guarantee. In addition, we demonstrate that our algorithm converges globally in total variation distance, bridging the theoretical gap between the dynamics and its practical implementation.