In this paper, we quantify the impact of using non-convergent Markov chains to train Energy-Based models (EBMs). In particular, we show analytically that EBMs trained with non-persistent short runs to estimate the gradient can perfectly reproduce a set of empirical statistics of the data, not at the level of the equilibrium measure, but through a precise dynamical process. Our results provide a first-principles explanation for the observations of recent works proposing the strategy of using short runs starting from random initial conditions as an efficient way to generate high-quality samples in EBMs, and lay the groundwork for using EBMs as diffusion models. After explaining this effect in generic EBMs, we analyze two solvable models in which the effect of the non-convergent sampling in the trained parameters can be described in detail. Finally, we test these predictions numerically on a ConvNet EBM and a Boltzmann machine.
Variational Transport: A Convergent Particle-BasedAlgorithm for Distributional Optimization
Princeton University（普林斯顿大学）；Northwestern University（西北大学）；Georgia Institute of Technology（佐治亚理工学院）；Simons Institute for the Theory of Computing（西蒙斯理论计算研究所）
A Neural Network MCMC sampler that maximizes Proposal Entropy
Redwood Center for theoretical Neuroscience（雷德伍德理论神经科学中心）；Department of Physics（物理系）；University of California Berkeley（加州大学伯克利分校）；Berkeley AI Research（伯克利人工智能研究中心）；Helen Wills Neuroscience Institute（海伦·威尔斯神经科学研究所）
MuseGNN: Forming Scalable, Convergent GNN Layers that Minimize a Sampling-Based Energy
New York University（纽约大学）；Southern University of Science and Technology（南方科技大学）；Fudan University（复旦大学）；UC Berkeley（加州大学伯克利分校）；Centre for Perceptual and Interactive Intelligence（感知与交互智能中心）；Amazon Web Services（亚马逊网络服务）
