Subspace-Restricted Planning under Action Compression in Latent World Models

Latent world models plan in a learned space, and many of them compress the action before it reaches the predictor. We show that this compression leaves the planner partly blind. On a released Cube-manipulation checkpoint, 15 of 25 action dimensions never reach the predictor, so the planning cost is exactly constant along them. These directions still move the robot. A perturbation along them changes the environment while the model's imagined rollout stays at numerical noise, so no check built on the model can detect it. The planner itself produces this motion. Along a blind direction no candidate looks better than another, so a sampling-based planner executes random motion that it never selected. Raising the sampling budget 27x does not remove this motion. We propose pruned sampling, which restricts the sampler to the directions the cost depends on. One SVD of the frozen weights gives those directions. The restriction needs no training and provably cannot worsen the best achievable plan. On Cube it raises success by 6 points at the standard budget. At that budget, projecting only the executed action gives a gain not distinguishable from this one. At the largest budget tested, pruned sampling keeps its gain and that projection does not. The same restriction extends beyond the exactly blind directions. The spectrum of the second moment of the cost gradient measures how many directions the cost varies along. On four of the five checkpoints studied, this spectrum collapses far inside the visible subspace. Sampling above its spectral gap raises success by 10.7 points on Cube and by 12.3 points on Cube-double. On Cube-double, pruned sampling alone gives no measurable gain. The gains hold for four samplers on Cube and three on Cube-double. A preregistered dose-response test and the same spectrum separate the two effects behind these gains, executed noise and sampling dilution. They tell apart the checkpoints where a restriction helps from the ones where it does not. Project page: https://subspace-restricted-planning.github.io/.