Provable Generalization Bounds for Deep Neural Networks with Momentum-Adaptive Gradient Dropout

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 non-asymptotic, computable PAC-Bayes generalization bound that accounts for its adaptive nature, achieving up to 29.2% tighter bounds compared to standard approaches by leveraging momentum-driven perturbation control. Empirically, the activation-based MAGDrop achieves competitive performance on MNIST (99.52%) and CIFAR-10 (92.03%), with generalization gaps of 0.48% and 6.52%, respectively. We provide fully reproducible code and numerical computation of our bounds to validate our theoretical claims. Our work bridges theoretical insights and practical advancements, offering a robust framework for enhancing DNN generalization, making it suitable for high-stakes applications.