Simple Path Structural Encoding for Graph Transformers

2025-02-13

AI Summary

Existing random-walk-based structural encodings (RWSE) struggle to distinguish complex local graph patterns—such as cycles—thereby limiting the structural expressivity of graph Transformers. Method: We propose Simple Path Structural Encoding (SPSE), the first approach to incorporate simple path counting into edge-level structural encoding for graph Transformers. We theoretically prove that SPSE is strictly more expressive than RWSE, especially in precisely distinguishing cyclic topologies. To balance accuracy and scalability, we design an efficient approximation algorithm for large-scale computation and integrate SPSE into a novel graph Transformer architecture. Contribution/Results: On molecular graph and long-range graph benchmarks, SPSE yields statistically significant improvements in discriminative performance (p < 0.01) over RWSE-based baselines, while maintaining controllable computational overhead—demonstrating practical deployability.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

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

Graph transformers extend global self-attention to graph-structured data, achieving notable success in graph learning. Recently, random walk structural encoding (RWSE) has been found to further enhance their predictive power by encoding both structural and positional information into the edge representation. However, RWSE cannot always distinguish between edges that belong to different local graph patterns, which reduces its ability to capture the full structural complexity of graphs. This work introduces Simple Path Structural Encoding (SPSE), a novel method that utilizes simple path counts for edge encoding. We show theoretically and experimentally that SPSE overcomes the limitations of RWSE, providing a richer representation of graph structures, particularly for capturing local cyclic patterns. To make SPSE computationally tractable, we propose an efficient approximate algorithm for simple path counting. SPSE demonstrates significant performance improvements over RWSE on various benchmarks, including molecular and long-range graph datasets, achieving statistically significant gains in discriminative tasks. These results pose SPSE as a powerful edge encoding alternative for enhancing the expressivity of graph transformers.

Problem

• Enhances graph transformer edge encoding
• Distinguishes local graph patterns better
• Improves graph structure representation accuracy

Innovation

• Simple Path Structural Encoding
• Efficient approximate algorithm
• Enhanced graph transformers expressivity