DeepAI
Log In Sign Up

Transferability Properties of Graph Neural Networks

12/09/2021
by   Luana Ruiz, et al.
0

Graph neural networks (GNNs) are deep convolutional architectures consisting of layers composed by graph convolutions and pointwise nonlinearities. Due to their invariance and stability properties, GNNs are provably successful at learning representations from network data. However, training them requires matrix computations which can be expensive for large graphs. To address this limitation, we investigate the ability of GNNs to be transferred across graphs. We consider graphons, which are both graph limits and generative models for weighted and stochastic graphs, to define limit objects of graph convolutions and GNNs – graphon convolutions and graphon neural networks (WNNs) – which we use as generative models for graph convolutions and GNNs. We show that these graphon filters and WNNs can be approximated by graph filters and GNNs sampled from them on weighted and stochastic graphs. Using these results, we then derive error bounds for transferring graph filters and GNNs across such graphs. These bounds show that transferability increases with the graph size, and reveal a tradeoff between transferability and spectral discriminability which in GNNs is alleviated by the pointwise nonlinearities. These findings are further verified empirically in numerical experiments in movie recommendation and decentralized robot control.

READ FULL TEXT

page 1

page 4

06/05/2020

Graphon Neural Networks and the Transferability of Graph Neural Networks

Graph neural networks (GNNs) rely on graph convolutions to extract local...
08/04/2020

Graph Neural Networks: Architectures, Stability and Transferability

Graph Neural Networks (GNNs) are information processing architectures fo...
04/15/2021

Convolutions for Spatial Interaction Modeling

In many different fields interactions between objects play a critical ro...
11/11/2022

Stable and Transferable Hyper-Graph Neural Networks

We introduce an architecture for processing signals supported on hypergr...
03/23/2020

Graph Neural Networks for Decentralized Controllers

Dynamical systems comprised of autonomous agents arise in many relevant ...
03/02/2020

Benchmarking Graph Neural Networks

Graph neural networks (GNNs) have become the standard toolkit for analyz...
03/29/2019

Invariance-Preserving Localized Activation Functions for Graph Neural Networks

Graph signals are signals with an irregular structure that can be descri...