Graph Anisotropic Diffusion

TL;DR

This paper introduces Graph Anisotropic Diffusion, a novel GNN architecture that incorporates directional information through anisotropic diffusion, improving multi-hop feature aggregation for molecular property prediction.

Contribution

The paper proposes a new GNN model that combines linear diffusion with local anisotropic filters, enabling efficient multi-hop anisotropic kernels with a closed-form solution.

Findings

Competitive performance on ZINC and QM9 benchmarks

Effective incorporation of directional information in GNNs

Efficient multi-hop anisotropic kernel computation

Abstract

Traditional Graph Neural Networks (GNNs) rely on message passing, which amounts to permutation-invariant local aggregation of neighbour features. Such a process is isotropic and there is no notion of `direction' on the graph. We present a new GNN architecture called Graph Anisotropic Diffusion. Our model alternates between linear diffusion, for which a closed-form solution is available, and local anisotropic filters to obtain efficient multi-hop anisotropic kernels. We test our model on two common molecular property prediction benchmarks (ZINC and QM9) and show its competitive performance.