Heterophily-informed Message Passing

TL;DR

This work tackles oversmoothing in graph neural networks by addressing the implicit homophily bias in message passing. It introduces heterophily-informed MP, a flexible, architecture-agnostic scheme that modulates messages across three channels (orig., hom., het.) using cosine-based similarity to preserve both low- and high-frequency information, and demonstrates substantial gains on node classification benchmarks. The authors extend the idea to molecular generation with HetFlows, a flow-based model that replaces MoFlow's GCNs with MixMP blocks, achieving improved chemoinformatics metrics and structured latent spaces on QM9 and zinc-250k. Collectively, the approach provides a label-free, generalizable prior for heterophily that enhances both discriminative and generative graph tasks, with clear implications for robust graph learning in diverse domains.

Abstract

Graph neural networks (GNNs) are known to be vulnerable to oversmoothing due to their implicit homophily assumption. We mitigate this problem with a novel scheme that regulates the aggregation of messages, modulating the type and extent of message passing locally thereby preserving both the low and high-frequency components of information. Our approach relies solely on learnt embeddings, obviating the need for auxiliary labels, thus extending the benefits of heterophily-aware embeddings to broader applications, e.g., generative modelling. Our experiments, conducted across various data sets and GNN architectures, demonstrate performance enhancements and reveal heterophily patterns across standard classification benchmarks. Furthermore, application to molecular generation showcases notable performance improvements on chemoinformatics benchmarks.

Figures (9)

• Figure 1: Comparison of heterophiliy-informed MP with original GNN on a graph describing the 3-Aminophenol molecule. The three channels show how $\gamma$ controls the scaling factor in \ref{['eq:scaling_facotrs']} and leads to different message passing behaviour, given the same input.
• Figure 2: Comparison over 15 data sets and 4 GNN architectures in terms of improvement in accuracy (%-points). $a_{\text{orig}}$, $a_{\text{hom}}$, $a_{\text{het}}$ and $a_{\text{mix}}$ denote the accuracy of original model and corresponding HomMP, HetMP, and MixMP versions. In \ref{['fig:sub_nc2']}, each node is the average performance over 10 random seeds for a specific dataset and GNN structure, it illustrates the accuracy advantage of MixMP above the original model. In \ref{['fig:sub_nc1']}, the $y$-axis denotes the accuracy improvement of HetMP and HomMP over the original structure.
• Figure 3: Chemoinformatics statistics for data ( qm9) and generated molecules from HetFlows (ours), MoFlow, and GraphDF. We report histograms for the Octanol-water partition coefficient (logP), synthetic accessibility score (SA), quantitative estimation of drug-likeness (QED), and molecular weight.
• Figure 4: Structured latent-space exploration ( qm9). Our approach yields a sensibly structured latent space as qualitatively demonstrated by this nearest neighbour search in the latent space with the seed molecule on the left and neighbours with the Tanimoto similarity (1 0) given for each molecule. For results on zinc-250k, see \ref{['fig:exploration-zinc']} in the appendix.
• Figure A5: The affine coupling layer. The coupling is defined through a coupling function $f$ and binary masking matrix ${\bm{M}}$ (seen in \ref{['eq:acl']}).