Foundation models struggle with spatial reasoning in topological space
MindTopo: Can Foundation Models Reason in Topological Space?
Artificial IntelligenceComputation and LanguageComputer Vision and Pattern Recognition
Summary
Understanding space involves knowing not just distances and shapes but also how objects stay connected or separated even when stretched or bent. The authors created MindTopo, a set of tests to see if large AI models understand these basic topological ideas like continuity and enclosure. They found that while these AI models can somewhat reason about these properties, they do much worse when asked to plan or act in ways that require this understanding. Even the best AI models still lag far behind humans in these tasks. Improvements with extra training helped reasoning but didn’t solve the problems with planning and following complex environment rules.
Foundation modelsTopological spaceSpatial reasoningContinuitySeparationOrderEnclosureKnotsReinforcement learningCognitive science
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
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 https://mind-topo.github.io/