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Large language models (LLMs) are capable of solving a wide range of tasks, yet they have struggled with reasoning. To address this, we propose $\textbf{Additional Logic Training (ALT)}$, which aims to enhance LLMs' reasoning capabilities by…

Machine Learning · Computer Science 2024-12-24 Terufumi Morishita , Gaku Morio , Atsuki Yamaguchi , Yasuhiro Sogawa

Existing research predominantly focuses on developing powerful language learning models (LLMs) for mathematical reasoning within monolingual languages, with few explorations in preserving efficacy in a multilingual context. To bridge this…

Computation and Language · Computer Science 2024-10-17 Nuo Chen , Zinan Zheng , Ning Wu , Ming Gong , Dongmei Zhang , Jia Li

Reinforcement Learning (RL) has been shown to significantly boost reasoning capabilities of large language models (LLMs) in math, coding, and multi-hop reasoning tasks. However, RL fine-tuning requires abundant high-quality verifiable data,…

Large Language Models (LLMs) display strikingly different generalization behaviors: supervised fine-tuning (SFT) often narrows capability, whereas reinforcement-learning (RL) tuning tends to preserve it. The reasons behind this divergence…

Machine Learning · Computer Science 2026-01-01 Haoyue Bai , Yiyou Sun , Wenjie Hu , Shi Qiu , Maggie Ziyu Huan , Peiyang Song , Robert Nowak , Dawn Song

Large Language Models (LLMs) have exhibited remarkable reasoning capabilities and become the foundation of language technologies. Inspired by the great success of code data in training LLMs, we naturally wonder at which training stage…

Computation and Language · Computer Science 2023-10-03 Yingwei Ma , Yue Liu , Yue Yu , Yuanliang Zhang , Yu Jiang , Changjian Wang , Shanshan Li

We have witnessed that strong LLMs like Qwen-Math, MiMo, and Phi-4 possess immense reasoning potential inherited from the pre-training stage. With reinforcement learning (RL), these models can improve dramatically on reasoning tasks. Recent…

Computation and Language · Computer Science 2025-06-06 Yubo Wang , Ping Nie , Kai Zou , Lijun Wu , Wenhu Chen

Enhancing the complex reasoning capabilities of Large Language Models (LLMs) attracts widespread attention. While reinforcement learning (RL) has shown superior performance for improving complex reasoning, its impact on cross-lingual…

Computation and Language · Computer Science 2025-09-30 Shulin Huang , Yiran Ding , Junshu Pan , Yue Zhang

With the rapid development of large language models (LLMs), the quality of training data has become crucial. Among the various types of training data, mathematical data plays a key role in enabling LLMs to acquire strong reasoning…

Computation and Language · Computer Science 2025-02-27 Hao Liang , Meiyi Qiang , Yuying Li , Zefeng He , Yongzhen Guo , Zhengzhou Zhu , Wentao Zhang , Bin Cui

Large Language Models (LLMs) have demonstrated exceptional capabilities in various natural language tasks, often achieving performances that surpass those of humans. Despite these advancements, the domain of mathematics presents a…

Computation and Language · Computer Science 2024-04-02 Ankit Satpute , Noah Giessing , Andre Greiner-Petter , Moritz Schubotz , Olaf Teschke , Akiko Aizawa , Bela Gipp

Despite their success in many natural language tasks, solving math problems remains a significant challenge for large language models (LLMs). A large gap exists between LLMs' pass-at-one and pass-at-N performance in solving math problems,…

Computation and Language · Computer Science 2023-10-17 Yixin Liu , Avi Singh , C. Daniel Freeman , John D. Co-Reyes , Peter J. Liu

Proof assistants like Lean have revolutionized mathematical proof verification, ensuring high accuracy and reliability. Although large language models (LLMs) show promise in mathematical reasoning, their advancement in formal theorem…

Artificial Intelligence · Computer Science 2024-05-24 Huajian Xin , Daya Guo , Zhihong Shao , Zhizhou Ren , Qihao Zhu , Bo Liu , Chong Ruan , Wenda Li , Xiaodan Liang

The growing disparity between the exponential scaling of computational resources and the finite growth of high-quality text data now constrains conventional scaling approaches for large language models (LLMs). To address this challenge, we…

Large Language Models (LLMs) exhibit significant disparities in performance across languages, primarily benefiting high-resource languages while marginalizing underrepresented ones. Continual Pretraining (CPT) has emerged as a promising…

Computation and Language · Computer Science 2025-10-09 Zihao Li , Shaoxiong Ji , Hengyu Luo , Jörg Tiedemann

Enhancing the mathematical reasoning of Large Language Models (LLMs) is a pivotal challenge in advancing AI capabilities. While Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL) are the dominant training paradigms, a systematic…

Machine Learning · Computer Science 2025-07-14 Hiroshi Yoshihara , Taiki Yamaguchi , Yuichi Inoue

This paper presents a study on strategies to enhance the translation capabilities of large language models (LLMs) in the context of machine translation (MT) tasks. The paper proposes a novel paradigm consisting of three stages: Secondary…

Computation and Language · Computer Science 2024-04-16 Jiaxin Guo , Hao Yang , Zongyao Li , Daimeng Wei , Hengchao Shang , Xiaoyu Chen

Large language models (LLMs) primarily rely on supervised fine-tuning (SFT) as a key method to adapt pre-trained models to domain-specific tasks such as mathematical reasoning. However, standard SFT uniformly penalizes all tokens,…

Computation and Language · Computer Science 2025-10-14 Zhiwen Ruan , Yixia Li , He Zhu , Yun Chen , Peng Li , Yang Liu , Guanhua Chen

To acquire instruction-following capabilities, large language models (LLMs) undergo instruction tuning, where they are trained on instruction-response pairs using next-token prediction (NTP). Efforts to improve instruction tuning often…

Computation and Language · Computer Science 2026-04-21 Yuxin Xiao , Shujian Zhang , Wenxuan Zhou , Marzyeh Ghassemi , Sanqiang Zhao

Large language models (LLMs) have demonstrated remarkable capabilities in problem-solving. However, their proficiency in solving mathematical problems remains inadequate. We propose MathScale, a simple and scalable method to create…

Computation and Language · Computer Science 2024-03-06 Zhengyang Tang , Xingxing Zhang , Benyou Wang , Furu Wei

Cognitive Reframing, a core element of Cognitive Behavioral Therapy (CBT), helps individuals reinterpret negative experiences by finding positive meaning. Recent advances in Large Language Models (LLMs) have demonstrated improved…

Computation and Language · Computer Science 2025-04-02 Yilin Qi , Dong Won Lee , Cynthia Breazeal , Hae Won Park

Mathematical reasoning has been challenging for large language models (LLMs), and the introduction of step-by-step Chain-of-Thought (CoT) inference has significantly advanced the mathematical capabilities of LLMs. However, current…

Artificial Intelligence · Computer Science 2025-09-23 Lang Cao , Yingtian Zou , Chao Peng , Renhong Chen , Wu Ning , Yitong Li