TimeOperator: A Function-to-Function Approach to Time Series Modeling

Most time-series foundation models operate on fixed temporal grids, representing signals as vectors, tokens, or patches and learning maps between discretized observations. This grid-to-grid view is convenient for standard forecasting, but it is not the natural object for reusable time-series modeling, where temporal resolution, forecast horizon, and query locations may change across tasks and deployments. We argue that time-series foundation models should instead learn sample-conditioned function-to-function operators. Given finite observations of an underlying signal, such an operator maps the observed context to an output function that can be evaluated at user-specified times. We propose \textbf{TimeOperator}, a compact branch-trunk backbone that realizes this view with a shared context encoder, spectrally informed query features, context-adaptive trunk parameters, and multi-basis temporal responses. Forecasting and imputation are handled by evaluating the same operator on different query sets, while classification reuses the shared context representation. Across deterministic and probabilistic forecasting, imputation, and classification benchmarks, TimeOperator is competitive with existing time-series foundation models. Further analyses show that cross-frequency and cross-horizon prediction can be handled by changing only the query set, rather than changing the decoder or relying on post-hoc resampling.