Title: Beyond the Exploration-Exploitation Trade-off: A Hidden State Approach for LLM Reasoning in RLVR
Primary area: reinforcement learning
Keywords: Large Language Models, Reinforcement Learning

Abstract: A prevailing view in Reinforcement Learning for Verifiable Rewards (RLVR) interprets recent progress through the lens of an exploration-exploitation trade-off, a perspective largely shaped by token-level metrics. We re-examine this perspective, proposing that this perceived trade-off may not be a fundamental constraint but rather an artifact of the measurement level. To investigate this, we shift the analysis to the semantically rich hidden-state space, adopting Effective Rank (ER) to quantify exploration and proposing its novel first- and second-order derivatives, named ER Velocity and ER Acceleration, to capture exploitation dynamics. Our analysis reveals that at the hidden-state level, exploration and exploitation could be decoupled (Sec.4). This finding reveals an opportunity to enhance both capacities simultaneously. This insight motivates our method, Velocity-Exploiting Rank-Learning (VERL), the first to operationalize the principle of synergistic exploration-exploitation enhancement by directly shaping the RL advantage function. The key innovation is leveraging the theoretically stable ERA as a predictive meta-controller to create a synergistic, dual-channel incentive structure. Instead of forcing a trade-off, VERL prospectively amplifies rewards for exploration to preempt overconfidence and reinforces exploitative gains to consolidate reasoning. Experiments across diverse LLMs and reasoning benchmarks show consistent gains, including up to 21.4\% absolute accuracy improvement on the challenging Gaokao 2024 dataset. The code is available at https://anonymous.4open.science/r/coding.

TL;DR: This paper challenges the conventional exploration-exploitation trade-off in LLM reasoning by introducing a reinforcement learning method that analyzes the model's hidden states to improve both capabilities simultaneously.