FISC: Time-Series Forecasting via First-Layer Statistical Calibration Constraints

Multivariate time-series forecasting requires reliable cross-series interaction, yet many attention- and mixing-based models couple heterogeneous variables without explicit entry-stage alignment. Such uncalibrated early interaction can lead to poorly conditioned optimization and degraded generalization when cross-series statistics drift. We propose First-layer Statistical Calibration (FISC), a simple framework that imposes statistical calibration constraints only on the first cross-series coupling layer while leaving deeper coupling layers learnable without repeated calibration. FISC estimates training-set cross-series statistics, converts them into a statistical affinity matrix, and convexly fuses this matrix with learnable coupling parameters. A row-wise simplex projection then yields a nonnegative row-stochastic mixing operator, providing bounded and interpretable entry-layer interaction. By restricting calibration to the first layer, FISC calibrates the entrance interaction without repeatedly constraining deeper feature transformations. To reduce temporal redundancy, FISC further combines a time-domain branch with a data-adaptive orthogonal-domain branch derived from training-time temporal statistics. Experiments on standard long- and short-term forecasting benchmarks show that FISC improves forecasting accuracy while maintaining favorable efficiency. Ablations and non-stationarity analyses further show that first-layer-only calibration consistently outperforms no calibration, last-layer calibration, and all-layer calibration, supporting a simple principle for robust cross-series learning: constrain the entrance interaction with training-set statistics, while letting deeper representations remain data-adaptive.