The paper investigates how different forms of compressed chain‑of‑thought (CoT) reasoning—Explicit, Composed, and Implicit—affect large language model (LLM) performance after supervised fine‑tuning (SFT). Using a synthetic compositional reasoning task, the authors show that coarser CoT requires more SFT data, that Composed and Implicit CoT benefit more from data scaling (with Composed also benefiting from repetition), and that reinforcement learning with verifiable rewards (RLVR) can decompose compressed steps learned during SFT. Additionally, unidirectional CoT ordering improves generalization on longer sequential tasks.
By Kohsei Matsutani, Gouki Minegishi, Takeshi Kojima, Yusuke Iwasawa, Yutaka Matsuo
arXiv:2505. 24273v2 Announce Type: replace Abstract: Recent advancements in large language models (LLMs) suggest that reinforcement learning (RL) effectively internalizes search strategies, yielding significant improvements on challenging reasoning tasks through extended chains of thought.
By Hongyi James Cai, Junlin Wang, Xiaoyin Chen, Bhuwan Dhingra
arXiv:2604. 08477v2 Announce Type: replace-cross Abstract: Reinforcement Learning with Verifiable Rewards (RLVR) has substantially improved reasoning in formal domains such as mathematics and code, but extending these gains beyond STEM remains challenging.
By Ashima Suvarna, Kendrick Phan, Mehrab Beikzadeh, Hritik Bansal, Saadia Gabriel
The paper introduces a method to enhance large language model (LLM) exploration in Reinforcement Learning with Verifiable Rewards (RLVR) by guiding the target model with partial reasoning trajectories from smaller, weaker language models. This weak-model guidance disrupts over‑confidence, preserves generative diversity, and mitigates entropy collapse without extra fine‑tuning or complex reward designs. Experiments on mathematical benchmarks show consistent improvements over vanilla RLVR, especially as the number of allowed attempts ($k$) increases, indicating broader reasoning coverage.
By Xingyu Shen, Huishuai Zhang, Peng Li, Yinchun Wang, Dongyan Zhao
arXiv:2509. 04027v4 Announce Type: replace Abstract: Test-time scaling, primarily manifested through multi-step Chain-of-Thought (CoT) reasoning via Reinforcement Learning (RL), has emerged as a pivotal paradigm for enhancing the reasoning capabilities of Large Language Models (LLMs).
By Zeyu Gan, Hao Yi, Yong Liu
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. 16097v1 Announce Type: cross Abstract: Reinforcement learning (RL) has become central to improving large language models (LLMs) on complex reasoning tasks, yet RL post-training is largely studied in isolation from the pretraining that precedes it.
By Jingyan Shen, Ang Li, Salman Rahman, Yifan Sun, Micah Goldblum, Matus Telgarsky, Pavel Izmailov
arXiv:2606. 04503v1 Announce Type: cross Abstract: Reinforcement learning with verifiable rewards (RLVR) has greatly advanced large reasoning models (LRMs), but it requires timely training on a huge fully-annotated dataset.
By Guangcheng Zhu, Shenzhi Yang, Haobo Wang, Xing Zheng, Yingfan MA, Xuening Feng, Zhongqi Chen, Bowen Song, Weiqiang Wang, Gang Chen
The paper investigates whether the high costs of training chain-of-thought reasoning models can be reduced through algorithmic design. It introduces an autocurriculum approach that lets the model select which problems to focus on during training, showing that this method provably improves both supervised fine‑tuning and reinforcement learning. For supervised fine‑tuning, autocurriculum requires exponentially fewer reasoning demonstrations by targeting prompts where the model struggles, while for reinforcement learning it decouples computational cost from the quality of the reference model, making the burn‑in cost nearly independent of target accuracy.
By Nived Rajaraman, Audrey Huang, Miro Dudik, Robert Schapire, Dylan J. Foster, Akshay Krishnamurthy
arXiv:2606. 01281v1 Announce Type: cross Abstract: Reinforcement learning with verifiable rewards (RLVR) has emerged as a powerful paradigm for enhancing the reasoning capabilities of large language models (LLMs).
By Yixiu Mao, Yun Qu, Qi Wang, Heming Zou, Xiangyang Ji
arXiv:2607. 26119v1 Announce Type: new Abstract: Large reasoning models trained via reinforcement learning (RL) have been increasingly shown to outperform their supervised fine-tuned (SFT) counterparts on mathematical reasoning tasks; Yet the mechanistic basis for this advantage remains unclear.
By Antyabha Rahman, Akshaj Gurugubelli, Omar Ankit, Kevin Zhu, Aishwarya Balwani
The paper introduces DATPO, a Difficulty‑Adaptive Sentence‑entropy‑guided Tree‑structured Policy Optimization method designed to improve reasoning coverage in Reinforcement Learning with Verifiable Rewards (RLVR). It builds on three design principles: adaptive difficulty rollouts, tree‑based rollouts, and sentence‑entropy‑guided forking to enhance semantic diversity. Experiments on mathematical reasoning benchmarks show that DATPO outperforms existing baselines, particularly in pass@k, leading to better test‑time scaling performance.
By Youngjun Yu, Sanghwan Jang, Hwanjo Yu