  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.
