Autoregressive Language Models are Secretly Energy-Based Models: Insights into the Lookahead Capabilities of Next-Token Prediction
This work provides foundational insights for researchers in machine learning and AI, particularly those working on language models and alignment, by unifying two major model classes and offering theoretical bounds for distillation.
The paper establishes a theoretical equivalence between autoregressive language models (ARMs) and energy-based models (EBMs), showing they are bijectively related through probability theory and reinforcement learning principles, which explains how ARMs can exhibit lookahead capabilities despite focusing on next-token prediction.
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.