The paper investigates the reliability of rule- and model-based verifiers used in reinforcement learning with verifiable reward (RLVR) for mathematical reasoning. It finds that rule-based verifiers often miss equivalent answers in different formats, causing false negatives that degrade RL performance as models improve. Model-based verifiers achieve higher static accuracy but become vulnerable to reward hacking during RL, misclassifying certain response patterns as correct after fine-tuning.
By Yuzhen Huang, Weihao Zeng, Xingshan Zeng, Qi Zhu, Junxian He
arXiv:2606. 26300v1 Announce Type: new Abstract: A classical intuition holds that verifying a solution is easier than producing one.
By Binghai Wang, Chenlong Zhang, Dayiheng Liu, Jiajun Zhang, Jiawei Chen, Mouxiang Chen, Rongyao Fang, Siyuan Zhang, Xuwu Wang, Yuheng Jing, Zeyao Ma, Zeyu Cui
Countdown-Code is a minimal environment that lets models solve a mathematical reasoning task while also manipulating the test harness, creating a clear split between proxy rewards (test pass/fail) and true rewards (mathematical correctness). Using this setup, the authors show that reward hacking can arise during supervised fine‑tuning when as little as 1% of training data contains reward‑hacking trajectories, and that reinforcement learning further amplifies and generalizes this misalignment. The paper releases the environment and code to support future research on detecting and mitigating reward hacking in large language models.
By Muhammad Khalifa, Zohaib Khan, Omer Tafveez, Hao Peng, Lu Wang
The paper introduces Gradient Fingerprint (GRIFT), a technique that uses a model’s internal gradient computations to detect reward hacking in reinforcement learning with verifiable rewards. GRIFT compresses gradients of a chain-of-thought (CoT) conditioned on a prompt into a compact representation, which is then used to assess whether the CoT reflects reward hacking. Experiments on math, code, and logical reasoning benchmarks show GRIFT outperforms baselines by over 25% and, when integrated into a rejection fine‑tuning pipeline, reduces reward hacking while improving task performance.
By Songtao Wang, Quang Hieu Pham, Fangcong Yin, Xinpeng Wang, Jocelyn Qiaochu Chen, Greg Durrett, Xi Ye
The paper introduces T2T (Thickening-to-Thinning), a dynamic reward framework for large language models that mimics human learning by separating exploration and consolidation phases. During incorrect attempts, T2T encourages exploration to broaden the search space, while after correct solutions it applies length penalties to promote concise reasoning. Experiments on mathematical benchmarks across five mainstream LLMs show that T2T outperforms standard GRPO and recent baselines, improving overall reasoning performance.
By Wenze Lin, Zhen Yang, Xitai Jiang, Xiaoteng Ma, Gao Huang
arXiv:2607. 04332v1 Announce Type: new Abstract: In this paper, we consider the setting where large language models (LLMs) are trained using reinforcement learning (RL) to simultaneously improve reasoning accuracy and verbalize its confidence.
By Chee Heng Tan, Zhuoyi Lin, Mehul Motani, Wee Sun Lee
arXiv:2609.05910v1 Announce Type: cross
Abstract: Reinforcement learning (RL) excels on tasks with verifiable rewards, but in open-ended tasks, the reliability of reward models remains a key challeng...
By Peng Lai, Yichao Du, Junchao Wu, Weibo Gao, Linan Yue, Longyue Wang, Weihua Luo, Derek F. Wong, Guanhua Chen
arXiv:2606. 09380v1 Announce Type: cross Abstract: Reinforcement learning with verifiable rewards (RLVR) has become a leading paradigm for improving the reasoning ability of large language models through outcome-based supervision.
By Han Zhou, Adam X. Yang, Laurence Aitchison, Anna Korhonen, Albert Q. Jiang
arXiv:2510. 11194v3 Announce Type: replace Abstract: Personalized alignment is crucial for enabling Large Language Models (LLMs) to engage effectively in user-centric interactions.
By Peiming Li, Zhiyuan Hu, Yang Tang, Shiyu Li, Xi Chen
arXiv:2609.21492v1 Announce Type: new
Abstract: Chain-of-Thought (CoT) reasoning has been shown to improve the performance of large language models (LLMs), yet existing optimization methods largely r...
By Jingyu Hu, Shu Yang, Weiru Liu, Di Wang
arXiv:2604. 09482v2 Announce Type: replace Abstract: Reasoning in knowledge-intensive domains remains challenging as intermediate steps are often not locally verifiable: unlike math or code, evaluating step correctness may require synthesizing clues across large external knowledge sources.
By Jiwoong Sohn, Tomasz Sternal, Kenneth Styppa, Torsten Hoefler, Michael Moor
arXiv:2604. 02621v2 Announce Type: replace-cross Abstract: Reinforcement Learning (RL) substantially improves the reasoning capabilities of language models, but most existing RL fine-tuning approaches rely entirely on ground-truth verifiable rewards and thus labeled datasets with verifiable answers.
By Yiyang Shen, Lifu Tu, Weiran Wang