Compositional Curvature Bounds for Deep Neural Networks
| Autor: | Entesari, Taha, Sharifi, Sina, Fazlyab, Mahyar |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | A key challenge that threatens the widespread use of neural networks in safety-critical applications is their vulnerability to adversarial attacks. In this paper, we study the second-order behavior of continuously differentiable deep neural networks, focusing on robustness against adversarial perturbations. First, we provide a theoretical analysis of robustness and attack certificates for deep classifiers by leveraging local gradients and upper bounds on the second derivative (curvature constant). Next, we introduce a novel algorithm to analytically compute provable upper bounds on the second derivative of neural networks. This algorithm leverages the compositional structure of the model to propagate the curvature bound layer-by-layer, giving rise to a scalable and modular approach. The proposed bound can serve as a differentiable regularizer to control the curvature of neural networks during training, thereby enhancing robustness. Finally, we demonstrate the efficacy of our method on classification tasks using the MNIST and CIFAR-10 datasets. Comment: Proceedings of the 41 st International Conference on Machine Learning (ICML 2024) |
| Databáze: | arXiv |
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