# Stability of Algebraic Neural Networks to Small Perturbations

arXiv: https://arxiv.org/abs/2010.11544 · HTML: https://mlsanity.com/paper/2010.11544/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2020.

## Built on by (most cited first, 8 of 8)

- [Convolutional Filtering and Neural Networks with Non Commutative Algebras](https://mlsanity.com/paper/2108.09923/) (2021)
- [Graphon Pooling for Reducing Dimensionality of Signals and Convolutional Operators on Graphs](https://mlsanity.com/paper/2212.08171/) (2022)
- [Stability of Aggregation Graph Neural Networks](https://mlsanity.com/paper/2207.03678/) (2022)
- [Sampling and Uniqueness Sets in Graphon Signal Processing](https://mlsanity.com/paper/2401.06279/) (2024)
- [Convolutional Filtering with RKHS Algebras](https://mlsanity.com/paper/2411.01341/) (2024)
- [RKHS Representation of Algebraic Convolutional Filters with Integral Operators](https://mlsanity.com/paper/2602.19094/) (2026)
- [Non Commutative Convolutional Signal Models in Neural Networks: Stability to Small Deformations](https://mlsanity.com/paper/2310.03879/) (2023)
- [Fundamental Limits of Transferability and Equivariance in Algebraic Signal Models I: Finite Dimensions](https://mlsanity.com/paper/2609.36106/) (2026)

## Abstract (arXiv)

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.