Dynamics-effective is used to describe an intervention that changes the model's future computation in a sustained and target-specific way under autonomous rollout under autonomous rollout.
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.
Modern world models -- Dreamer, transformer world models (IRIS, Genie), and JEPA / next-latent architectures -- learn dynamics from observed trajectories but share a weakness: their transition map is disciplined only where data were seen, so it degrades under policy-induced distribution shift and on counterfactual states off the training path. We argue that a Dynamic Stochastic General Equilibrium (DSGE) model is a structured world model: its state is a belief state -- the very object a latent world model learns, but supplied with causal structure and hard cross-equation constraints. We introduce DSGE-Gym, a benchmark of eight DSGE environments with off-path counterfactual test sets, scaling to the ECB's 230-variable New Area-Wide Model. We find that (i)learned world models match the dynamics on-path but collapse off-path (5{\sigma} tail RMSE up to \sim 40 the on-path level), and (ii)training the same architectures on data the DSGE generates across rare and counterfactual-policy states -- coverage only a structural model can synthesize -- roughly halves tail error and cuts policy-regime error 10--280 where the counterfactual rule shifts the ergodic support. Because such coverage cannot be sampled from any single history, this measures structure's ability to manufacture the missing distribution. DSGE-Gym and all code are released as a reproducible testbed for counterfactual generalization.
Latent world models are trained to predict future states in a learned representation and are then deployed inside a planner that selects actions by simulating them forward. Current practice adopts the prediction error, the single- or multi-step rollout loss on held-out data, as the training and model-selection objective, on the assumption that a lower prediction error yields better control. We show that this assumption is unreliable for a structural reason: a planner does not query the model on the training distribution but on the states that its candidate actions reach, which generally leave the data manifold, so an error averaged over the data cannot by itself govern control. We therefore reframe the objective as the discrepancy between the predicted and the true plan-cost at the plan the planner commits to, and prove that the planner's suboptimality is bounded by twice this discrepancy, whereas the data-averaged prediction error neither bounds nor tracks it. Under a linear-control premise the discrepancy separates into two terms. The first is a small on-manifold residual, on which the predicted and true dynamics agree and which a spectral tax prices through the non-normality of the latent transition operator. The second is an off-manifold divergence, on which an action carries the state off the manifold and the two dynamics diverge; this divergence is the binding term and is bounded by no data-averaged error. Synthetic operators confirm the pricing formulas, and latent model-predictive control experiments confirm the decoupling: across seeds, the single-step validation error is essentially uncorrelated with control success, whereas a fidelity score on the planner-reachable measure tracks it.
Hanzhe You, Yonggang Zhang, Maohao Ran et al.· 2 citations
A minibatch can influence training beyond the update at which it is observed because AdamW stores past gradient information in its optimizer states. We study this delayed effect through paired trajectories that differ only in one gradient update and share the same subsequent training sequence. We formulate AdamW as a finite-horizon input--state--output (ISO) system whose state contains the model parameters and first- and second-moment estimates. Linearizing the joint dynamics yields a signed response operator that maps a localized gradient perturbation to its future loss effects, revealing how optimizer memory shapes their magnitude, timing, and sign. We further derive an exact multistep error decomposition and establish first-order finite-horizon accuracy under local smoothness and controlled activation switching. Experiments validate the response mechanism and optimizer-state effects, while repeated-future analyses reveal substantial prospective structure in delayed influence that can be partially recovered from ISO approximations. Code is available at https://github.com/Kanyooo/Loss_ISO.
Learning structured and control-relevant latent representations remains a key challenge for world models. Recent JEPA-based world models learn action-conditioned predictive latent dynamics from observation sequences. However, their forward-prediction objectives do not explicitly enforce reliable identifiability of robot-centric physical state from individual latents or state changes from latent pairs, which can limit downstream planning and policy performance. We propose PSG-JEPA, a physically grounded JEPA world model that shapes its latent space with two complementary grounding objectives beyond forward prediction: grounding individual latents in robot proprioceptive state, and grounding latent pairs in multi-horizon joint-angle changes. Both objectives are applied only during training, leaving the inference architecture and computational cost unchanged. To comprehensively evaluate PSG-JEPA, we conduct experiments at three levels: (1) latent identifiability via probing, (2) goal-conditioned planning on frozen latents, and (3) policy learning in simulation and on a real robot. Experiments demonstrate that our PSG-JEPA consistently outperforms state-of-the-art latent world-model baselines at all three levels.
Haodong Yan, Jiaguang Zhu, Ming-Ming Jia et al.· 2 citations
Joint-embedding predictive architectures (JEPAs) learn dynamics by predicting future observations in representation space. Yet most JEPA world models return one latent successor, even when hidden intent, partial observation, or stochastic dynamics make several futures plausible. We introduce Branch-JEPA, which replaces this point-valued transition with a context-weighted finite set of latent successors. Every branch is decoded independently, and the complete set is retained at inference. The architecture supports two complementary training regimes: specialization for recovering separated successors and full-set Energy-Score training for distributional fidelity. In a locked five-seed evaluation on the Argoverse~2 official validation split, full-set training improves trajectory Energy Score by $5.8$--$6.5\%$ and probability-weighted trajectory distance by $9.3$--$10.4\%$ over matched-$K{=}6$ assignment and transport objectives, while retaining $5.36$ endpoint-deduplicated effective branches. In a parameter-exact official-validation comparison, latent branching retains $10.3\%$ more effective modes and improves Energy Score, expected ADE, and Brier in all five paired seeds over branching only at the output decoder; every paired 95\% interval excludes zero. In an OGBench graph audit, Branch-JEPA increases teleport verified-route existence to $19.2\%$ versus $3.9\%$ for the MDN. Its raw-support advantage also persists with 29-D state and RGB observations. Together, latent branching preserves more distinct futures, while full-set scoring improves the quality of the resulting predictive distribution.
Zhi Song, Ximing Xing, Zhenchao Tang et al.· 0 citations
World model serves as a promising tool to infer environment dynamics under high-dimensional observations and candidate actions. Recently, LeCun's JEPA provides a compelling framework for learning such models in representation space. Its action-conditioned extension plays a central role in visual control and latent-space planning, but leaves a fundamental question: can it recover the controlled dynamics from nonlinear observations? This paper presents a joint identifiability condition for controlled world models with Gaussian latent states, which consists of two coupled components: (1) representation identifiability and (2) transition identifiability. The former depends on the spectral separation property while the latter is related to non-degenerate variation of conditional action. We prove that when this condition holds, minimizing the LeJEPA-style predictive objective can recover both latent states and controlled dynamics in the sense of orthogonal transformation. We further prove that the upper bound of transition prediction error is inversely proportional to the spectral separation margin. We also characterize an attainable amplification of counterfactual prediction error that scales inversely with the weakest conditional action-excitation margin. The theoretical predictions are empirically supported across four nonlinear observation settings.
Xiangteng Zhang, Yang Guan, Bo Zhang et al.· 0 citations
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