@inproceedings{huang-etal-2026-low,
title = "Low-probability Tokens Sustain Exploration in Reinforcement Learning with Verifiable Reward",
author = "Huang, Guanhua and
Xu, Tingqiang and
Wang, Mingze and
Yi, Qi and
Gong, Xue and
Li, Siheng and
Xiong, Ruibin and
Li, Kejiao and
Jiang, Yuhao and
Zhou, Bo",
editor = "Liakata, Maria and
Moreira, Viviane P. and
Zhang, Jiajun and
Jurgens, David",
booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {ACL} 2026",
month = jul,
year = "2026",
address = "San Diego, California, United States",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.findings-acl.1209/",
pages = "24158--24188",
ISBN = "979-8-89176-395-1",
abstract = "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 low-probability 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 GPU-hours, Lp-Reg demonstrates highly competitive performance in off-policy settings and consistently achieves state-of-the-art results in on-policy training across diverse model families, sizes, and domains, with relative accuracy improvements ranging from 3.06{\%} to 7.98{\%}."
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<abstract>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 low-probability 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 GPU-hours, Lp-Reg demonstrates highly competitive performance in off-policy settings and consistently achieves state-of-the-art results in on-policy training across diverse model families, sizes, and domains, with relative accuracy improvements ranging from 3.06% to 7.98%.</abstract>
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%0 Conference Proceedings
%T Low-probability Tokens Sustain Exploration in Reinforcement Learning with Verifiable Reward
%A Huang, Guanhua
%A Xu, Tingqiang
%A Wang, Mingze
%A Yi, Qi
%A Gong, Xue
%A Li, Siheng
%A Xiong, Ruibin
%A Li, Kejiao
%A Jiang, Yuhao
%A Zhou, Bo
%Y Liakata, Maria
%Y Moreira, Viviane P.
%Y Zhang, Jiajun
%Y Jurgens, David
%S Findings of the Association for Computational Linguistics: ACL 2026
%D 2026
%8 July
%I Association for Computational Linguistics
%C San Diego, California, United States
%@ 979-8-89176-395-1
%F huang-etal-2026-low
%X 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 low-probability 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 GPU-hours, Lp-Reg demonstrates highly competitive performance in off-policy settings and consistently achieves state-of-the-art results in on-policy training across diverse model families, sizes, and domains, with relative accuracy improvements ranging from 3.06% to 7.98%.
%U https://aclanthology.org/2026.findings-acl.1209/
%P 24158-24188
Markdown (Informal)
[Low-probability Tokens Sustain Exploration in Reinforcement Learning with Verifiable Reward](https://aclanthology.org/2026.findings-acl.1209/) (Huang et al., Findings 2026)
ACL
- Guanhua Huang, Tingqiang Xu, Mingze Wang, Qi Yi, Xue Gong, Siheng Li, Ruibin Xiong, Kejiao Li, Yuhao Jiang, and Bo Zhou. 2026. Low-probability Tokens Sustain Exploration in Reinforcement Learning with Verifiable Reward. In Findings of the Association for Computational Linguistics: ACL 2026, pages 24158–24188, San Diego, California, United States. Association for Computational Linguistics.