Position-aware Structure Learning for Graph Topology-imbalance by Relieving Under-reaching and Over-squashing

TL;DR

This paper introduces PASTEL, a position-aware graph structure learning framework that addresses topology-imbalance in GNNs by enhancing intra-class connectivity and optimizing information propagation, leading to improved performance.

Contribution

It provides a new understanding of topology-imbalance and proposes a novel framework with anchor-based position encoding and class-wise conflict measures to mitigate under-reaching and over-squashing.

Findings

PASTEL improves GNN performance across various datasets.

The framework effectively enhances intra-class connectivity.

Experimental results show superior adaptability of PASTEL.

Abstract

Topology-imbalance is a graph-specific imbalance problem caused by the uneven topology positions of labeled nodes, which significantly damages the performance of GNNs. What topology-imbalance means and how to measure its impact on graph learning remain under-explored. In this paper, we provide a new understanding of topology-imbalance from a global view of the supervision information distribution in terms of under-reaching and over-squashing, which motivates two quantitative metrics as measurements. In light of our analysis, we propose a novel position-aware graph structure learning framework named PASTEL, which directly optimizes the information propagation path and solves the topology-imbalance issue in essence. Our key insight is to enhance the connectivity of nodes within the same class for more supervision information, thereby relieving the under-reaching and over-squashing phenomena. Specifically, we design an anchor-based position encoding mechanism, which better incorporates relative topology position and enhances the intra-class inductive bias by maximizing the label influence. We further propose a class-wise conflict measure as the edge weights, which benefits the separation of different node classes. Extensive experiments demonstrate the superior potential and adaptability of PASTEL in enhancing GNNs' power in different data annotation scenarios.