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

TL;DR

This paper reveals that autoregressive language models can be viewed as energy-based models, providing a unified framework that explains their lookahead capabilities and planning ability.

Contribution

It establishes a bijection between ARMs and EBMs, connecting them through the soft Bellman equation, and analyzes their equivalence and distillation error bounds.

Findings

ARMs and EBMs are mathematically equivalent in function space.

ARMs' lookahead capabilities can be explained via energy-based model interpretation.

Theoretical bounds on distilling EBMs into ARMs are derived.

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.