Imagined Rollouts are Kinematic, Not Dynamic: A Diagnosis of Long-Horizon World-Model Failure

Technical Summary: Imagined Rollouts Are Kinematic, Not Dynamic

Problem Statement
Long-horizon failure in world models is conventionally attributed to "compounding error," a framing that accurately describes error accumulation but fails to distinguish the type of error or the specific feature dimensions that deteriorate. The authors argue that this generic framing obscures a specific structural signature: world models tend to imagine motion that is kinematically consistent (extrapolating position, velocity, and acceleration trajectories based on linear update rules) but dynamically inconsistent (failing to account for the physical constraints, such as mass, friction, and contact, that govern real motion). This "kinematic fallback" represents a distinct layer of failure alongside existing theories of representation engineering and error-compounding bounds.

Methodology
To diagnose this structural deficit, the authors propose a reframing of world model evaluation based on the distinction between kinematic and dynamic motion.

1. Imagined Kinematic-Consistency Error (iKCE):
   The authors define a per-step diagnostic metric, iKCE, which measures the deviation of an imagined rollout from a closed-form kinematic null (e.g., constant velocity or constant acceleration).

   • Definition: $iKCE = \frac{1}{T} \sum_{t=0}^{T-1} \| \hat{x}^{WM}_{t+1} - kin(\hat{x}^{WM}_t) \|^2$.
   • Interpretation: Contrary to intuition, a low iKCE indicates that the model is successfully extrapolating kinematic patterns (kinematic imagination). A high iKCE, particularly one that grows with horizon and responds to physical regime changes, is the signature of dynamic imagination.

2. Conditioning-Perturbation Protocol:
   To distinguish between kinematic and dynamic imagination, the authors drive the iKCE through a dose-response curve by perturbing physically meaningful conditioning parameters (e.g., friction coefficient $\mu$, initial velocity, payload).

   • Signature 1 (Regime Invariance): A kinematic imaginer produces an iKCE curve that scales smoothly with perturbation magnitude regardless of the physical regime, as it extrapolates the same linear structure. A dynamic imaginer should show sensitivity to regime boundaries (e.g., gait collapse).
   • Signature 2 (Monotone Consistency): The model should respect physical monotonicities (e.g., higher friction $\to$ shorter stopping distance) only when those relationships hold physically. Kinematic models respect linear monotonicities but fail regime-conditional ones.

Experimental Setup
The diagnostic was instantiated on a released DreamerV3 checkpoint trained on the DMC walker-walk environment.

• Baselines: Comparisons were made against real-physics rollouts driven by the trained policy.
• Conditions: The study included a friction sweep across 13 magnitudes ($\mu \in [0.1, 1.7]$), crossing the empirically determined gait-collapse boundary at $\mu=0.20$.
• Controls: Experiments included actor-training-horizon ablations and domain-randomization controls to rule out policy out-of-distribution (OOD) artifacts.

Key Results

1. Magnitude of Error (Hypothesis 1): The imagined iKCE of the DreamerV3 world model was significantly higher than that of matched real-physics rollouts.

   • At horizon $T=16$, the ratio was $\sim 180\times$ ($7.7 \times 10^{-3}$ vs. $4.2 \times 10^{-5}$).
   • At horizon $T=64$, the ratio was $\sim 30\times$, with the narrowing attributed to per-step dilution in the model's smooth long-horizon tail.
   • This confirms the model's imagination carries a substantial residual against a kinematic null.

2. Regime Invariance (Hypothesis 2): Across the friction sweep, the trained policy's reward collapsed from $\sim 650$ to $\sim 200$ as friction dropped below the gait-collapse boundary ($\mu=0.20$). However, the imagined iKCE remained statistically flat across the entire range.

   • Regression analysis showed the slope of the world model's iKCE vs. friction contained zero ($\beta_{WM} = -0.009$, 95% CI $[-0.096, +0.082]$), whereas the real-physics slope was significantly negative ($\beta_{phys} = -0.220$).
   • This indicates the world model is "blind" to the physical regime change, confirming the kinematic-not-dynamic signature.

Significance and Claims
The paper claims that long-horizon world model failure is not merely a variance or representation engineering issue, but a structural deficit where models learn rich kinematic features but systematically under-represent dynamic features.

• Diagnostic Value: The iKCE protocol provides a falsifiable evaluation diagnostic that distinguishes kinematic from dynamic imagination at horizons longer than the embodiment's gait period.
• Implication for Training: The authors suggest that if imagined rollouts are kinematically structured but dynamically unfaithful, policy gradients propagated through long horizons optimize the actor against a trajectory distribution diverging from real dynamics. This is consistent with observations that long-horizon actor training (e.g., $h=64$) yields unstable convergence and weaker deployed policies compared to shorter horizons ($h=15$).
• Modesty: The authors explicitly state that the diagnostic is structural, not predictive. A low iKCE identifies a model as kinematic but does not certify it as a useful predictor; conversely, a high iKCE with friction sensitivity certifies a model as dynamic but not necessarily accurate. The results are currently bounded to a single embodiment (DMC walker) and a specific world model family, though the protocol is designed to be generalizable.