Simple Path Structural Encoding for Graph Transformers

TL;DR

This paper introduces Simple Path Structural Encoding (SPSE), a new edge encoding method for graph transformers that captures richer structural information, especially local cyclic patterns, leading to improved performance on various graph learning benchmarks.

Contribution

The paper proposes SPSE, a novel simple path counting-based encoding that overcomes RWSE limitations, with an efficient approximation algorithm and demonstrated superior results.

Findings

SPSE outperforms RWSE on molecular and long-range graph datasets.

SPSE captures local cyclic patterns more effectively.

The proposed approximation algorithm makes path counting computationally feasible.

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.