| Paper ID | SPTM-9.5 |
| Paper Title |
STABILITY OF ALGEBRAIC NEURAL NETWORKS TO SMALL PERTURBATIONS |
| Authors |
Alejandro Parada-Mayorga, Alejandro Ribeiro, University of Pennsylvania, United States |
| Session | SPTM-9: Estimation, Detection and Learning over Networks 3 |
| Location | Gather.Town |
| Session Time: | Wednesday, 09 June, 14:00 - 14:45 |
| Presentation Time: | Wednesday, 09 June, 14:00 - 14:45 |
| Presentation |
Poster
|
| Topic |
Signal Processing Theory and Methods: [SIPG] Signal and Information Processing over Graphs |
| IEEE Xplore Open Preview |
Click here to view in IEEE Xplore |
| Virtual Presentation |
Click here to watch in the Virtual Conference |
| Abstract |
Algebraic neural networks (AlgNNs) are composed of a cas- cade 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 op- erators 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 particu- lar 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. |
