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In mathematical reasoning tasks, the advancement of Large Language Models (LLMs) relies heavily on high-quality training data with clearly defined and well-graded difficulty levels. However, existing data synthesis methods often suffer from…

Machine Learning · Computer Science 2026-01-27 Xuchen Li , Jing Chen , Xuzhao Li , Hao Liang , Xiaohuan Zhou , Taifeng Wang , Wentao Zhang

Recent large reasoning models (LRMs) have demonstrated strong reasoning capabilities through reinforcement learning (RL). These improvements have primarily been observed within the short-context reasoning tasks. In contrast, extending LRMs…

Computation and Language · Computer Science 2025-05-28 Fanqi Wan , Weizhou Shen , Shengyi Liao , Yingcheng Shi , Chenliang Li , Ziyi Yang , Ji Zhang , Fei Huang , Jingren Zhou , Ming Yan

Reinforcement Learning is a mature technology, often suggested as a potential route towards Artificial General Intelligence, with the ambitious goal of replicating the wide range of abilities found in natural and artificial intelligence,…

Machine Learning · Computer Science 2025-11-25 Markus D. Solbach , John K. Tsotsos

Reinforcement learning from verifiable rewards (RLVR) stimulates the thinking processes of large language models (LLMs), substantially enhancing their reasoning abilities on verifiable tasks. It is often assumed that similar gains should…

Computation and Language · Computer Science 2026-03-24 Kaiyuan Li , Jing-Cheng Pang , Yang Yu

Recent advancements in Large Language Models (LLMs) have significantly enhanced their ability to perform complex reasoning tasks, transitioning from fast and intuitive thinking (System 1) to slow and deep reasoning (System 2). While System…

Computation and Language · Computer Science 2025-04-01 Rui Wang , Hongru Wang , Boyang Xue , Jianhui Pang , Shudong Liu , Yi Chen , Jiahao Qiu , Derek Fai Wong , Heng Ji , Kam-Fai Wong

We introduce SLR, an end-to-end framework for systematic evaluation and training of Large Language Models (LLMs) via Scalable Logical Reasoning. Given a user's task specification, SLR automatically synthesizes (i) an instruction prompt for…

Retrieval-Augmented Generation (RAG) integrates external knowledge with Large Language Models (LLMs) to enhance factual correctness and mitigate hallucination. However, dense retrievers often become the bottleneck of RAG systems due to…

Computation and Language · Computer Science 2025-10-27 Yuan Li , Qi Luo , Xiaonan Li , Bufan Li , Qinyuan Cheng , Bo Wang , Yining Zheng , Yuxin Wang , Zhangyue Yin , Xipeng Qiu

Reinforcement learning (RL) has demonstrated considerable potential for enhancing reasoning in large language models (LLMs). However, existing methods suffer from Gradient Starvation and Policy Degradation when training directly on samples…

Machine Learning · Computer Science 2025-11-13 Renda Li , Hailang Huang , Fei Wei , Feng Xiong , Yong Wang , Xiangxiang Chu

We demonstrate that a developmentally ordered curriculum markedly improves reasoning transparency and sample-efficiency in small language models (SLMs). Concretely, we train Cognivolve, a 124 M-parameter GPT-2 model, on a four-stage…

Computation and Language · Computer Science 2025-05-20 Xiang Fu

Reinforcement Learning with Verifiable Rewards (RLVR) plays a key role in stimulating the explicit reasoning capability of Large Language Models (LLMs). We can achieve expert-level performance in some specific domains via RLVR, such as…

Artificial Intelligence · Computer Science 2026-03-12 Haoqing Wang , Xiang Long , Ziheng Li , Yilong Xu , Tingguang Li , Yehui Tang

Reinforcement learning (RL) has recently become the dominant paradigm for strengthening the reasoning abilities of large language models (LLMs). Yet the rule-based reward functions commonly used on mathematical or programming benchmarks…

Artificial Intelligence · Computer Science 2025-09-09 Haoyang He , Zihua Rong , Kun Ji , Chenyang Li , Qing Huang , Chong Xia , Lan Yang , Honggang Zhang

Reinforcement learning (RL) has become a standard paradigm for refining large language models (LLMs) beyond pre-training and instruction tuning. A prominent line of work is RL with verifiable rewards (RLVR), which leverages automatically…

Machine Learning · Computer Science 2025-09-23 Bonan Zhang , Zhongqi Chen , Bowen Song , Qinya Li , Fan Wu , Guihai Chen

We show that reinforcement learning with verifiable reward using one training example (1-shot RLVR) is effective in incentivizing the math reasoning capabilities of large language models (LLMs). Applying RLVR to the base model…

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a prevailing paradigm for enhancing reasoning in Multimodal Large Language Models (MLLMs). However, relying solely on outcome supervision risks reward hacking, where…

Computation and Language · Computer Science 2026-03-04 Yukun Chen , Jiaming Li , Longze Chen , Ze Gong , Jingpeng Li , Zhen Qin , Hengyu Chang , Ancheng Xu , Zhihao Yang , Hamid Alinejad-Rokny , Qiang Qu , Bo Zheng , Min Yang

Reasoning large language models (LLMs) excel in complex tasks, which has drawn significant attention to reinforcement learning (RL) for LLMs. However, existing approaches allocate an equal number of rollouts to all questions during the RL…

Machine Learning · Computer Science 2025-10-21 Mengqi Liao , Xiangyu Xi , Ruinian Chen , Jia Leng , Yangen Hu , Ke Zeng , Shuai Liu , Huaiyu Wan

Reasoning in large language models has long been a central research focus, and recent studies employing reinforcement learning (RL) have introduced diverse methods that yield substantial performance gains with minimal or even no external…

Enhancing the reasoning capabilities of large language models (LLMs) typically relies on massive computational resources and extensive datasets, limiting accessibility for resource-constrained settings. Our study investigates the potential…

Machine Learning · Computer Science 2026-01-21 Quy-Anh Dang , Chris Ngo

While the reasoning abilities of large language models (LLMs) continue to advance, it remains unclear how such ability varies across languages in multilingual LLMs and whether different languages produce reasoning paths that complement each…

Computation and Language · Computer Science 2025-09-22 Sara Rajaee , Rochelle Choenni , Ekaterina Shutova , Christof Monz

Curriculum learning plays a crucial role in enhancing the training efficiency of large language models (LLMs) on reasoning tasks. However, existing methods often fail to adequately account for variations in prompt difficulty or rely on…

Machine Learning · Computer Science 2026-03-24 Yongcheng Zeng , Zexu Sun , Bokai Ji , Erxue Min , Hengyi Cai , Shuaiqiang Wang , Dawei Yin , Haifeng Zhang , Xu Chen , Jun Wang

Mathematical reasoning is essential for problem-solving in education, science, and industry, serving as a crucial benchmark for evaluating artificial intelligence systems. As Large Language Models (LLMs) improve their reasoning…

Computation and Language · Computer Science 2026-05-20 Husnain Amjad , Raja Khurram Shahzad , Aamir Shahzad , Mehwish Fatima