TOPODUET: ONE TOPOLOGY, TWO RELATIONAL FIELDS FOR SPATIO-TEMPORAL FORECASTING

Spatio-temporal graph forecasters typically encode observations and temporal variations in a single latent tensor, although locations that look alike need not change alike. We introduce TOPODUET, which separates these relational roles into a Configuration Field \(L\) induced by absolute observations and a Transition Field \(I\) induced by signed first- and second-order variations. The Dual-Field Spatio-Temporal Encoder learns independent temporal and spatial relations for the two fields. Field-Adaptive Road Attention supplies both fields with forward–backward road support while learning field- and layer-specific prior strengths, and Progressive Cross-Field Coupling exchanges their evidence after each block without collapsing their identities. A horizon-adaptive dual-path readout then balances nonlinear correction with historical persistence. Our structural analysis quantifies the distortion caused by forcing one shared relation, identifies the minimal direction-complete closure of a directed road prior, and characterizes when a common soft prior yields identical field relations. Experiments on eight traffic forecasting datasets show that TOPODUET ranks first on all 12 MAE/RMSE comparisons across six graph-based highway datasets, reducing the best competing error by up to 4.9% in MAE and 7.3% in RMSE. The same architecture also transfers effectively across the T-Drive and CHIBike grid benchmarks, extending the dual-field formulation from sensor graphs to urban-flow fields. Controlled ablations further show that removing field separation increases MAE/RMSE by 0.10/0.62 on PeMS08 and 0.28/0.95 on T-Drive, supporting the value of modeling configuration and transition relations separately.