Low-Rank Dynamics-Effective Latent Carriers for Counterfactual Rollout in Learned World Models

Abstract

World models may predict the future without making clear which parts of their hidden state actually drive those predictions. We ask whether a small, directly addressable hidden-state change can place a learned world model on the intended counterfactual trajectory and then let the model continue that future on its own. We study a recurrent world model with a 192-dimensional hidden state in a controlled two-object, two-dimensional collision environment. For a bounded family of local velocity edits, we first verify that the model can natively represent and roll out the edited future. We then construct candidate low-rank carriers from training-only factual-to-counterfactual hidden differences and learn a map from the factual state and requested edit to carrier coefficients. On the registered rank grid, rank 4 is the smallest tested rank that satisfies the full development-panel criteria. A single rank-4 patch at the anchor is sufficient to redirect a 12-step autonomous rollout, with no future observations, teacher forcing, or repeated correction. The frozen procedure satisfies the preregistered replication rule across independently trained checkpoints and remains usable across nearby intervention times. Random equal-norm, wrong-object, and wrong-time controls do not explain the effect. A position-edit stress test provides a negative contrast: the intended position patch can pass the raw rollout criteria, but no-patch and random controls can pass the same criteria, and wrong-object specificity is not established. Thus, successful editing alone is not enough. We use dynamics-effective to describe an intervention that changes the model's future computation in a sustained and target-specific way under autonomous rollout. The rank-4 result identifies a compact intervention interface for the tested velocity-edit family, not a closed four-dimensional state or an intrinsic state dimension.