Bounds all around: training energy-based models with bidirectional bounds

Part of Advances in Neural Information Processing Systems 34 pre-proceedings (NeurIPS 2021)

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Authors

Cong Geng, Jia Wang, Zhiyong Gao, Jes Frellsen, Søren Hauberg

Abstract

Energy-based models (EBMs) provide an elegant framework for density estimation, but they are notoriously difficult to train. Recent work has established links to generative adversarial networks, where the EBM is trained through a minimax game with a variational value function. We propose a bidirectional bound on the EBM log-likelihood, such that we maximize a lower bound and minimize an upper bound when solving the minimax game. We link one bound to a gradient penalty that stabilizes training, thereby provide grounding for best engineering practice. To evaluate the bounds we develop a new and efficient estimator of the Jacobi-determinant of the EBM generator. We demonstrate that these developments significantly stabilize training and yield high-quality density estimation and sample generation.