Energy-based Model Training Objective Robust to Inaccurate SGLD Samples

Martin Sustek, Lukáš Burget

Keywords: EBM, Energy-based Model, Stochastic Gradient Langevin Dynamics, SGLD, Self-Normalizd Importance Sampling, SNIS, Joint Energy-based Model, JEM

Abstract: We propose a novel technique for training Energy-based Models (EBMs), which are neural network-based models capable of modeling complex probability distributions. The standard approach to EBM training relies on samples generated from the modeled distribution using Stochastic Gradient Langevin Dynamics (SGLD). However, this training method is known to be unstable, as SGLD may fail to provide reliable samples. Compared to other popular generative models, EBMs can directly evaluate unnormalized log-likelihoods for input observations. Unfortunately, trained EBMs typically fail to robustly estimate the likelihoods for distant input observations, as the training procedure only considers the gradients of the log-likelihood with respect to the observations and not the actual log-likelihood values. This paper proposes a generalization of the standard training objective that addresses both issues. The proposed objective explicitly incorporates estimated unscaled log-likelihoods, allowing the EBM to estimate the likelihoods more reliably. Notably, EBMs do not need to (and as we point out, cannot) correctly estimate log-likelihoods to be effective for sampling using the non-convergent SGLD procedure. The proposed objective is controlled by a single hyper-parameter, which balances the trade-off between the quality of the estimated log-likelihoods and the generated samples. A specific setting of this parameter recovers the standard EBM training objective. Moreover, the proposed objective enhances robustness to unreliable SGLD samples by de-weighting contributions from samples that appear inconsistent with the modeled distribution, i.e., samples with very low estimated likelihoods compared to other generated samples or real training data. We demonstrate the improvement in log-likelihood modeling on toy datasets and enhanced stability in a real data scenario, where this stability leads to better performance.

Primary Area: generative models

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Submission Number: 10072