Calibration-Aware Temporal Representation Learning under Feature Estimation Noise

Temporal models typically treat the representation available at each time step as deterministic, although in practice intermediate features may be estimated under sensor noise, stochastic encoding, missing observations, or limited measurement precision. Unlike static prediction, representation error in a temporal model can alter the hidden state and subsequently propagate through all later transitions. We study this trajectory-level effect and its consequences for probabilistic prediction. Our analysis separates local uncertainty injection from downstream dynamical amplification: finite-perturbation bounds characterise worst-case error propagation, a local Jacobian analysis describes how feature covariance is transformed through the hidden trajectory, and a second-order expansion shows that even zeromean feature noise can induce systematic hidden-state bias through nonlinear curvature. Motivated by this analysis, we propose Calibration-Aware Temporal Representation Learning (CaTRe), whose core mechanism is an uncertaintyconditioned gate that attenuates unreliable hidden-state updates before their perturbations propagate through time. We evaluate CaTRe on Room Occupancy Estimation and Occupancy Detection with GRU and liquid time-constant (LTC) backbones under clean evaluation, additive representation noise, channel missingness, and temporal thinning. The empirical effect is strongly regime dependent. When GRU baselines are already near saturation or have low probabilistic error, CaTRe produces limited gains and can trade off across metrics. In contrast, the largest improvements occur for LTC settings with high baseline probabilistic error: on Room Occupancy, CaTRe improves clean accuracy from 0.241 to 0.807, reduces NLL from 11.855 to 0.737, and reduces ECE from 0.753 to 0.203. Ablations further show that uncertainty gating is the dominant contributor, while auxiliary probabilistic and trajectory-stability losses are not always complementary. These results support a trajectory-level view of representation uncertainty: its effect depends not only on local noise magnitude, but also on how temporal dynamics transform that uncertainty before prediction.