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

Summary

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.

Abstract Summary

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.

Key Points

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

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

|Authors: Yuming Chen, Yang Liu

|Venue: arXiv preprint | Year: 2026

|arXiv: 2609.21787v1

Abstract

Key Contributions

Learned world models may have compact interventions even when their recurrent state is high-dimen…
We study this question in a controlled recurrent world model where prior work identified a checkp…
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 …
Restarts using the tangent-predicted correction preserve substantial counterfactual future function

Topics

vision
reinforcement-learning
control

Code & Data

GitHub repository: https://github.com/lysea8282/future-response-dynamics

BibTeX

@article{Chen2026_260921787v1,
  title     = {Compact but Moving: Intervention-Relevant Geometry in Recurrent World Models},
  author    = {Yuming Chen and Yang Liu},
  year      = {2026},
  eprint    = {2609.21787v1},
  archivePrefix = {arXiv},
  primaryClass  = {cs.RO},
  url       = {https://arxiv.org/abs/2609.21787v1}
}