Provable Generalization Bounds for Deep Neural Networks with Adaptive Regularization

Deep neural networks (DNNs) achieve remarkable performance but often suffer from overfitting due to their high capacity. We introduce Momentum-Adaptive Gradient Dropout (MAGDrop), a novel regularization method that dynamically adjusts dropout rates on activations based on current gradients and accumulated momentum, enhancing stability in non-convex optimization landscapes. To theoretically justify MAGDrop's effectiveness, we derive a tightened PAC-Bayes generalization bound that accounts for its adaptive nature, achieving up to 20% sharper bounds compared to standard approaches by leveraging momentum-driven perturbation control. Empirically, the activation-based MAGDrop outperforms baseline regularization techniques, including standard dropout and adaptive gradient regularization, by 1-2% in test accuracy on MNIST (99.52%) and CIFAR-10 (90.63%), with generalization gaps of 0.48% and 7.14%, respectively. Our work bridges theoretical insights and practical advancements, offering a robust framework for enhancing DNN generalization suitable for high-stakes applications.