Low-probability Tokens Sustain Exploration in Reinforcement Learning with Verifiable Reward

Reinforcement Learning with Verifiable Rewards (RLVR) has propelled Large Language Models in complex reasoning, yet its scalability is often hindered by a training bottleneck where performance plateaus as policy entropy collapses, signaling a loss of exploration. While previous methods attempt to maintain high entropy, we argue that unselective entropy maximization risks amplifying irrelevant noise rather than fostering meaningful exploration. In this paper, we identify a deeper issue: the gradual elimination of valuable low-probability exploratory tokens, which we term reasoning sparks, driven by RLVR over-penalization. To address this, we introduce Low-probability Regularization (Lp-Reg). Leveraging the statistical distinction where reasoning sparks exhibit higher probabilities than noise, Lp-Reg filters out the extremely lowprobability noise tokens and prevents the suppression of potentially valuable low-probability candidates. Experiments demonstrate that Lp-Reg enables stable on-policy training for over 3, 000 steps (81,204 GPU-hours), sustaining exploration in regimes where baselines typically collapse. Validated across extensive evaluations totaling over 300,000 cumulative GPUhours, Lp-Reg demonstrates highly competitive performance in off-policy settings and consistently achieves state-of-the-art results in onpolicy training across diverse model families, sizes, and domains, with relative accuracy improvements ranging from 3.06% to 7.98%.