Spatial Adapter: Structured Residual Representation for Frozen Predictors
The Spatial Adapter serves as a parameter-efficient layer that can be applied post-hoc, providing any static first-stage predictor with a structured spatial depiction of its residual field along with a closed-form spatial covariance. Functioning as a second-stage cascade on the residuals, it concurrently learns a spatially regularized orthonormal basis and individual sample scores through a manageable mini-batch ADMM process, without altering any parameters of the first stage. This adapter does not retrain the backbone; instead, it offers a condensed distributional summary of the residual field. By incorporating smoothness, sparsity, and orthogonality, it transforms a generic low-rank factorization into a recognizable spatial representation, enabling a closed-form low-rank-plus-noise estimator for the induced residual covariance. The effective rank is adaptively determined through spectral thresholding, while the nominal rank K is an operation.
Key facts
- Spatial Adapter is a parameter-efficient post-hoc layer.
- It equips frozen first-stage predictors with structured spatial representation.
- It uses a mini-batch ADMM procedure for learning.
- First-stage parameters remain frozen.
- The adapter provides a compressed distributional summary of residual field.
- Smoothness, sparsity, and orthogonality enable identifiable spatial representation.
- Residual covariance has a closed-form low-rank-plus-noise estimator.
- Effective rank is determined by spectral thresholding.
Entities
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