Loop Corrections to the Training and Generalization Errors of Random Feature Models

• URL: http://arxiv.org/abs/2604.12827v1
• Date: Tue, 14 Apr 2026 14:48:41 GMT
• Title: Loop Corrections to the Training and Generalization Errors of Random Feature Models
• Abstract summary: We study the training, test, and generalization errors beyond the mean- kernel approximation.<n>Within an effective field-theoretic framework, these finite-width contributions naturally appear as loop corrections.<n>We derive the loop corrections to the training, test, and generalization errors, obtain their scaling laws, and support the theory with experimental verification.
• Score: 11.824913874212802
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate random feature models in which neural networks sampled from a prescribed initialization ensemble are frozen and used as random features, with only the readout weights optimized. Adopting a statistical-physics viewpoint, we study the training, test, and generalization errors beyond the mean-kernel approximation. Since the predictor is a nonlinear functional of the induced random kernel, the ensemble-averaged errors depend not only on the mean kernel but also on higher-order fluctuation statistics. Within an effective field-theoretic framework, these finite-width contributions naturally appear as loop corrections. We derive the loop corrections to the training, test, and generalization errors, obtain their scaling laws, and support the theory with experimental verification.

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