论文标题
代数神经网络对小扰动的稳定性
Stability of Algebraic Neural Networks to Small Perturbations
论文作者
论文摘要
代数神经网络（ALGNNS）由与和代数信号模型相关联的层次组成，并通过非线性函数在层之间映射信息。 ALGNN提供了使用正式卷积操作员的神经网络体系结构的概括，例如传统神经网络（CNN）和图神经网络（GNNS）。在本文中，我们研究了Algnns在代数信号处理框架上的稳定性。我们展示了任何使用正式卷积概念的体系结构如何在移动运算符的特定选择之外稳定，并且这种稳定性取决于模型中代数的子集的结构。我们将注意力集中在单个发电机的代数情况下。
Algebraic neural networks (AlgNNs) are composed of a cascade of layers each one associated to and algebraic signal model, and information is mapped between layers by means of a nonlinearity function. AlgNNs provide a generalization of neural network architectures where formal convolution operators are used, like for instance traditional neural networks (CNNs) and graph neural networks (GNNs). In this paper we study stability of AlgNNs on the framework of algebraic signal processing. We show how any architecture that uses a formal notion of convolution can be stable beyond particular choices of the shift operator, and this stability depends on the structure of subsets of the algebra involved in the model. We focus our attention on the case of algebras with a single generator.
