From Physical Change to Action: Causal Attribution in World Action Models

World Action Models (WAMs) couple future prediction with robot action generation, yet how prediction causally contributes to action and whether this contribution survives reduced predictive computation remain unclear. We use matched physical counterfactuals to define action responses and representation interventions to trace their transmission across four frozen WAM configurations. Model-specific interfaces strongly transmit these responses, although Fast-WAM-IDM shows that strong transmission need not reconstruct the complete counterfactual action. In Fast-WAM-Joint, fixing the action decoder’s future inputs sharply reduces the effect of replacing representations associated with the current observation, revealing substantial propagation through downstream future representations. Under blocking, restoring future inputs in a predefined late window of decoder layers recovers substantially more of the response than an equally sized early window. Targeted RoboTwin experiments likewise find larger propagation-allowed effects than future-fixed current effects, with the additional propagated effect opposing the latter in signed mean. Reducing Fast-WAM-Joint’s world-branch computation lowers cumulative policy-computation time by a median of 23.7% while all evaluated LIBERO continuations still complete. However, matched action responses change, with little held-out improvement from a shared scalar rescaling. Together, these findings show that prediction’s causal contribution to action can change with the inference procedure even when task completion is preserved.