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HTG-GCL: Leveraging Hierarchical Topological Granularity from Cellular Complexes for Graph Contrastive Learning

Qirui Ji, Bin Qin, Yifan Jin, Yunze Zhao, Chuxiong Sun, Changwen Zheng, Jianwen Cao, Jiangmeng Li

TL;DR

HTG-GCL addresses the limitation of fixed topological granularity in graph contrastive learning by transforming graphs into a hierarchy of ring-based cellular complexes to capture multiple topology scales. It introduces multi-granularity decoupled contrastive learning with an uncertainty-based weighting mechanism to downweight uninformative views, and uses a common space contrast alongside granularity-specific spaces. Empirically, HTG-GCL achieves state-of-the-art performance on TU benchmarks in both unsupervised and semi-supervised settings, with ablations confirming the value of multi-granularity integration and MGDC. This work advances higher-order topology in GCL and enables adaptive, task-aware use of complex topological structures for improved graph representations.

Abstract

Graph contrastive learning (GCL) aims to learn discriminative semantic invariance by contrasting different views of the same graph that share critical topological patterns. However, existing GCL approaches with structural augmentations often struggle to identify task-relevant topological structures, let alone adapt to the varying coarse-to-fine topological granularities required across different downstream tasks. To remedy this issue, we introduce Hierarchical Topological Granularity Graph Contrastive Learning (HTG-GCL), a novel framework that leverages transformations of the same graph to generate multi-scale ring-based cellular complexes, embodying the concept of topological granularity, thereby generating diverse topological views. Recognizing that a certain granularity may contain misleading semantics, we propose a multi-granularity decoupled contrast and apply a granularity-specific weighting mechanism based on uncertainty estimation. Comprehensive experiments on various benchmarks demonstrate the effectiveness of HTG-GCL, highlighting its superior performance in capturing meaningful graph representations through hierarchical topological information.

HTG-GCL: Leveraging Hierarchical Topological Granularity from Cellular Complexes for Graph Contrastive Learning

TL;DR

HTG-GCL addresses the limitation of fixed topological granularity in graph contrastive learning by transforming graphs into a hierarchy of ring-based cellular complexes to capture multiple topology scales. It introduces multi-granularity decoupled contrastive learning with an uncertainty-based weighting mechanism to downweight uninformative views, and uses a common space contrast alongside granularity-specific spaces. Empirically, HTG-GCL achieves state-of-the-art performance on TU benchmarks in both unsupervised and semi-supervised settings, with ablations confirming the value of multi-granularity integration and MGDC. This work advances higher-order topology in GCL and enables adaptive, task-aware use of complex topological structures for improved graph representations.

Abstract

Graph contrastive learning (GCL) aims to learn discriminative semantic invariance by contrasting different views of the same graph that share critical topological patterns. However, existing GCL approaches with structural augmentations often struggle to identify task-relevant topological structures, let alone adapt to the varying coarse-to-fine topological granularities required across different downstream tasks. To remedy this issue, we introduce Hierarchical Topological Granularity Graph Contrastive Learning (HTG-GCL), a novel framework that leverages transformations of the same graph to generate multi-scale ring-based cellular complexes, embodying the concept of topological granularity, thereby generating diverse topological views. Recognizing that a certain granularity may contain misleading semantics, we propose a multi-granularity decoupled contrast and apply a granularity-specific weighting mechanism based on uncertainty estimation. Comprehensive experiments on various benchmarks demonstrate the effectiveness of HTG-GCL, highlighting its superior performance in capturing meaningful graph representations through hierarchical topological information.

Paper Structure

This paper contains 34 sections, 12 equations, 5 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Higher-order Representations of Graphs
  4. Background
  5. Cellular Complex
  6. Example 1 (Graph as a 1-dim cellular complex):
  7. Example 2 (2-dim cellular complex from cycles):
  8. Cellular Adjacencies
  9. Cellular Complex Neural Networks
  10. Methodology
  11. Ring‑based Graph‑to‑Complex Preprocessing
  12. Multi-scale Topological Granularity Decoupled Contrastive Learning
  13. Common Space Contrast
  14. Multi-Granularity Decoupled Contrast
  15. Granularity-specific Weighting
  16. ...and 19 more sections

Figures (5)

  • Figure 1: Visualization of graph structures graphvisual and classification performance across different ring sizes on two TU datasets: NCI1 and IMDB-B. The results reveal that topological granularity significantly affects downstream performance, and indiscriminate inclusion of high-order structures may harm accuracy when they misalign with domain-specific semantics. For example, IMDB-B benefits from smaller rings (triangles), while NCI1 favors larger ring structures, highlighting the need for scenario-adaptive granularity modeling.
  • Figure 2: Performance comparison on four TU datasets under different single-ring granularities (6, 9, 12) and their multi-granularity integration. The multi-granularity setting consistently outperforms any single fixed granularity, demonstrating the complementary nature of hierarchical topological views.
  • Figure 3: The framework of HTG-GCL.
  • Figure 4: Hyper-parameter analysis.
  • Figure 5: t-SNE visualization of six methods on MUTAG.

Theorems & Definitions (2)

  • Definition 1: Ring-based Cellular Complexes Transformation
  • Definition 2: Hierarchical Topological Granularity