Reasoning with Exploration: An Entropy Perspective

Abstract

Balancing exploration and exploitation is a central goal in reinforcement learning (RL). Despite recent advances in enhancing large language model (LLM) reasoning, most methods lean toward exploitation, and increasingly encounter performance plateaus. In this work, we revisit entropy -- a signal of exploration in RL -- and examine its relationship to exploratory reasoning in LLMs. Through empirical analysis, we uncover positive correlations between high-entropy regions and three types of exploratory reasoning actions: (1) pivotal tokens that determine or connect logical steps, (2) reflective actions such as self-verification and correction, and (3) rare behaviors under-explored by the base LLMs. Motivated by this, we introduce a minimal modification to standard RL with only one line of code: augmenting the advantage function with an entropy-based term. Unlike traditional maximum-entropy methods which encourage exploration by promoting uncertainty, we encourage exploration by promoting longer and deeper reasoning chains. Notably, our method achieves significant gains on the Pass@K metric -- an upper-bound estimator of LLM reasoning capabilities -- even when evaluated with extremely large K values, pushing the boundaries of LLM reasoning.