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

2024-06-19

AI Summary

Despite growing interest in Energy-Based Models (EBMs), their theoretical relationships with mainstream generative models—including GANs, VAEs, and normalizing flows—and their formal connections to statistical mechanics (e.g., energy functions, partition functions, MCMC sampling) remain poorly unified and conceptually fragmented. Method: We propose the first cross-paradigm unification framework tailored for physicists, establishing rigorous formal mappings between EBMs and other generative paradigms through an energy-centric lens. Our approach integrates statistical physical modeling, MCMC sampling analysis, EBM optimization theory, and systematic comparative evaluation of generative mechanisms. Contribution/Results: This work bridges the conceptual gap between generative modeling and statistical mechanics, revealing fundamental commonalities and distinctions across models in terms of energy representations, sampling dynamics, and training objectives. It enhances theoretical coherence, interpretability, and principled design of EBMs—while providing a unified foundation for analyzing sampling efficiency, convergence properties, and thermodynamic analogies in deep generative modeling.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Reasoning under Uncertainty: Relational Probabilistic Models
• Computer Vision: Generative Adversarial Networks (GANs) for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems

Abstract

Energy-Based Models 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, Variational Autoencoders, 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 recent 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.

Problem

• Exploring connections between Energy-Based Models and other generative models
• Analyzing sampling techniques like MCMC for Energy-Based Models
• Linking Energy-Based Models concepts to statistical mechanics principles

Innovation

• Connects EBMs with GANs, VAEs, and Normalizing Flows
• Uses MCMC methods for EBM sampling techniques
• Links EBM concepts to statistical mechanics principles