PathMLP: Smooth Path Towards High-order Homophily

TL;DR

PathMLP introduces a novel high-order path sampling and a lightweight MLP-based model to effectively learn node representations in heterophilous graphs, outperforming existing methods while avoiding over-smoothing and maintaining high efficiency.

Contribution

The paper proposes a similarity-based path sampling strategy and a lightweight MLP model, PathMLP, to leverage high-order homophily in heterophilous graphs, addressing limitations of traditional GNNs.

Findings

Outperforms baselines on 16 out of 20 datasets.

Effectively alleviates heterophily issues in graphs.

Avoids over-smoothing and maintains high computational efficiency.

Abstract

Real-world graphs exhibit increasing heterophily, where nodes no longer tend to be connected to nodes with the same label, challenging the homophily assumption of classical graph neural networks (GNNs) and impeding their performance. Intriguingly, from the observation of heterophilous data, we notice that certain high-order information exhibits higher homophily, which motivates us to involve high-order information in node representation learning. However, common practices in GNNs to acquire high-order information mainly through increasing model depth and altering message-passing mechanisms, which, albeit effective to a certain extent, suffer from three shortcomings: 1) over-smoothing due to excessive model depth and propagation times; 2) high-order information is not fully utilized; 3) low computational efficiency. In this regard, we design a similarity-based path sampling strategy to capture smooth paths containing high-order homophily. Then we propose a lightweight model based on multi-layer perceptrons (MLP), named PathMLP, which can encode messages carried by paths via simple transformation and concatenation operations, and effectively learn node representations in heterophilous graphs through adaptive path aggregation. Extensive experiments demonstrate that our method outperforms baselines on 16 out of 20 datasets, underlining its effectiveness and superiority in alleviating the heterophily problem. In addition, our method is immune to over-smoothing and has high computational efficiency. The source code will be available in https://github.com/Graph4Sec-Team/PathMLP.