论文标题
Lipschitz的神经网络分析
Lipschitz Bound Analysis of Neural Networks
论文作者
论文摘要
Lipschitz Bound估计是使深度神经网络正规化以使其与对抗性攻击的强大方法的有效方法。这在从增强学习到自主系统的各种应用中很有用。在本文中，我们强调了卷积神经网络（CNN）的非平凡LIPSCHITZ BOND证书的显着差距，并通过广泛的图形分析在经验上支持它。我们还表明，可以使用展开的卷积层或Toeplitz矩阵将卷积神经网络（CNN）转换为完全连接的网络。此外，我们提出了一种简单的算法，以显示实际Lipschitz常数和所获得的紧密结合之间的特定数据分布中现有的20x-50x差距。我们还对各种网络体系结构进行了一组彻底的实验，并在MNIST和CIFAR-10等数据集上对其进行了基准测试。所有这些建议都通过广泛的测试，图形，直方图和比较分析来支持。
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.
