{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/mathematical-reasoning-in-large-language","title":"Mathematical Reasoning in Large Language Models: Assessing Logical and Arithmetic Errors across Wide Numerical Ranges","arxiv_id":"2502.08680","date":"2025-02-12","proceeding":null,"authors":["Safal Shrestha","Minwu Kim","Keith Ross"],"abstract":"Mathematical reasoning in Large Language Models (LLMs) is often evaluated using benchmarks with limited numerical ranges, failing to reflect real-world problem-solving across diverse scales. Furthermore, most existing evaluation methods only compare model outputs to ground-truth answers, obscuring insights into reasoning processes. To address these limitations, we introduce GSM-Ranges, a dataset generator derived from GSM8K that systematically perturbs numerical values in math problems to assess model robustness across varying numerical scales. Additionally, we propose a novel grading methodology that distinguishes between logical and non-logical errors, offering a more precise evaluation of reasoning processes beyond computational accuracy. Our experiments with various models reveal a significant increase in logical error rates-up to 14 percentage points-as numerical complexity rises, demonstrating a general weakness in reasoning with out-of-distribution numerical values. Moreover, while models demonstrate high accuracy on standalone arithmetic tasks, their performance deteriorates substantially when computations are embedded within word problems. These findings provide a comprehensive evaluation of LLMs' mathematical reasoning capabilities and inform future research directions for improving numerical generalization in language models.","url_abs":"https://arxiv.org/abs/2502.08680v1","url_pdf":"https://arxiv.org/pdf/2502.08680v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"mathematical-reasoning-in-large-language","repo_url":"https://github.com/minwukim/GSM-Ranges","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"gsm8k","task_name":"GSM8K"},{"task_slug":"math","task_name":"Math"},{"task_slug":"mathematical-reasoning","task_name":"Mathematical Reasoning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2502.08680","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}