Learning What to Share: Expert Specialization for Time-Series Forecasting

Overview & Synopsis

A central challenge in multivariate forecasting is deciding what to share across channels and where to specialize. Mixture-of-experts models offer flexible sharing, yet it remains unclear how much of their forecasting gains comes from added capacity or expert allocation. Through controlled comparisons across eleven datasets and three backbones, we show that informative channel assignments improve forecasting beyond matched shared capacity and random allocation. On frozen transformer backbones, persistent channel-specific mixtures outperform input-dependent routing on average. To examine when and how much specialization helps, we introduce GalaxyTS, a controlled synthetic dataset with exact shared and channel-specific forecasting references. It reveals how persistent channel mixtures exploit predictive differences concealed by short input windows and measures gains over matched shared corrections. These insights motivate Persistent Closed-Form Routing (PCR), a plug-and-play method that alternates exact conditional estimation of channel-specific mixture weights with gradient-based training of low-rank residual experts around a frozen pretrained forecaster. Averaged over four forecasting horizons, PCR-K4 achieves dataset-balanced mean squared error reductions of 3.86-14.25% relative to the three frozen backbones. In matched comparisons, PCR outperforms competing specialization methods on average while requiring substantially fewer trainable parameters.