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Chain-of-Thought (CoT) plays a crucial role in reasoning for math problem solving. We conduct a comprehensive examination of methods for designing CoT, comparing conventional natural language CoT with various program CoTs, including the…

Computation and Language · Computer Science 2023-10-03 Zhanming Jie , Trung Quoc Luong , Xinbo Zhang , Xiaoran Jin , Hang Li

Large language models (LLMs) have made impressive progress in handling simple math problems, yet they still struggle with more challenging and complex mathematical tasks. In this paper, we introduce a series of LLMs that employs the…

Computation and Language · Computer Science 2024-07-18 Chengpeng Li , Guanting Dong , Mingfeng Xue , Ru Peng , Xiang Wang , Dayiheng Liu

Pragmatic reasoning helps interlocutors infer intended meaning from ambiguous or underspecified messages by considering shared context and counterfactual alternatives. Similar challenges arise in natural language-to-code generation, where…

Computation and Language · Computer Science 2026-05-26 Zhuchen Cao , Sven Apel , Adish Singla , Vera Demberg

Vision-language models (VLMs) lag behind text-only language models on mathematical reasoning when the same problems are presented as images rather than text. We empirically characterize this as a modality gap: the same question in text form…

Artificial Intelligence · Computer Science 2026-03-18 Saeed Khaki , Ashudeep Singh , Nima Safaei , Kamal Ginotra

Tool-integrated reasoning (TIR) augments large language models (LLMs) with the ability to invoke external tools during long-form reasoning, such as search engines and code interpreters, to solve tasks beyond the capabilities of internal…

Artificial Intelligence · Computer Science 2025-06-03 Hongru Wang , Cheng Qian , Wanjun Zhong , Xiusi Chen , Jiahao Qiu , Shijue Huang , Bowen Jin , Mengdi Wang , Kam-Fai Wong , Heng Ji

Recently, there has been significant progress in teaching language models to perform step-by-step reasoning to solve complex numerical reasoning tasks. Chain-of-thoughts prompting (CoT) is by far the state-of-art method for these tasks. CoT…

Computation and Language · Computer Science 2023-10-24 Wenhu Chen , Xueguang Ma , Xinyi Wang , William W. Cohen

Enhancing reasoning capabilities remains a central focus in the LLM reasearch community. A promising direction involves requiring models to simulate code execution step-by-step to derive outputs for given inputs. However, as code is often…

Computation and Language · Computer Science 2025-07-15 Keqin Bao , Nuo Chen , Xiaoyuan Li , Binyuan Hui , Bowen Yu , Fuli Feng , Xiangnan He , Dayiheng Liu

Tool-integrated reasoning (TIR) offers a direct way to extend thinking models beyond the limits of text-only reasoning. Paradoxically, we observe that tool-enabled evaluation can degrade reasoning performance even when the strong thinking…

Computation and Language · Computer Science 2026-05-08 Qianjia Cheng , Yuchen Zhang , Zhilin Wang , Yuxin Zuo , Shunkai Zhang , Yuchen Fan , Yu Qiao , Bowen Zhou , Ning Ding , Yu Cheng , Yun Luo , Ganqu Cui

The tool-use Large Language Models (LLMs) that integrate with external Python interpreters have significantly enhanced mathematical reasoning capabilities for open-source LLMs, while tool-free methods chose another track: augmenting math…

Computation and Language · Computer Science 2024-05-14 Shuo Yin , Weihao You , Zhilong Ji , Guoqiang Zhong , Jinfeng Bai

We introduce a method to improve the zero-shot reasoning abilities of large language models on general language understanding tasks. Specifically, we build an autonomous agent to instruct the reasoning process of large language models. We…

Computation and Language · Computer Science 2024-08-15 Nicholas Crispino , Kyle Montgomery , Fankun Zeng , Dawn Song , Chenguang Wang

Automated test case generation from natural language requirements remains a challenging problem in software engineering due to the ambiguity of requirements and the need to produce structured, executable test artifacts. Recent advances in…

Software Engineering · Computer Science 2026-04-09 Milad Moradi , Ke Yan , David Colwell , Rhona Asgari

Large Reasoning Models (LRMs) like o1 and DeepSeek-R1 have shown remarkable progress in natural language reasoning with long chain-of-thought (CoT), yet they remain inefficient or inaccurate when handling complex mathematical operations.…

Computation and Language · Computer Science 2025-06-13 Chengpeng Li , Zhengyang Tang , Ziniu Li , Mingfeng Xue , Keqin Bao , Tian Ding , Ruoyu Sun , Benyou Wang , Xiang Wang , Junyang Lin , Dayiheng Liu

Large language models (LLMs) excel in complex tasks through advanced prompting techniques like Chain-of-Thought (CoT) and Tree-of-Thought (ToT), but their reliance on manually crafted, task-specific prompts limits adaptability and…

Computation and Language · Computer Science 2025-07-04 Tao Xiong , Xavier Hu , Wenyan Fan , Shengyu Zhang

Bilingual mathematical problem solving needs a clear link between language reasoning and symbolic calculation. Large language models often handle language well but are weak in accurate computation. This paper presents HERALD (Hybrid…

Artificial Intelligence · Computer Science 2025-12-23 Peiqing Lu , Yuan Zhang , Haoyun Zhang , Jiasen Zheng , Kejian Tong , Wenjun Wu

Mathematical reasoning is a cornerstone of artificial general intelligence and a primary benchmark for evaluating the capabilities of Large Language Models (LLMs). While state-of-the-art models show promise, they often falter when faced…

Computation and Language · Computer Science 2025-07-29 Yifan Hao , Fangning Chao , Yaqian Hao , Zhaojun Cui , Huan Bai , Haiyu Zhang , Yankai Liu , Chao Deng , Junlan Feng

The rapid advancement of Large Language Models (LLMs) in the realm of mathematical reasoning necessitates comprehensive evaluations to gauge progress and inspire future directions. Existing assessments predominantly focus on problem-solving…

Computation and Language · Computer Science 2024-06-05 Xiaoyuan Li , Wenjie Wang , Moxin Li , Junrong Guo , Yang Zhang , Fuli Feng

We study why Tool-Integrated Reasoning (TIR) makes Large Language Models (LLMs) more capable. While LLMs integrated with tools like Python code interpreters show great promise, a principled theory explaining why this paradigm is effective…

Machine Learning · Computer Science 2025-08-27 Heng Lin , Zhongwen Xu

We present $\textbf{Research Math Agents (RMA)}$, an agentic framework for automated reasoning on research-level mathematical problems. Unlike prior studies centered on competition mathematics or formal theorem proving, RMA targets…

Artificial Intelligence · Computer Science 2026-05-25 Zelin Zhao , Bo Yuan , Jaemoo Choi , Yongxin Chen

Tool-integrated reasoning (TIR) has emerged as a dominant paradigm for mathematical problem solving in language models, combining natural language (NL) reasoning with code execution. However, this interleaved setup has three key…

Computation and Language · Computer Science 2026-05-12 Hyeon Hwang , Jiwoo Lee , Jaewoo Kang

Recent studies have demonstrated that Large Language Models (LLMs) have strong mathematical reasoning abilities but rely on hundreds of billions of parameters. To tackle the challenge of poor reasoning in Small Language Models (SLMs),…

Computation and Language · Computer Science 2025-08-19 Xinhe Li , Jiajun Liu , Peng Wang