MindTopo: Can Foundation Models Reason in Topological Space?

While spatial evaluations for foundation models typically measure metric properties like distance and bounding boxes, real-world understanding relies heavily on topological relations invariant to continuous deformation. MindTopo introduces a benchmark of 11,030 procedurally generated instances testing five core topological concepts—continuity, separation, order, enclosure, and knots—across static reasoning and closed-loop agent planning. Evaluating 14 multimodal models revealed a uniform shortfall: models consistently perform worse at planning than reasoning, lagging significantly behind human baselines. Even when paired with video generation, rollouts struggle to preserve physical dynamics and topological integrity across transitions.