Does LeWorldModel Preserve Local Action Geometry?

Does LeWorldModel Preserve Local Action Geometry?. By Vasil Vasilev and one other, from the Technological School Electronic Systems and the Massachusetts Institute of Technology. Published on the twenty-second of October. No code repository is linked to it.

The question is narrow. When the action fed to a pretrained LeWorldModel, LeWM, changes by a small amount, does the model reproduce the effect that change would really have? The answer here is: only partly, and how well depends on the scale of the change. At the smallest scale, the action directions the model is most sensitive to point in different directions from the simulator's.

The method pairs simulator responses with model responses to the same perturbations, and summarises action sensitivity with Gram matrices at three perturbation scales. Across nearly a thousand states from Reacher and from OGBench Cube, the most sensitive directions disagree by a median angle of about thirty-six degrees on Reacher and forty-two degrees on Cube, at the smallest scale.

Making the perturbation tenfold larger cuts the median normalized Gram discrepancy by roughly seventy percent on Reacher and forty-seven percent on Cube. Geometry measured in pixels and in embeddings shifts more across scales than the chosen physical-state geometry does.

On held-out directions, the environment's own Grams give median embedding response errors of seventeen percent on Reacher and twenty-eight percent on Cube. An isotropic reference with the same trace gives twenty-six percent and thirty-eight percent. LeWM's own errors are higher at this scale.

This is one pretrained model, two environments, and three perturbation scales. What the results support is evaluating action sensitivity at a specific scale. Whether these geometric gaps matter for control is left explicitly open.

Asked whether small action changes come out right in LeWM, the measurements say that at the smallest scale the model's sensitive directions point elsewhere, and that the Gram discrepancy shrinks as the step grows. Any check of this geometry therefore has to name the scale it was taken at.