A Differential Geometric View and Explainability of GNN on Evolving Graphs

TL;DR

This paper introduces a differential geometric approach to model and interpret the evolution of Graph Neural Networks' predictions on dynamic graphs, enhancing explainability and interpretability.

Contribution

It proposes a smooth parameterization of GNN prediction distributions on a low-dimensional manifold and a convex optimization method for human-understandable interpretation of graph evolution.

Findings

Improved sparsity and faithfulness in explanations.

Enhanced interpretability of GNN responses to graph changes.

Better performance on evolving graph tasks.

Abstract

Graphs are ubiquitous in social networks and biochemistry, where Graph Neural Networks (GNN) are the state-of-the-art models for prediction. Graphs can be evolving and it is vital to formally model and understand how a trained GNN responds to graph evolution. We propose a smooth parameterization of the GNN predicted distributions using axiomatic attribution, where the distributions are on a low-dimensional manifold within a high-dimensional embedding space. We exploit the differential geometric viewpoint to model distributional evolution as smooth curves on the manifold. We reparameterize families of curves on the manifold and design a convex optimization problem to find a unique curve that concisely approximates the distributional evolution for human interpretation. Extensive experiments on node classification, link prediction, and graph classification tasks with evolving graphs demonstrate the better sparsity, faithfulness, and intuitiveness of the proposed method over the state-of-the-art methods.