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Large Language Models (LLMs) solely trained on next-token prediction learn to solve a wide range of problems involving mathematical reasoning. But how does this ability evolve during training? We show the first analysis of how mathematical…

Artificial Intelligence · Computer Science 2025-12-15 Shubhra Mishra , Gabriel Poesia , Noah D. Goodman

Large Language Models (LLMs) have limited performance when solving arithmetic reasoning tasks and often provide incorrect answers. Unlike natural language understanding, math problems typically have a single correct answer, making the task…

Computation and Language · Computer Science 2023-03-10 Shima Imani , Liang Du , Harsh Shrivastava

Large language models (LLMs) demonstrate their promise in tackling complicated practical challenges by combining action-based policies with chain of thought (CoT) reasoning. Having high-quality prompts on hand, however, is vital to the…

Machine Learning · Computer Science 2024-03-01 Xue Yan , Yan Song , Xinyu Cui , Filippos Christianos , Haifeng Zhang , David Henry Mguni , Jun Wang

Large language models (LLMs) face challenges in solving complex mathematical problems that require comprehensive capacities to parse the statements, associate domain knowledge, perform compound logical reasoning, and integrate the…

Artificial Intelligence · Computer Science 2023-12-19 Haoran Liao , Qinyi Du , Shaohua Hu , Hao He , Yanyan Xu , Jidong Tian , Yaohui Jin

Multimodal Large Language Models (MLLMs) excel in solving text-based mathematical problems, but they struggle with mathematical diagrams since they are primarily trained on natural scene images. For humans, visual aids generally enhance…

Computation and Language · Computer Science 2024-09-26 Wenwen Zhuang , Xin Huang , Xiantao Zhang , Jin Zeng

Mathematical reasoning remains a challenging area for large language models (LLMs), prompting the development of math-specific LLMs such as LLEMMA, DeepSeekMath, and Qwen2-Math, among others. These models typically follow a two-stage…

Computation and Language · Computer Science 2025-03-25 Zui Chen , Tianqiao Liu , Mi Tian , Qing Tong , Weiqi Luo , Zitao Liu

The evaluation of Large Language Models (LLMs) on mathematical reasoning has largely focused on elementary problems, competition-style questions, or formal theorem proving, leaving graduate-level and computational mathematics relatively…

Computation and Language · Computer Science 2026-03-05 Bianca Raimondi , Francesco Pivi , Davide Evangelista , Maurizio Gabbrielli

Advances in large language models (LLMs) have spurred research into enhancing their reasoning capabilities, particularly in math-rich STEM (Science, Technology, Engineering, and Mathematics) documents. While LLMs can generate equations or…

Computation and Language · Computer Science 2025-06-03 Jiaru Zou , Qing Wang , Pratyush Thakur , Nickvash Kani

Prompting techniques have significantly enhanced the capabilities of Large Language Models (LLMs) across various complex tasks, including reasoning, planning, and solving math word problems. However, most research has predominantly focused…

Computation and Language · Computer Science 2024-05-24 Neisarg Dave , Daniel Kifer , C. Lee Giles , Ankur Mali

Language models frequently produce plausible yet incorrect reasoning traces that are difficult to verify. We investigate fine-tuning models to use Prolog as an external symbolic reasoning tool, training Qwen2.5-3B-Instruct with Group…

Computation and Language · Computer Science 2026-04-21 Niklas Mellgren , Peter Schneider-Kamp , Lukas Galke Poech

Large Language Models (LLMs) have demonstrated remarkable proficiency across diverse tasks, exhibiting emergent properties such as semantic prompt comprehension, In-Context Learning (ICL), and Chain-of-Thought (CoT) reasoning. Despite their…

Computation and Language · Computer Science 2026-03-13 Yuling Jiao , Yanming Lai , Huazhen Lin , Wensen Ma , Houduo Qi , Defeng Sun

Large Language Models (LLMs) have exhibited exceptional performance across a broad range of tasks and domains. However, they still encounter difficulties in solving mathematical problems due to the rigorous and logical nature of…

Computation and Language · Computer Science 2024-10-01 Linzhuang Sun , Hao Liang , Jingxuan Wei , Bihui Yu , Conghui He , Zenan Zhou , Wentao Zhang

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

Leveraging mathematical Large Language Models (LLMs) for proof generation is a fundamental topic in LLMs research. We argue that the ability of current LLMs to prove statements largely depends on whether they have encountered the relevant…

Causal structure discovery from observations can be improved by integrating background knowledge provided by an expert to reduce the hypothesis space. Recently, Large Language Models (LLMs) have begun to be considered as sources of prior…

Machine Learning · Computer Science 2024-05-24 Victor-Alexandru Darvariu , Stephen Hailes , Mirco Musolesi

Considering the challenges faced by large language models (LLMs) in logical reasoning and planning, prior efforts have sought to augment LLMs with access to external solvers. While progress has been made on simple reasoning problems,…

Computation and Language · Computer Science 2025-11-11 Yu Zhang , Hui-Ling Zhen , Zehua Pei , Yingzhao Lian , Lihao Yin , Mingxuan Yuan , Bei Yu

Long-context reasoning is essential for complex real-world applications, yet remains a significant challenge for Large Language Models (LLMs). Despite the rapid evolution in long-context reasoning, current research often overlooks the…

Computation and Language · Computer Science 2026-04-10 Yanling Xiao , Huaibing Xie , Guoliang Zhao , Shihan Dou , Shaolei Wang , Yiting Liu , Nantao Zheng , Cheng Zhang , Pluto Zhou , Zhisong Zhang , Lemao Liu

Large language models (LLMs) have pushed the limits of natural language understanding and exhibited excellent problem-solving ability. Despite the great success, most existing open-source LLMs (e.g., LLaMA-2) are still far away from…

Computation and Language · Computer Science 2024-05-06 Longhui Yu , Weisen Jiang , Han Shi , Jincheng Yu , Zhengying Liu , Yu Zhang , James T. Kwok , Zhenguo Li , Adrian Weller , Weiyang Liu

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

Code has become a standard component of modern foundation language model (LM) training, yet its role beyond programming remains unclear. We revisit the claim that code improves reasoning through controlled pretraining experiments on a…

Artificial Intelligence · Computer Science 2026-05-20 Yuze Zhao , Junpeng Fang , Lu Yu , Zhenya Huang , Kai Zhang , Qing Cui , Qi Liu , Jun Zhou , Enhong Chen