Geometric instability of graph neural networks on large graphs

TL;DR

This paper introduces a new graph-native index to measure the geometric instability of GNN embeddings on large graphs, enabling analysis of their stability across tasks like node classification and link prediction.

Contribution

It proposes the Graph Gram Index (GGI), a simple, efficient, and permutation-invariant measure for geometric instability in GNN embeddings on large graphs.

Findings

GGI effectively measures instability across large graphs.

GNN embeddings show varying instability behaviors depending on graph size and task.

The method is applicable to both node classification and link prediction tasks.

Abstract

We analyse the geometric instability of embeddings produced by graph neural networks (GNNs). Existing methods are only applicable for small graphs and lack context in the graph domain. We propose a simple, efficient and graph-native Graph Gram Index (GGI) to measure such instability which is invariant to permutation, orthogonal transformation, translation and order of evaluation. This allows us to study the varying instability behaviour of GNN embeddings on large graphs for both node classification and link prediction.