Lipschitz Bound Estimation is an effective method of regularizing deep neural
networks to make them robust against adversarial attacks. This is useful in a
variety of applications ranging from reinforcement learning to autonomous
systems. In this paper, we highlight the significant gap in obtaining a
non-trivial Lipschitz bound certificate for Convolutional Neural Networks
(CNNs) and empirically support it with extensive graphical analysis. We also
show that unrolling Convolutional layers or Toeplitz matrices can be employed
to convert Convolutional Neural Networks (CNNs) to a Fully Connected Network.
Further, we propose a simple algorithm to show the existing 20x-50x gap in a
particular data distribution between the actual lipschitz constant and the
obtained tight bound. We also ran sets of thorough experiments on various
network architectures and benchmark them on datasets like MNIST and CIFAR-10.
All these proposals are supported by extensive testing, graphs, histograms and
comparative analysis.

本文提出了利用 Lipschitz Bound Estimation 保证深度神经网络对抗攻击鲁棒性的有效方法，并通过图形分析支持 CNN 获得非平凡 Lipschitz constant 的困难。同时，采用 Toeplitz 矩阵将 CNN 转换为完全连接的网络，并运用实验证明了在特定数据分布中实际 Lipschitz constant 与获得紧密界定之间存在的 20-50 倍的差距。针对不同网络架构在 MNIST 和 CIFAR-10 上进行全面实验和比较分析。