A Differential Geometric View and Explainability of GNN on Evolving
  Graphs
Yazheng Liu Xi Zhang Sihong Xie
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.