FORECASTING AS CONDITIONAL TRANSPORT: DOOB- REVERSIBLE GIBBS DYNAMICS ON SPATIO-TEMPORAL GRAPHS

Observed variation in a spatio-temporal graph mixes history-predictable evolution with conditional surprise. Their distinction depends on the same available history, motivating coordinates that expose both the learned predictable reference and its residual. We frame forecasting around the construction and transport of predictive coordinates: represent variation relative to available history, propagate the resulting evidence through graph-informed interactions, and retain access to it across forecast horizons. DR-GIBBSFORMER realizes this view with a causal multi-offset Student-t projector, dual-stream temporal–spatial Gibbs attention, triangular exchange, and horizon-specific full-history functionals. The analysis characterizes coordinate bias and residual-score behavior, content–graph factorization, operator sensitivity, recoverability under exchange, and linear readout expressivity. Across ten highway and urban-flow tasks, the framework improves 18 of 20 aggregate MAE/RMSE comparisons, with gains reaching 8.26% in MAE and 7.61% in RMSE. Component and projector ablations support the value of learned conditional coordinates, structural interaction, and access to the terminal history. These findings connect the choice of predictive coordinates to the way historical evidence is exchanged and used for forecasting.