Studying and Improving Graph Neural Network-based Motif Estimation

TL;DR

This paper introduces a novel GNN-based approach for network motif significance-profile estimation, shifting from subgraph counting to direct regression, and demonstrates its effectiveness on synthetic and real-world graphs.

Contribution

It presents the first GNN-based method for direct motif significance-profile estimation, improving interpretability, stability, and scalability over traditional subgraph counting methods.

Findings

1-WL limited models struggle with precise SP estimation.

Models can generalize to approximate network generation processes.

Direct SP estimation can overcome theoretical limitations of subgraph counting.

Abstract

Graph Neural Networks (GNNs) are a predominant method for graph representation learning. However, beyond subgraph frequency estimation, their application to network motif significance-profile (SP) prediction remains under-explored, with no established benchmarks in the literature. We propose to address this problem, framing SP estimation as a task independent of subgraph frequency estimation. Our approach shifts from frequency counting to direct SP estimation and modulates the problem as multitarget regression. The reformulation is optimised for interpretability, stability and scalability on large graphs. We validate our method using a large synthetic dataset and further test it on real-world graphs. Our experiments reveal that 1-WL limited models struggle to make precise estimations of SPs. However, they can generalise to approximate the graph generation processes of networks by comparing their predicted SP with the ones originating from synthetic generators. This first study on GNN-based motif estimation also hints at how using direct SP estimation can help go past the theoretical limitations that motif estimation faces when performed through subgraph counting.