SHIFT: INPUT-CONDITIONED STOCHASTIC TEMPORAL REPARAMETERIZATION FOR NEURAL OPERATOR FORECASTING

Time-series forecasting becomes challenging when observations are irregularly sampled, partially missing, asynchronously recorded, or unevenly informative in physical time. Most temporal neural operators operate on a fixed temporal coordinate system, leaving the allocation of latent temporal resolution deterministic. We introduce SHIFT, a neural-operator forecasting architecture that represents this allocation through an input-conditioned stochastic monotone reparameterization of physical time. Given observed values, masks, timestamps, and time gaps, SHIFT samples positive interval rates whose normalized cumulative sums define a strictly monotone mapping from physical time to a normalized latent-time domain. This stochastic temporal mapping resamples the encoded history onto a uniform latent-time grid, where adaptively fused multi-scale spectral–temporal branches process the resulting representation. Multiple sampled temporal reparameterizations define a finite Monte Carlo predictive mixture, allowing predictive uncertainty to be decomposed into conditional value uncertainty and temporal-geometry-induced uncertainty. The latter measures forecast sensitivity to alternative sampled latent time representations. Across regular, irregular, partially observed, and spatiotemporal benchmarks, SHIFT improves over KRNO in several settings, although the gains remain dataset- and variable-dependent.