用验证梯度自动调节正则化，让模型自适应复杂度。
Cross-regularization: Adaptive Model Complexity through Validation Gradients
- 训练时用验证集梯度动态调整正则化强度
- 在神经网络中注入噪声，发现意外高抗噪性
- 适合需要高效调参与自动复杂度控制的场景
模型正则化需大量人工调参以平衡复杂度与过拟合。交叉正则化通过训练过程中验证梯度直接自适应调节正则化参数，解决了这一权衡问题。该方法将参数优化解耦：训练数据指导特征学习，验证数据调控复杂度控制，可证明收敛至交叉验证最优解。在神经网络中通过噪声注入实现时，揭示出显著现象：出人意料的高噪声容忍度，以及训练中自然涌现的、与架构相关的正则化模式。该框架不仅支持复杂度控制，还可无缝集成数据增强、不确定性校准和增量数据集，且通过简单梯度方法保持单次运行效率。
原文摘要 · Abstract (English)
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.
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