Autoregressive Language Models are Secretly Energy-Based Models: Insights into the Lookahead Capabilities of Next-Token Prediction

2025-12-17

AI Summary

Autoregressive models (ARMs) and energy-based models (EBMs) have been studied in isolation, with their theoretical relationship—particularly regarding sequential decision-making and planning—remaining unclear. Method: This work establishes a rigorous functional-space equivalence between ARMs and EBMs, showing that ARMs implicitly satisfy the soft Bellman equation from maximum-entropy reinforcement learning. Leveraging the probability chain rule and soft optimal control theory, we derive a unified supervised learning objective and propose a provably bounded error distillation framework from EBMs to ARMs, with an analytically derived error upper bound. Contribution/Results: (1) We theoretically demonstrate that ARMs perform implicit sequential decision-making without explicit planning; (2) we provide a novel theoretical foundation for controllable text generation, alignment optimization, and reasoning enhancement in large language models; (3) we formally bridge generative modeling and reinforcement learning, unifying two major paradigms under a common variational and control-theoretic framework.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Reasoning under Uncertainty: Relational Probabilistic Models
• Multiagent Systems: Adversarial Agents

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

Autoregressive models (ARMs) currently constitute the dominant paradigm for large language models (LLMs). Energy-based models (EBMs) represent another class of models, which have historically been less prevalent in LLM development, yet naturally characterize the optimal policy in post-training alignment. In this paper, we provide a unified view of these two model classes. Taking the chain rule of probability as a starting point, we establish an explicit bijection between ARMs and EBMs in function space, which we show to correspond to a special case of the soft Bellman equation in maximum entropy reinforcement learning. Building upon this bijection, we derive the equivalence between supervised learning of ARMs and EBMs. Furthermore, we analyze the distillation of EBMs into ARMs by providing theoretical error bounds. Our results provide insights into the ability of ARMs to plan ahead, despite being based on the next-token prediction paradigm.

Problem

• Unify autoregressive and energy-based models theoretically
• Establish equivalence between ARM and EBM learning objectives
• Explain ARMs' lookahead capability via EBM connections

Innovation

• Establishes bijection between autoregressive and energy-based models
• Derives equivalence between supervised learning of both model types
• Analyzes distillation with theoretical error bounds