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Cross-regularization: Adaptive Model Complexity through Validation Gradients

Machine Learning 2025-06-25 v1 Artificial Intelligence Statistics Theory Machine Learning Statistics Theory

Abstract

Model regularization requires extensive manual tuning to balance complexity against overfitting. Cross-regularization resolves this tradeoff by directly adapting regularization parameters through validation gradients during training. The method splits parameter optimization - training data guides feature learning while validation data shapes complexity controls - converging provably to cross-validation optima. When implemented through noise injection in neural networks, this approach reveals striking patterns: unexpectedly high noise tolerance and architecture-specific regularization that emerges organically during training. Beyond complexity control, the framework integrates seamlessly with data augmentation, uncertainty calibration and growing datasets while maintaining single-run efficiency through a simple gradient-based approach.

Keywords

Cite

@article{arxiv.2506.19755,
  title  = {Cross-regularization: Adaptive Model Complexity through Validation Gradients},
  author = {Carlos Stein Brito},
  journal= {arXiv preprint arXiv:2506.19755},
  year   = {2025}
}

Comments

21 pages, 13 figures. Accepted at ICML 2025