Executability, Not Optimality: Offline Planning on Learned Cognitive Maps

Animals reach places they were never shown how to reach, and hippocampal place cells are thought to support this by encoding a predictive map of where the animal can get to next. One computational form of that map is the multi-scale random-walk transition kernel, whose non-negative spectral embeddings reproduce localized place fields, compose across scales by matrix squaring, and yield a route by climbing a similarity field rather than searching a graph. Whether it survives being fitted to offline trajectories, which supply neither the known lattice nor the exact kernel its demonstrations assume, and what it is then worth as a planner, has been open. Here we show that it survives the fit and that what its ascent buys over shortest-path search on the same support is executability, not optimality: it leads A${}^{\ast }$ on 13 of 16 embodied OGBench datasets, and support geometry alone recovers three quarters of what that preference is worth to search. Two received rules fail there: greedy ascent, sufficient on the exact kernel, falls on the fitted map into limit cycles that one sampled alternative escapes; and distance-optimal search loses to the map, while fast marching told what the ascent prefers, as a cost $n(x{)}^{-1/2}$ on the visit count $n(x)$, beats everything here, 20 points past the published baselines. Offline planning on a recovered support is therefore not a shortest-distance problem: the support's boundary is not the world's, and the same cost improves every planner we tested. A predictive map is a usable offline planner whose value lies less in the routes it produces than in what it reveals about which routes are worth producing.