Cheeger--Hodge Contrastive Learning for Structurally Robust Graph Representation Learning

TL;DR

This paper introduces Cheeger--Hodge Contrastive Learning (CHCL), a novel framework that enhances the robustness of graph representations by aligning global and higher-order structural signatures across augmented views.

Contribution

It proposes a new signature combining algebraic connectivity and Hodge Laplacian spectra, improving robustness and generalization in graph contrastive learning.

Findings

CHCL outperforms existing methods on standard benchmarks.

It demonstrates increased robustness to structural perturbations.

The approach improves transfer learning performance.

Abstract

Graph Contrastive Learning (GCL) has emerged as a prominent framework for unsupervised graph representation learning. However, relying on augmentation design alone to define the invariances learned by GCL can be brittle under structural perturbations. To address this issue, we propose Cheeger--Hodge Contrastive Learning (CHCL), a framework that aligns a perturbation-stable Cheeger--Hodge joint signature across augmented views for robust graph representation learning. The proposed signature combines a Cheeger-inspired connectivity signature derived from the algebraic connectivity \(\lambda_2\) with the low-frequency spectrum of the 1-Hodge Laplacian, thereby capturing both global connectivity and higher-order structural information. By aligning encoder representations with the proposed Cheeger--Hodge joint signature across augmented views, CHCL learns graph embeddings that are robust to local structural perturbations. Extensive experiments on standard benchmarks, transfer settings demonstrate that CHCL consistently improves performance, robustness, and generalization.