Graph Classification with GNNs: Optimisation, Representation and Inductive Bias

TL;DR

This paper investigates the optimization and inductive biases of GNNs in graph classification, revealing how their architecture influences the types of features they learn and proposing ways to incorporate domain knowledge.

Contribution

It highlights the gap between GNNs' theoretical representation power and their practical optimization, and introduces a theoretical and empirical analysis of their implicit biases.

Findings

GNNs tend to learn either discriminative subgraphs or dispersed discriminative nodes.

Different global pooling layers influence the types of features GNNs focus on.

Attention mechanisms can incorporate domain knowledge to improve subgraph discrimination.

Abstract

Theoretical studies on the representation power of GNNs have been centered around understanding the equivalence of GNNs, using WL-Tests for detecting graph isomorphism. In this paper, we argue that such equivalence ignores the accompanying optimization issues and does not provide a holistic view of the GNN learning process. We illustrate these gaps between representation and optimization with examples and experiments. We also explore the existence of an implicit inductive bias (e.g. fully connected networks prefer to learn low frequency functions in their input space) in GNNs, in the context of graph classification tasks. We further prove theoretically that the message-passing layers in the graph, have a tendency to search for either discriminative subgraphs, or a collection of discriminative nodes dispersed across the graph, depending on the different global pooling layers used. We empirically verify this bias through experiments over real-world and synthetic datasets. Finally, we show how our work can help in incorporating domain knowledge via attention based architectures, and can evince their capability to discriminate coherent subgraphs.