Humans do not understand space through distances and angles alone: whether something is inside something else, a path is cut, or a loop is knotted are properties preserved under continuous deformation. The MindTopo benchmark tests exactly this: five topological properties across 13 tasks and 14 multimodal models, split between reasoning about a situation and planning in an environment that needs sequential actions.
The main finding is a distinction: models are better at static reasoning than closed-loop planning. Even when a model correctly reads a relation from an image, keeping that same constraint across an action sequence is harder. Fine-tuning and reinforcement learning improve reasoning more than planning — knowing a concept is not the same as stably applying it.
This distinction matters for agents: recognizing a relation is not enough; the relation must survive state updates. Of course, the benchmark's procedural world is simpler than the real one, and planning failures could come from vision or memory rather than a missing topological representation. Still, it is a good measure of 'understanding' because it tests unfamiliar structures, not just verbal answers.