MindTopo: Can Foundation Models Reason in Topological Space?
MindTopo benchmark with 11,030 topological tasks shows 14 multimodal LLMs reason better than they plan and remain far below human performance.
MindTopo is a benchmark of topological intuition across five properties grounded in cognitive science and formal topology: continuity, separation, order, enclosure, and knots, evaluated at reasoning and closed-loop planning levels. It contains 11,030 instances across 13 procedurally generated task types with controllable difficulty, benchmarking 14 multimodal LLMs plus agent configurations using image and video generation, including three video generative models. 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, and audited generated rollouts often fail to follow environment dynamics or preserve topology across transitions.
- Benchmark spans continuity, separation, order, enclosure, and knots at reasoning and planning levels.
- 11,030 instances across 13 procedurally generated task types with controllable difficulty.
- All 14 tested MLLMs score higher on reasoning than planning; the best trails humans substantially.
- Fine-tuning and RL on Qwen3-VL-2B-Instruct improve reasoning more than planning; rollouts often violate environment dynamics.
Full article198 words · extracted from arxiv.org · click to collapse
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/
Text extracted automatically; images, tables and formatting may be missing. Original: https://arxiv.org/abs/2609.11900