The paper introduces EquivAug, a data augmentation framework that applies symbolic equivalence transformations to chain-of-thought (CoT) solutions, generating diverse yet provably correct reasoning paths for supervised fine-tuning (SFT). By converting CoT solutions into formal symbolic representations, applying equivalence transformations, and reconstructing natural-language explanations, EquivAug produces training data that varies in reasoning steps rather than surface-level lexical differences. Experiments on GSM8K and FOLIO show that EquivAug consistently achieves the highest reasoning path diversity after SFT and the strongest accuracy after GRPO, establishing a positive correlation between CoT diversity during SFT and downstream reinforcement learning with verifiable rewards (RLVR) performance.
By Xiaoou Liu, Tiejin Chen, Hanyang Chen, Yuan Ling, Hua Wei
The paper introduces MIMIC, a framework that uses executable code to generate rigorous reasoning data for large language models (LLMs). By converting algorithms into verifiable reasoning trajectories through narrative fusion, code-guided test synthesis, and dynamic code instrumentation, MIMIC creates a Code-Instrumented Reward (CIR) that supplies dense, high‑fidelity supervision for reinforcement learning. Models trained with MIMIC’s synthetic dataset show significant, consistent improvements in general reasoning, complex mathematics, and fine‑grained deterministic tasks.
By Jinyang Zhang, Weibin Liao, Keqin Bao, Sihang Li, Shaobo Wang, Muyang Ye, Hongxin Ding, Yue Fang, Tianyi Tang, Fei Huang, Kexin Yang, Xingzhang Ren, Dayiheng Liu
arXiv:2604. 23333v2 Announce Type: replace Abstract: Scaling test-time computation with reinforcement learning (RL) has emerged as a reliable path to improve large language models (LLM) reasoning ability.
By Liaoyaqi Wang, Chunsheng Zuo, William Jurayj, Benjamin Van Durme, Anqi Liu
arXiv:2604. 10788v2 Announce Type: replace-cross Abstract: Tool-Integrated Reasoning (TIR) has emerged as a promising direction by extending Large Language Models' (LLMs) capabilities with external tools during reasoning.
By Qiancheng Xu, Yongqi Li, Fan Liu, Hongru Wang, Min Yang, Wenjie Li
arXiv:2606. 29481v1 Announce Type: cross Abstract: While reinforcement learning (RL) significantly enhances LLM reasoning, its efficacy is severely undermined by Pre-RL data overlap, where RL datasets overlap with pretraining or SFT corpora, causing models to exploit shortcuts by memorizing correct answers and fabricating post-hoc reasoning.
By Jiuheng Lin, Chen Zhang, Yansong Feng
The paper introduces LSR‑Ben, a benchmark designed to evaluate process reward models (PRMs) on scientific and logical reasoning tasks, addressing a gap left by existing math‑focused benchmarks. Experiments on 22 models reveal that PRMs and LLMs perform poorly in non‑mathematical domains, with LLMs tending to over‑identify errors while PRMs tend to overlook them. LSR‑Ben aims to spur research that broadens PRM applicability and improves LLM reasoning.
By Zhouhao Sun, Xuan Zhang, Xiao Ding, Bibo Cai, Li Du, Kai Xiong, Xinran Dai, Fei Zhang, weidi tang, Zhiyuan Kan, Yang Zhao, Bing Qin, Ting Liu
arXiv:2507. 04136v2 Announce Type: replace Abstract: This survey offers a comprehensive foundation on the integration of RL with language models, highlighting prominent algorithms such as Proximal Policy Optimization (PPO), Q-Learning, and Actor-Critic methods.
By Saksham Sahai Srivastava, Vaneet Aggarwal
arXiv:2602. 09305v2 Announce Type: replace Abstract: Large Language Models (LLMs) demonstrate transformative potential, yet their reasoning remains inconsistent and unreliable.
By Pei-Chi Pan, Yingbin Liang, Sen Lin
arXiv:2509. 03059v2 Announce Type: replace-cross Abstract: Recent advances in Large Language Models (LLMs) have shown that their reasoning capabilities can be significantly improved through Reinforcement Learning with Verifiable Reward (RLVR), particularly in domains like mathematics and programming, where ground-truth correctness can be automatically evaluated.
By Xingyue Huang, Rishabh, Gregor Franke, Ziyi Yang, Jiamu Bai, Weijie Bai, Jinhe Bi, Zifeng Ding, Yiqun Duan, Chengyu Fan, Wendong Fan, Xin Gao, Ruohao Guo, Yuan He, Zhuangzhuang He, Xianglong Hu, Neil Johnson, Bowen Li, Fangru Lin, Siyu Lin, Tong Liu, Yunpu Ma, Hao Shen, Hao Sun, Beibei Wang, Fangyijie Wang, Hao Wang, Haoran Wang, Yang Wang, Yifeng Wang, Zhaowei Wang, Ziyang Wang, Yifan Wu, Zikai Xiao, Chengxing Xie, Fan Yang, Junxiao Yang, Qianshuo Ye, Ziyu Ye, Guangtao Zeng, Yuwen Ebony Zhang, Zeyu Zhang, Zihao Zhu, Bernard Ghanem, Philip Torr, Guohao Li
arXiv:2606. 03234v1 Announce Type: new Abstract: Reinforcement Learning from Verifiable Rewards (RLVR) has become the dominant approach for improving mathematical reasoning in large language models, yet current methods reduce each correct rollout to a single reward bit, ignoring the geometric structure shared among their hidden states.
By Ziyue Wang, Aomufei Yuan, Yongfu Zhu, Shuai Dong, Wenpu Liu, Yiran Yao, Weichu Xie, Yuqi Xu, Caoyuan Ma, Wenqi Shao, Xiaoying Zhang, Nan Duan, Jiaqi Wang
arXiv:2603.18614v2 Announce Type: replace
Abstract: Tool-augmented large language models (LLMs) must tightly couple multi-step reasoning with external actions, yet existing benchmarks often confound...
By Wanjia Zhao, Ludwig Schmidt, Yejin Choi, James Zou, Vidhisha Balachandran, Lingjiao Chen
arXiv:2604.02007v3 Announce Type: replace
Abstract: Building general-purpose reasoning models using reinforcement learning with verifiable rewards (RLVR) across diverse domains has been widely adopte...
By Rafael Pardinas, Ehsan Kamalloo, David Vazquez, Alexandre Drouin