MindTopo：基础模型能否在拓扑空间中推理？

Computer Science > Artificial Intelligence arXiv:2609.11900v1 (cs) [Submitted on 10 Sep 2026] Title:MindTopo: Can Foundation Models Reason in Topological Space? Authors:Yunfei Ge, Anbang Liu, Qineng Wang, Johnalbert Garnica, Jianwen Lyu, Zihan Wang, Reuben Tan, Jianfeng Gao, Ruohan Zhang, Yining Hong, Jiajun Wu, Manling Li View a PDF of the paper titled MindTopo: Can Foundation Models Reason in Topological Space?, by Yunfei Ge and 11 other authors View PDF HTML (experimental) Abstract:Spatial reasoning depends not only on metric properties such as distance, angle, and shape, but also on topological relations that remain invariant under continuous deformation. Cognitive science identifies these relations as foundational to spatial understanding, yet foundation-model evaluations largely focus on metric or viewpoint-dependent relations. We introduce MindTopo, a benchmark of topological intuition across five properties grounded in cognitive science and formal topology: continuity, separation, order, enclosure, and knots. MindTopo evaluates each property at two cognitive levels. Reasoning asks a model to identify topological relations or infer how they change. Planning instantiates a foundation model as a closed-loop agent whose policy selects environment actions. MindTopo contains 11,030 instances across 13 procedurally generated task types with controllable difficulty. We benchmark 14 MLLMs and study agent configurations augmented with image and video generation, including 3 video generative models in planning settings. Every MLLM performs better on reasoning than on planning, and the best-performing model remains far below observed human performance. On Qwen3-VL-2B-Instruct, supervised fine-tuning and reinforcement learning improve reasoning more than planning. Generated observations retain local cues and reach plausible endpoints, but audited rollouts do not reliably follow environment dynamics or preserve topology across transitions. Our website is at this https URL Comments: Subjects: Artificial Intelligence (cs.AI); Computation and Language (cs.CL); Computer Vision and Pattern Recognition (cs.CV) Cite as: arXiv:2609.11900 [cs.AI] (or arXiv:2609.11900v1 [cs.AI] for this version) https://doi.org/10.48550/arXiv.2609.11900 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Qineng Wang [view email] [v1] Thu, 10 Sep 2026 17:54:32 UTC (14,851 KB) Full-text links: Access Paper: View a PDF of the paper titled MindTopo: Can Foundation Models Reason in Topological Space?, by Yunfei Ge and 11 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.AI new | recent | 2026-09 Change to browse by: cs cs.CL cs.CV References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark 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?)