Epistemic Forward Models: Learning Predictive States for Action-Conditioned Future Distinguishability

Robot actions determine future observations and which pose-space directions become identifiable. Scalar information-gain scores collapse this geometry and cannot distinguish actions that resolve different directions. We formalize the epistemic predictive state as a history representation sufficient for predicting action-conditioned identifiability geometry. We introduce Epistemic Forward Models (EFO) to predict numerical rank, identifiable subspaces, and ambiguous subspaces for the 4-DoF target pose $(p_x,p_y,p_z,\theta )$ from history and a candidate action, without reconstructing future observations. Offline supervision is derived from finite-difference Jacobians of a fixed RGB-D feature encoder in Habitat. Inference needs no simulator access. Across 95 trials, 93.6% of 285 decision points exhibit action-dependent geometry. Against a capacity-matched unstructured positive-semidefinite predictor, EFO reduces projector error from 0.500 to 0.221 and maximum principal-angle error from $45.6^{\circ }$ to $24.3^{\circ }$. Shuffling candidate actions raises projector error to 0.265. Held-out-block gains persist, while degradation under controlled one-factor shifts tracks the induced geometry change. Even among matched-current-view pairs, 23.3% have different future geometries. On these history-sensitive pairs, swapping histories increases projector error by 0.064. Across 22 counterfactual pairs matched in rank and scalar score, subspace-aware action selection reduces directional regret by 72.1%. Against a matched-capacity RSSM with an identifiability probe, EFO reduces projector error from 0.553 to 0.534 and padded principal-angle error from $61.3^{\circ }$ to $55.4^{\circ }$. These results support action-conditioned future identifiability as a structured, learnable target for robot representation learning.