ST-FGDIR: Spatiotemporal Traffic Forecasting with Forecast-Gain-Guided Deviation-Invariance Routing

Accurate multi-step traffic forecasting requires models to respond to genuine traffic-state transitions while resisting deviations caused by missing or noisy observations. Existing deviation-aware methods characterize departures from recurrent patterns, but deviation magnitude alone does not indicate whether the resulting correction will improve a node-wise forecast. Guided by the insight that correction strength should depend on forecast gain rather than deviation magnitude, we propose Spatiotemporal Traffic Forecasting with Forecast-Gain-Guided Deviation-Invariance Routing (ST-FGDIR). ST-FGDIR constructs an anchor-conditioned stable endpoint and a deviation-corrected candidate through weight-shared current-anchor graph encoding and multi-view deviation evidence. Signed candidate-error differences provide soft forecast-gain targets for a node-wise continuous router, while selective risk extrapolation and a false-activation loss control stable-endpoint risk across perturbation environments and suppress perturbation-induced increases in residual injection. Experiments on METR-LA, PEMS-BAY, PEMS04, and PEMS08 show competitive forecasting performance relative to published baseline results. The inference gates exhibited Spearman correlations of 0.49-0.53 with realized correction gain, and the complete model yielded an average relative MAE increase of 9.38% across 12 controlled dataset-perturbation conditions. These results demonstrate that forecast-gain-guided routing coordinates stable periodic prediction with adaptive deviation correction under both clean and perturbed inputs.