Robot World Models Are Not Invariant to How the Actions Are Written

Ahmed Karim, Leon Chlon

A robot policy is trained with one of two action parameterizations: absolute joint targets, or deltas relative to the current state. The choice is a live engineering decision in robot learning, and a world model conditioned on actions inherits it silently. We show the inheritance is catastrophic. A latent dynamics model trained on one parameterization and handed the identical commanded trajectory written in the other collapses: retrieval degrades by 2.6-13.4x across three robot datasets and two morphologies, goal-conditioned action selection falls from 53% to 15%, and on PushT the two beliefs about the same future are near-orthogonal (cos = 0.067, worst case -0.377), so the predictor does not degrade gracefully, it answers a different question. This is not a distribution-shift artifact in the usual sense: the two encodings are mutually reconstructible at R^2 = 0.996 given the joint input, so no information is lost, and we give the test that separates a valid re-parameterization from a lossy summary or a sensor swap. The test rejected three of the four axes we proposed. The defect lives in the action channel, which the invariance literature for visual models does not examine: work…