A1906
Title: Spatial adapter: Structured spatial decomposition and closed-form covariance for frozen predictors
Authors: HaoYun Huang - National Dong Hwa University (Taiwan) [presenting]
Abstract: The Spatial Adapter is a parameter-efficient post-hoc layer that equips any frozen first-stage predictor with a structured Spatial representation of its residual field and an induced closed-form Spatial covariance. The Adapter operates as a cascade second stage on residuals, jointly learning a spatially regularized orthonormal basis and per-sample scores via a tractable mini-batch ADMM procedure. Without retraining the frozen backbone, its role is to supply a compressed distributional summary of the residual field. Smoothness, sparsity, and orthogonality together turn a generic low-rank factorization into an identifiable Spatial representation whose induced residual covariance admits a closed-form low-rank-plus-noise estimator; the effective rank is determined data-adaptively by spectral thresholding, while the nominal rank $K$ is an optimization-side upper bound. This covariance enables kriging-style Spatial prediction at unobserved locations, yielding plug-in uncertainty quantification. Across synthetic data, Weather2K (Spatial-holdout prediction), and GWHD patch grids (basis-transferability diagnostic), the Adapter recovers residual Spatial structure when paired with frozen first stages from linear models to deep spatiotemporal and vision backbones; the added representation uses fewer than $K(N+T)$ parameters alongside a compact residual-trend network.
