Compositional Curvature Bounds for Deep Neural Networks

• URL: http://arxiv.org/abs/2406.05119v1
• Date: Fri, 7 Jun 2024 17:50:15 GMT
• Title: Compositional Curvature Bounds for Deep Neural Networks
• Authors: Taha Entesari, Sina Sharifi, Mahyar Fazlyab,
• Abstract summary: A key challenge that threatens the widespread use of neural networks in safety-critical applications is their vulnerability to adversarial attacks. We study the second-order behavior of continuously differentiable deep neural networks, focusing on robustness against adversarial perturbations. We introduce a novel algorithm to analytically compute provable upper bounds on the second derivative of neural networks.
• Score: 7.373617024876726
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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