Pyramidal Reservoir Graph Neural Network

TL;DR

This paper introduces a pyramidal graph neural network combining reservoir computing-inspired layers with graph pooling to enhance efficiency and accuracy in graph embedding tasks.

Contribution

It presents a novel pyramidal GNN architecture that integrates reservoir computing and graph pooling, with formal analysis of complexity reduction and convergence improvements.

Findings

Reduces computational complexity via graph pooling.

Achieves faster convergence of vertex features.

Demonstrates improved accuracy on multiple datasets.

Abstract

We propose a deep Graph Neural Network (GNN) model that alternates two types of layers. The first type is inspired by Reservoir Computing (RC) and generates new vertex features by iterating a non-linear map until it converges to a fixed point. The second type of layer implements graph pooling operations, that gradually reduce the support graph and the vertex features, and further improve the computational efficiency of the RC-based GNN. The architecture is, therefore, pyramidal. In the last layer, the features of the remaining vertices are combined into a single vector, which represents the graph embedding. Through a mathematical derivation introduced in this paper, we show formally how graph pooling can reduce the computational complexity of the model and speed-up the convergence of the dynamical updates of the vertex features. Our proposed approach to the design of RC-based GNNs offers an advantageous and principled trade-off between accuracy and complexity, which we extensively demonstrate in experiments on a large set of graph datasets.