Does Your World Model Know Actions Have Consequences?

Ayush Gaggar, Jared Berry, Todd D. Murphey

November 2026

TL;DR An Action Perturbation (AP) metric scores whether a world model predicts how the state changes when an action is perturbed, which state error does not capture. With TD-MPC2 on two simulated tasks, a dynamics head trained on noise-injected demonstrations has state error similar to one trained on clean demonstrations but predicts action sensitivity about 16% (Push) and 48% (Peg) better.

What they do

World models are valued because they can imagine what happens under alternative actions, yet they are usually judged by reconstruction quality, prediction error or task success. This short paper argues that these metrics never test the dynamics predictor’s response to counterfactual actions. It borrows sensitivity analysis from system identification to measure that response directly.

How it works

AP metric. Perturb the first action of a trajectory by δ, roll out the rest open-loop, and compare the predicted change in state with the simulator’s: AP = ‖Δ̂ − Δ‖ / ‖Δ‖, weighted by the size of the true response. AP = 0 is exact; AP = 1 means the model ignores the perturbation.
Readout. A ridge-regression linear probe maps the 512-D TD-MPC2 latent to a 7-D state (end-effector, gripper, object position), with 0.015 m and 0.009 m RMSE on the two tasks.
Controlled comparison. Released TD-MPC2 checkpoints stay frozen; only the dynamics head is finetuned on 100k interactions from a workspace raster, from expert demonstrations, or from demonstrations with injected action noise.
Evaluation. 50 on-policy trajectories per task (cube push, peg insertion), 8 perturbation directions per step: 34,400 perturbed rollouts.

Results

At horizon 5 and ‖δ‖ = 0.2, AP for the imitation / noise-injected / raster heads is 0.72 / 0.62 / 2.28 on Push and 1.39 / 0.75 / 1.53 on Peg; the probe-limited floor is 0.37 and 0.19.
State error at the same horizon is close for imitation and noise-injected heads (0.039 vs 0.033 on Push), so state error alone hides the gap.
The imitation head exceeds AP = 1 on Peg from horizon 4 on, i.e. worse than ignoring the action. The noise-injected head does the same at horizon 1 on Push (1.31).

Limitations

AP needs exact environment resets to compare perturbed and nominal rollouts, so it is limited to simulation for now. Only two tasks and one world model are tested, and the link between action-sensitivity accuracy and planning performance is left open.

Figures

From Figure 1: The parts of a world-model stack (perception, dynamics, planner, reward) and the metric that tests eac... — From Figure 1: The parts of a world-model stack (perception, dynamics, planner, reward) and the metric that tests each one; current metrics skip the dynamics predictor, which sensitivity analysis targets.

From Figure 3: Workspace coverage of the three 100k-interaction datasets used to retrain only the TD-MPC2 dynamics he... — From Figure 3: Workspace coverage of the three 100k-interaction datasets used to retrain only the TD-MPC2 dynamics head: a uniform workspace raster, successful demonstrations only, and the same demonstrations with Gaussian action noise.

From Figure 4: State error against error in predicted action sensitivity for the three dynamics heads on Push and Peg... — From Figure 4: State error against error in predicted action sensitivity for the three dynamics heads on Push and Peg, with four example settings (warehouse, surgical, Roomba, space) placed by which error matters more for them.

Abstract

Embodied world models (WMs) are implicit learning systems that predict the next future latent state directly from observations and actions. Unique from other end-to-end learning systems, the dynamics predictor of WMs can simulate the environment's response to alternative actions without physical deployment nor pre-specifying states of the dynamical system. Current metrics focus on the quality of model outputs, e.g., clarity of reconstructions or task success, but fail to assess the fidelity of modeling consequences of counterfactual actions. Inspecting the forced response to action perturbations through sensitivity analysis is one way to audit how well WMs can predict the consequences of counterfactual actions. Deploying WMs on hardware will require new evaluation frameworks to analyze the tradeoffs between state error and accurate sensitivity prediction.

Summaries are written automatically from each paper's text. Figures and videos come from the paper and its project page; all credit goes to the authors.

Matt Strong