Hitchhiker's guide on Energy-Based Models: a comprehensive review on the relation with other generative models, sampling and statistical physics

Energy-Based Models (EBMs) have emerged as a powerful framework in the realm of generative modeling, offering a unique perspective that aligns closely with principles of statistical mechanics. This review aims to provide physicists with a comprehensive understanding of EBMs, delineating their connection to other generative models such as Generative Adversarial Networks (GANs), Variational Autoencoders (VAEs), and Normalizing Flows. We explore the sampling techniques crucial for EBMs, including Markov Chain Monte Carlo (MCMC) methods, and draw parallels between EBM concepts and statistical mechanics, highlighting the significance of energy functions and partition functions. Furthermore, we delve into state-of-the-art training methodologies for EBMs, covering recent advancements and their implications for enhanced model performance and efficiency. This review is designed to clarify the often complex interconnections between these models, which can be challenging due to the diverse communities working on the topic.

Wavelet Scattering Transform for Bioacustics: Application to Watkins Marine Mammal Sound Database

Marine mammal communication is a complex field, hindered by the diversity of vocalizations and environmental factors. The Watkins Marine Mammal Sound Database (WMMD) is an extensive labeled dataset used in machine learning applications. However, the methods for data preparation, preprocessing, and classification found in the literature are quite disparate. This study first focuses on a brief review of the state-of-the-art benchmarks on the dataset, with an emphasis on clarifying data preparation and preprocessing methods. Subsequently, we propose the application of the Wavelet Scattering Transform (WST) in place of standard methods based on the Short-Time Fourier Transform (STFT). The study also tackles a classification task using an ad-hoc deep architecture with residual layers. We outperform the existing classification architecture by $6\%$ in accuracy using WST and $8\%$ using Mel spectrogram preprocessing, effectively reducing by half the number of misclassified samples, and reaching a top accuracy of $96\%$.

Efficient Training of Energy-Based Models Using Jarzynski Equality

Energy-based models (EBMs) are generative models inspired by statistical physics with a wide range of applications in unsupervised learning. Their performance is best measured by the cross-entropy (CE) of the model distribution relative to the data distribution. Using the CE as the objective for training is however challenging because the computation of its gradient with respect to the model parameters requires sampling the model distribution. Here we show how results for nonequilibrium thermodynamics based on Jarzynski equality together with tools from sequential Monte-Carlo sampling can be used to perform this computation efficiently and avoid the uncontrolled approximations made using the standard contrastive divergence algorithm. Specifically, we introduce a modification of the unadjusted Langevin algorithm (ULA) in which each walker acquires a weight that enables the estimation of the gradient of the cross-entropy at any step during GD, thereby bypassing sampling biases induced by slow mixing of ULA. We illustrate these results with numerical experiments on Gaussian mixture distributions as well as the MNIST dataset. We show that the proposed approach outperforms methods based on the contrastive divergence algorithm in all the considered situations.