Inverse-Conditioned World Models: Co-Designing Latent Geometry for Search-Free Planning

摘要

Latent world models predict how actions change an environment, but using these predictions for control often requires an online search. A goal-conditioned inverse model avoids this search, yet on frozen features it must recover actions from a representation learned for prediction. We introduce IC-LeWM, which adapts world-model training for inverse control through two independently usable components. Inverse co-training (ICT) lets the action-regression loss update the encoder, while action-Jacobian regularization (AJR) encourages a scaled-isometric response to actions in the predictor. We show that an isotropic latent marginal can coexist with arbitrarily poor conditioning on identifiable action directions. This conditioning determines worst-case relative error amplification in local linearized inversion. In a linear-Gaussian model, we separate ambiguity in unobservable actions from estimation error in observable directions, where equal singular values minimize inverse risk at fixed rank and gain. This analysis motivates AJR as a soft geometric regularizer of the predictor. We also provide separate diagnostics of predictor and environment-response geometry. At deployment, the controller selects actions with a single inverse-head evaluation and no online search.