Spatial Adapter: Structured Spatial Decomposition and Closed-Form Covariance for Frozen Predictors

arXiv:2605.11394v1 Announce Type: cross Abstract: We present the Spatial Adapter, 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 modifying any first-stage paramet