MindTopo: Can Foundation Models Reason in Topological Space?
Do AI models understand shapes that bend but don't break?
AI models can identify topological relationships like holes and connectivity when asked directly, but struggle dramatically when they have to plan actions in environments where those relationships matter. Even the best-performing model fell far short of human-level performance, and when models generated their own observations to plan with, they frequently violated the very topological rules they were supposed to be reasoning about.
Topological reasoning—understanding which spatial properties survive deformation—is fundamental to navigation, manipulation, and physical reasoning. Current AI systems that power robots and autonomous agents may be unable to reliably predict or plan for situations involving tangles, holes, or continuous deformation, potentially causing failures in real-world tasks like robotic manipulation or path planning through complex environments.