待翻译：SHAPE of Chain-of-Thought in Math Reasoning
AI 服务暂时不可用，以下为来源摘要，待恢复后补全翻译：arXiv:2608.28600v1 Announce Type: new Abstract: Large language models (LLMs) achieve strong performance on mathematical reasoning benchmarks, yet the mathematically meaningful skills underlying their reasoning remain underexplored. We introduce \texttt{SHAPE}, a framework that analyzes Chain-of-Thought (CoT) trajectories through two lenses developed in mathematics education: (1) semantic spaces: the model's evolving mathematical interpretations of a problem (e.g., algebraic, geometric), and (2) heuristics: the specific mathematical actions taken within those spaces (e.g., simplifying the problem, working backward). We first use \texttt{SHAPE} to analyze the reasoning patterns of various models. Our findings reveal that the mathematical heuristics employed by a model better explain final answer correctness than traditional CoT features. Furthermore, models are likely to reach correct solutions by concentrating their reasoning effort within a few semantic spaces rather than exploring many disparate ones -- a pattern consistent with human behavior. Next, we utilize the \texttt{SHAPE} lens to evaluate whether post-training truly enhances mathematical proficiency. We find that reinforcement learning induces mode-seeking in heuristic usage. Lastly, we post-train LLMs by promoting diverse heuristics and demonstrate its effectiveness in improving accuracy. Overall, \texttt{SHAPE} provides a theoretically-grounded diagnostic framework for decoding LLM reasoning and offers a new path toward post-training LLMs for math reasoning. The code for our model is available at https://github.com/holi-lab/SHAPE-of-CoT
AI 服务暂时不可用，以下为来源正文，待恢复后补全翻译。
--> [Submitted on 28 Jun 2026] Title:SHAPE of Chain-of-Thought in Math Reasoning View a PDF of the paper titled SHAPE of Chain-of-Thought in Math Reasoning, by Jonghyun Song and 5 other authors View PDF HTML (experimental) Abstract:Large language models (LLMs) achieve strong performance on mathematical reasoning benchmarks, yet the mathematically meaningful skills underlying their reasoning remain underexplored. We introduce \texttt{SHAPE}, a framework that analyzes Chain-of-Thought (CoT) trajectories through two lenses developed in mathematics education: (1) semantic spaces: the model's evolving mathematical interpretations of a problem (e.g., algebraic, geometric), and (2) heuristics: the specific mathematical actions taken within those spaces (e.g., simplifying the problem, working backward). We first use \texttt{SHAPE} to analyze the reasoning patterns of various models. Our findings reveal that the mathematical heuristics employed by a model better explain final answer correctness than traditional CoT features. Furthermore, models are likely to reach correct solutions by concentrating their reasoning effort within a few semantic spaces rather than exploring many disparate ones -- a pattern consistent with human behavior. Next, we utilize the \texttt{SHAPE} lens to evaluate whether post-training truly enhances mathematical proficiency. We find that reinforcement learning induces mode-seeking in heuristic usage. Lastly, we post-train LLMs by promoting diverse heuristics and demonstrate its effectiveness in improving accuracy. Overall, \texttt{SHAPE} provides a theoretically-grounded diagnostic framework for decoding LLM reasoning and offers a new path toward post-training LLMs for math reasoning. The code for our model is available at this https URL Comments: accepted to The 3rd AI for Math Workshop at ICML 2026 Subjects: Artificial Intelligence (cs.AI) Cite as: arXiv:2608.28600 [cs.AI] (or arXiv:2608.28600v1 [cs.AI] for this version) https://doi.org/10.48550/arXiv.2608.28600 arXiv-issued DOI via DataCite Submission history From: Jonghyun Song [view email] [v1] Sun, 28 Jun 2026 11:15:59 UTC (190 KB) Full-text links: Access Paper: View a PDF of the paper titled SHAPE of Chain-of-Thought in Math Reasoning, by Jonghyun Song and 5 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.AI new | recent | 2026-08 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)