This paper introduces a novel representation of convolutional Neural Networks (CNNs) in terms of 2-D dynamical systems. To this end, the usual description of convolutional layers with convolution kernels, i.e., the impulse responses of linear filters, is realized in state space as a linear time-invariant 2-D system. The overall convolutional Neural Network composed of convolutional layers and nonlinear activation functions is then viewed as a 2-D version of a Lur'e system, i.e., a linear dynamical system interconnected with static nonlinear components. One benefit of this 2-D Lur'e system perspective on CNNs is that we can use robust control theory much more efficiently for Lipschitz constant estimation than previously possible.

翻译：本文提出了卷积神经网络在二维动力系统框架下的一种新型表示方法。为此，我们将卷积层中通常使用的卷积核（即线性滤波器的脉冲响应）在状态空间中实现为线性时不变二维系统。由卷积层与非线性激活函数组成的整体卷积神经网络随后被视作二维Lur'e系统——即与静态非线性分量互联的线性动力系统。这种基于二维Lur'e系统的视角为CNN带来的优势之一是：相比现有方法，我们能够更高效地运用鲁棒控制理论进行Lipschitz常数估计。