GatedLinear: Adaptive Routing of Complementary Linear Bases for Time Series Forecasting

Time series forecasting requires models to capture diverse temporal dynamics, from smooth trend continuation to nonstationary drift and strict phase-aligned recurrence. While recent deep learning models have improved accuracy, many process these diverse patterns through a shared computational backbone with fixed architectural inductive biases. Representative mixture-of-experts models introduce multiple experts but retain homogeneous expert architectures, leaving their forecasting roles to emerge through training. To address temporal heterogeneity directly at the level of prediction mechanisms, we propose GatedLinear: a lightweight framework that frames forecasting as the adaptive routing of complementary linear bases. GatedLinear leverages three heterogeneous forecasting experts: a global trend-seasonal basis for smooth projection, a difference-based incremental basis for nonstationary drift, and a phase-aligned recurrence basis for explicit cyclic reuse. These experts build distinct extrapolation priors directly into their forecasting operations. To combine their predictions, we introduce a Tri-Factorized Fusion Gate that decomposes routing logits into channel-specific preferences, horizon-aware offsets, and phase-indexed biases derived from known future time marks. This design enables point-wise soft routing across variables, forecast steps, and periodic phases without stacking computationally heavy neural modules. Experiments on eight standard benchmarks show that our method achieves the lowest average MSE and MAE among the evaluated baselines, while offering interpretable routing patterns and a favorable accuracy–cost trade-off.