Compact but Moving: Intervention-Relevant Geometry in Recurrent World Models

Abstract:Learned world models may have compact interventions even when their recurrent state is high-dimensional, but it is unclear what happens to such a correction after it enters the model. We study this question in a controlled recurrent world model where prior work identified a checkpoint-specific rank-4 interface for one-shot counterfactual velocity interventions. The correction rapidly leaves this fixed entry subspace during autonomous rollout. Nevertheless, a low-rank image obtained by transporting the entry directions through the factual recurrent Jacobian chain continues to capture most of the nonlinear correction. Restarts using the tangent-predicted correction preserve substantial counterfactual future function. This transport/function pattern recurs across independently trained structured-GRU models and a parameter-matched LSTM initialized with a privileged compact correction. We further characterize a finite-horizon future-response operator over the full recurrent carrier. Patching shifts its leading future-sensitive directions toward the matched native-counterfactual organization, and the local operator accurately ranks finite perturbation effects over the registered direction panels at the patched and native-counterfactual basepoints. A separate full-amplitude assay finds substantial factual-endpoint tangent residuals and supports response reconfiguration in two of three checkpoints. Together, these results show that compact intervention structure can persist as a moving, state-dependent local geometry embedded in high-dimensional recurrent dynamics, without implying a fixed or dynamically closed low-dimensional state.

Robotics (cs.RO)

arXiv:2609.21787 [cs.RO]

(or arXiv:2609.21787v1 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2609.21787 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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