level: technical
the spatial adapter is a lightweight add-on for any already-trained model. it works on the residuals, the differences between predictions and true values, without changing the original model's parameters. the adapter learns a structured spatial representation of these errors using a method called admm, which runs efficiently on small batches of data. this representation is built from a set of orthogonal basis functions that are smooth and sparse, making the spatial patterns easy to interpret.
from this learned basis, the adapter directly computes a closed-form covariance matrix for the residuals. the covariance is a low-rank-plus-noise estimate, where the rank is chosen automatically by looking at the spectrum of the data. this means the adapter not only captures where the model is wrong but also quantifies the uncertainty in those errors across space. the whole process is data-adaptive, adjusting to the specific patterns in the residuals without manual tuning.
because the adapter is post-hoc, it can be applied to any frozen predictor, from simple linear models to complex neural networks. it provides a compressed summary of the residual field, which can be used for downstream tasks like uncertainty quantification, anomaly detection, or improving predictions. the method is parameter-efficient, adding only a small number of extra parameters relative to the original model. this makes it practical for large-scale applications where retraining is too costly or impossible.
why it matters: it gives data scientists a plug-and-play way to understand and quantify spatial errors in any existing model, enabling better uncertainty estimates and model diagnostics without expensive retraining.