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：本文提出了一种基于二维动态系统的卷积神经网络（CNN）新表示方法。为此，我们将在状态空间中实现卷积层与卷积核（即线性滤波器的冲激响应）的常规描述，将其构建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，即静态非线性组件与线性动态系统相互耦合的架构。这种二维Lur'e系统视角的核心优势在于：相较于以往方法，我们能更高效地运用鲁棒控制理论进行Lipschitz常数估计。