Spatial-as-Refinement: Gated Graph Operators over Strong Temporal Predictors for Scalable Spatio-Temporal Forecasting

Graph-based spatio-temporal forecasters route information through a learned adjacency at every encoder layer, with graph operators as the substrate and temporal operators interleaved at every depth. We argue this convention is structurally fragile when the learned adjacency is noisy, as it often is on fragmented sensor networks. Under a perturbed-adjacency model, we show that substrate placement yields a noise bound that compounds multiplicatively through the operator norms of all other layers, so the optimizer cannot silence one bad layer without discarding the signal it carries. We propose GraFT, built on a structural reordering we call spatial-as-refinement: a per-sensor temporal predictor first produces a complete forecast, and a small stack of $\alpha$-gated graph blocks refines it through residual updates $y\leftarrow y+\alpha \cdot \mathrm{LN}(\mathcal{G}(y))$, each gate initialized to zero. Under the same model, this reordering replaces the multiplicative bound with one that is exactly zero when gates are closed and confines noise to a channel each layer's gate controls independently. The same operator is therefore a liability or an asset depending only on where it sits, and the optimizer decides how much to use it from data alone. Experiments on controlled synthetic and real-world data confirm the theory's three predictions (substrate models diverge under adjacency noise, refinement-structured models degrade gracefully, and the mean gate closes under fragmentation) and let us verify the multiplicative-versus-gated mechanism directly. Across fourteen real-world benchmarks spanning traffic, energy, meteorology, and mobility, a single GraFT instantiation establishes new state-of-the-art performance, attaining the best average rank against strong published baselines, and the learned gates reveal where the graph actually helps.