Equivariant Neural Forecasting: Pair Structure for Prediction and Analysis

Multivariate forecasters increasingly exploit cross-variable dependencies to improve prediction, yet they typically treat these relationships as ephemeral computational pathways that dissolve after inference, leaving a divide between predictive accuracy and physical understanding. We introduce the Equivariant Neural Forecaster (ENF), an architecture that unifies coordinate consistency with explicit, disentangled relational modeling. Operating within an invertible normalization frame that guarantees joint equivariance across channel permutations and affine unit changes, ENF orthogonally decomposes channel states into global consensus and local deviation subspaces, while deploying algebraic double-centering to isolate bilateral interactions from unilateral baseline drifts. These disentangled interactions supply target-dependent messages to cross-channel attention and retain an explicit relational substrate for post-hoc analysis. By integrating equivariant sensor identity conditioning with relational subspace routing, the ENF framework achieves an overall 17.5% MSE reduction over iTransformer on four traffic benchmarks. Controlled tasks further confirm that the retained pair field renders multi-hop relational composition directly accessible to linear readouts, without requiring higher-order decoders. Beyond forecasting, diagnostic probes indicate that the learned field captures partially transferable coupling signals in chaotic circuits and guides symbolic distillation into analytical expressions that transfer to wind-tunnel measurements.