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Large Language Models (LLMs) have demonstrated significant improvements in reasoning capabilities through supervised fine-tuning and reinforcement learning. However, when training reasoning models, these approaches are primarily applicable…

Computation and Language · Computer Science 2025-05-16 Yoichi Ishibashi , Taro Yano , Masafumi Oyamada

In recent years, large language models (LLMs) have demonstrated significant potential in complex reasoning tasks like mathematical problem-solving. However, existing research predominantly relies on reinforcement learning (RL) frameworks…

Machine Learning · Computer Science 2026-01-12 ShaoZhen Liu , Xinting Huang , Houwen Peng , Xin Chen , Xinyang Song , Qi Li , Zhenan Sun

Mathematical reasoning is a challenging task for large language models (LLMs), while the scaling relationship of it with respect to LLM capacity is under-explored. In this paper, we investigate how the pre-training loss, supervised data…

Computation and Language · Computer Science 2023-09-14 Zheng Yuan , Hongyi Yuan , Chengpeng Li , Guanting Dong , Keming Lu , Chuanqi Tan , Chang Zhou , Jingren Zhou

Mathematical reasoning has long represented one of the most fundamental and challenging frontiers in artificial intelligence research. In recent years, large language models (LLMs) have achieved significant advances in this area. This…

Artificial Intelligence · Computer Science 2025-06-11 Peng-Yuan Wang , Tian-Shuo Liu , Chenyang Wang , Yi-Di Wang , Shu Yan , Cheng-Xing Jia , Xu-Hui Liu , Xin-Wei Chen , Jia-Cheng Xu , Ziniu Li , Yang Yu

Mathematical reasoning continues to be a critical challenge in large language model (LLM) development with significant interest. However, most of the cutting-edge progress in mathematical reasoning with LLMs has become \emph{closed-source}…

Computation and Language · Computer Science 2024-10-08 Shubham Toshniwal , Wei Du , Ivan Moshkov , Branislav Kisacanin , Alexan Ayrapetyan , Igor Gitman

Large language models (LLMs) with enormous pre-training tokens and parameters emerge diverse abilities, including math reasoning, code generation, and instruction following. These abilities are further enhanced by supervised fine-tuning…

Computation and Language · Computer Science 2024-06-10 Guanting Dong , Hongyi Yuan , Keming Lu , Chengpeng Li , Mingfeng Xue , Dayiheng Liu , Wei Wang , Zheng Yuan , Chang Zhou , Jingren Zhou

In this paper, we investigate the underlying factors that potentially enhance the mathematical reasoning capabilities of large language models (LLMs). We argue that the data scaling law for math reasoning capabilities in modern LLMs is far…

Artificial Intelligence · Computer Science 2024-07-18 Liang Zeng , Liangjun Zhong , Liang Zhao , Tianwen Wei , Liu Yang , Jujie He , Cheng Cheng , Rui Hu , Yang Liu , Shuicheng Yan , Han Fang , Yahui Zhou

Large Language Models (LLMs) have shown remarkable performance in various natural language processing tasks but face challenges in mathematical reasoning, where complex problem-solving requires both linguistic understanding and mathematical…

Computation and Language · Computer Science 2025-03-20 Shuguang Chen , Guang Lin

The reasoning capabilities of Large Language Models (LLMs) play a critical role in many downstream tasks, yet depend strongly on the quality of training data. Despite various proposed data construction methods, their practical utility in…

Computation and Language · Computer Science 2025-10-09 Yike Zhao , Simin Guo , Ziqing Yang , Shifan Han , Dahua Lin , Fei Tan

While large models pre-trained on high-quality data exhibit excellent performance on mathematical reasoning (e.g., GSM8k, MultiArith), it remains challenging to specialize smaller models for these tasks. Common approaches to address this…

Computation and Language · Computer Science 2026-03-19 Neeraj Gangwar , Suma P Bhat , Nickvash Kani

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

Large language models (LLMs) have demonstrated remarkable capabilities in various natural language processing tasks. However, achieving strong performance in specialized domains like mathematical reasoning and non-English languages often…

Computation and Language · Computer Science 2025-03-19 Huy Hoang Ha

Despite recent advances in training and prompting strategies for Large Language Models (LLMs), these models continue to face challenges with complex logical reasoning tasks that involve long reasoning chains. In this work, we explore the…

Computation and Language · Computer Science 2024-12-18 Jiaming Zhou , Abbas Ghaddar , Ge Zhang , Liheng Ma , Yaochen Hu , Soumyasundar Pal , Mark Coates , Bin Wang , Yingxue Zhang , Jianye Hao

Instruction Fine-Tuning (IFT) significantly enhances the zero-shot capabilities of pretrained Large Language Models (LLMs). While coding data is known to boost LLM reasoning abilities during pretraining, its role in activating internal…

Artificial Intelligence · Computer Science 2024-12-13 Xinlu Zhang , Zhiyu Zoey Chen , Xi Ye , Xianjun Yang , Lichang Chen , William Yang Wang , Linda Ruth Petzold

Large Language Models (LLMs) have shown impressive progress in mathematical reasoning. While data augmentation is promising to enhance mathematical problem-solving ability, current approaches are predominantly limited to instance-level…

Computation and Language · Computer Science 2025-06-17 Qizhi Pei , Lijun Wu , Zhuoshi Pan , Yu Li , Honglin Lin , Chenlin Ming , Xin Gao , Conghui He , Rui Yan

Mathematical reasoning is an important capability of large language models~(LLMs) for real-world applications. To enhance this capability, existing work either collects large-scale math-related texts for pre-training, or relies on stronger…

Computation and Language · Computer Science 2024-05-24 Kun Zhou , Beichen Zhang , Jiapeng Wang , Zhipeng Chen , Wayne Xin Zhao , Jing Sha , Zhichao Sheng , Shijin Wang , Ji-Rong Wen

There has been a growing interest in enhancing the mathematical problem-solving (MPS) capabilities of large language models. While the majority of research efforts concentrate on creating specialized models to solve mathematical problems,…

Computation and Language · Computer Science 2025-07-08 Ruochen Zhou , Minrui Xu , Shiqi Chen , Junteng Liu , Yunqi Li , Xinxin Lin , Zhengyu Chen , Junxian He

Large Language Models (LLMs) are increasingly used in math education not only as problem solvers but also as assessors of learners' reasoning. However, it remains unclear whether stronger math problem-solving ability is associated with…

Artificial Intelligence · Computer Science 2026-03-27 Liang Zhang , Yu Fu , Xinyi Jin

Large language models (LLMs) have obtained promising results in mathematical reasoning, which is a foundational skill for human intelligence. Most previous studies focus on improving and measuring the performance of LLMs based on textual…

Computation and Language · Computer Science 2024-11-04 Wentao Liu , Qianjun Pan , Yi Zhang , Zhuo Liu , Ji Wu , Jie Zhou , Aimin Zhou , Qin Chen , Bo Jiang , Liang He

Recent supervised fine-tuning (SFT) approaches have significantly improved language models' performance on mathematical reasoning tasks, even when models are trained at a small scale. However, the specific capabilities enhanced through such…

Artificial Intelligence · Computer Science 2026-01-12 Yiyou Sun , Georgia Zhou , Haoyue Bai , Hao Wang , Dacheng Li , Nouha Dziri , Dawn Song
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