Cross-regularization: Adaptive Model Complexity through Validation Gradients

Model regularization requires extensive manual tuning to balance complexity against overfitting. Crossregularization 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.