Loop Corrections in Random Feature Models: Training Error and Generalization Gap
Read the original on arXiv Machine Learning →The paper investigates fixed‑design random feature ridge regression beyond the mean‑kernel approximation, focusing on how the predictor’s nonlinear dependence on the empirical kernel affects training error, test error, and the conditional generalization gap. By deriving covariance‑level (one‑loop) corrections via a finite resolvent identity, the authors avoid an almost‑sure Neumann‑series assumption and provide explicit remainder bounds for training error. Numerical experiments demonstrate that including mixed train–test covariance tensors is essential for accurate test error predictions and reveal a width–regularization boundary where second‑order truncation becomes unreliable.
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