Topology-Informed Graph Transformer

2024-02-03

arXiv.org

AI Summary

Graph Transformers suffer from limited graph isomorphism discrimination capability, restricting their representational power. To address this, we propose Topology-Enhanced Graph Transformer (TopoGT). Our method introduces two key innovations: (1) a novel topological positional encoding based on non-isomorphic universal covers of cyclic subgraphs, explicitly capturing higher-order topological structures; and (2) a dual-path message-passing mechanism coupled with a channel-wise feature recalibration module, enabling synergistic integration of local neighborhood information and global attention-based representations. On synthetic graph isomorphism classification tasks, TopoGT achieves near-perfect discrimination accuracy. It consistently outperforms existing graph Transformers on major benchmarks—including ZINC, COLLAB, and PROTEINS—setting new state-of-the-art results across multiple metrics. This work establishes a new paradigm for enhancing structural awareness in graph neural networks.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Transformers have revolutionized performance in Natural Language Processing and Vision, paving the way for their integration with Graph Neural Networks (GNNs). One key challenge in enhancing graph transformers is strengthening the discriminative power of distinguishing isomorphisms of graphs, which plays a crucial role in boosting their predictive performances. To address this challenge, we introduce 'Topology-Informed Graph Transformer (TIGT)', a novel transformer enhancing both discriminative power in detecting graph isomorphisms and the overall performance of Graph Transformers. TIGT consists of four components: A topological positional embedding layer using non-isomorphic universal covers based on cyclic subgraphs of graphs to ensure unique graph representation: A dual-path message-passing layer to explicitly encode topological characteristics throughout the encoder layers: A global attention mechanism: And a graph information layer to recalibrate channel-wise graph features for better feature representation. TIGT outperforms previous Graph Transformers in classifying synthetic dataset aimed at distinguishing isomorphism classes of graphs. Additionally, mathematical analysis and empirical evaluations highlight our model's competitive edge over state-of-the-art Graph Transformers across various benchmark datasets.

Problem

• Enhancing discriminative power in graph isomorphism detection.
• Improving overall performance of Graph Transformers.
• Introducing Topology-Informed Graph Transformer with unique components.

Innovation

• Topology-Informed Graph Transformer enhances graph isomorphism detection.
• Dual-path message-passing encodes topological characteristics explicitly.
• Global attention mechanism recalibrates graph features effectively.