The authors designed a plug-in layer (the "Spatial Adapter") that sits on top of any frozen model and learns a compressed spatial summary of the model's prediction errors. The layer represents the residual field using an orthonormal basis plus per-sample scores, learned via mini-batch optimization, and produces a closed-form estimate of how errors are spatially correlated—enabling predictions at new locations with uncertainty estimates. Because the original model stays frozen, this is strictly a post-hoc add-on that doesn't retrain the backbone.
Main takeaways:
- Attaches to any frozen predictor (linear, deep vision, or spatiotemporal) without retraining it, purely to model the leftover errors
- Learns a structured low-rank decomposition of residual spatial patterns plus a covariance estimate, so you can predict at unobserved locations and quantify uncertainty
- Uses fewer than K(N+T) parameters (K is an upper bound on rank, N is spatial dimension, T is time steps) plus a small residual network
- Tested on synthetic data, Weather2K spatial-holdout forecasting, and GWHD patch grids; recovers spatial structure across all backbone types
- The effective rank is chosen adaptively by spectral thresholding rather than fixed in advance