
Stability of Graph Neural Networks to Relative Perturbations
Graph neural networks (GNNs), consisting of a cascade of layers applying...
read it

Graph and graphon neural network stability
Graph neural networks (GNNs) are learning architectures that rely on kno...
read it

Graph Neural Networks: Architectures, Stability and Transferability
Graph Neural Networks (GNNs) are information processing architectures fo...
read it

Stability Properties of Graph Neural Networks
Data stemming from networks exhibit an irregular support, whereby each d...
read it

Stability of Algebraic Neural Networks to Small Perturbations
Algebraic neural networks (AlgNNs) are composed of a cascade of layers e...
read it

Surface Networks
We study datadriven representations for threedimensional triangle mesh...
read it

Convolutional Filtering and Neural Networks with Non Commutative Algebras
In this paper we provide stability results for algebraic neural networks...
read it
Stability of Manifold Neural Networks to Deformations
Stability is an important property of graph neural networks (GNNs) which explains their success in many problems of practical interest. Existing GNN stability results depend on the size of the graph, restricting applicability to graphs of moderate size. To understand the stability properties of GNNs on large graphs, we consider neural networks supported on manifolds. These are defined in terms of manifold diffusions mediated by the LaplaceBeltrami (LB) operator and are interpreted as limits of GNNs running on graphs of growing size. We define manifold deformations and show that they lead to perturbations of the manifold's LB operator that consist of an absolute and a relative perturbation term. We then define filters that split the infinite dimensional spectrum of the LB operator in finite partitions, and prove that manifold neural networks (MNNs) with these filters are stable to both, absolute and relative perturbations of the LB operator. Stability results are illustrated numerically in resource allocation problems in wireless networks.
READ FULL TEXT
Comments
There are no comments yet.