TWINWORLD: Contrast-Consistent Causal Response-Surface Learning for Reality–Belief Counterfactuals

Reliable counterfactual modeling requires distinguishing changes in the physical world from changes in an agent's belief about that world. Under partial observability, the same behavioral response can arise from different underlying causes, making conventional intervention-based evaluation insufficient to identify whether behavior changes are driven by physical conditions, beliefs, or their interaction. We formulate this challenge as a causal response-surface learning problem and introduce a paired factorial intervention framework that independently manipulates physical state and initial belief across four counterfactual worlds, $(P,K)\in \{(0,0),(1,0),(0,1),(1,1)\}$. This design identifies three interpretable causal contrasts: the physical main effect, the belief main effect, and their interaction.Building on this formulation, we develop TWINWORLD, a contrast-consistent response-surface estimator that jointly recovers physical openness, belief openness, and target relevance, and reconstructs the four potential-response cells through a shared structured decoder with a bounded residual. The resulting factorization couples latent-state prediction with intervention algebra, providing an explicit inductive bias for counterfactual consistency rather than treating intervention conditions as unrelated outcomes. We further characterize the identifiability of belief from behavioral evidence, showing that belief-independent actions provide no information about the hidden belief state, whereas repeated observations can improve recoverability under persistent beliefs and conditional independence.We evaluate the framework using controlled interventions and semi-synthetic traffic environments with map and motion-history evidence. The experiments examine route-response estimation, latent-state recovery, intervention contrasts, and negative controls, demonstrating that temporal evidence supports hidden-state recovery and that contrast-consistent structure improves counterfactual response estimation. Overall, TWINWORLD provides an operational causal framework for separating reality from belief and for learning structured counterfactual response surfaces when latent beliefs mediate observed behavior.