Schreier-Coset Graph Propagation

TL;DR

This paper introduces Schreier-Coset Graph Propagation (SCGP), a novel group-theoretic method that enhances GNNs' ability to propagate information over long distances efficiently without increasing graph complexity.

Contribution

SCGP enriches node features using Schreier-coset embeddings, enabling scalable, long-range message passing in GNNs without altering the original graph topology.

Findings

SCGP achieves comparable or better performance than existing methods on standard benchmarks.

SCGP improves scalability and reduces memory footprint for large graphs.

SCGP enhances processing of hierarchical and modular graph structures.

Abstract

Graph Neural Networks (GNNs) offer a principled framework for learning over graph-structured data, yet their expressive capacity is often hindered by over-squashing, wherein information from distant nodes is compressed into fixed-size vectors. Existing solutions, including graph rewiring and bottleneck-resistant architectures such as Cayley and expander graphs, avoid this problem but introduce scalability bottlenecks. In particular, the Cayley graphs constructed over $SL(2,\mathbb{Z}_n)$ exhibit strong theoretical properties, yet suffer from cubic node growth $O(n^3)$, leading to high memory usage. To address this, this work introduces Schrier-Coset Graph Propagation (SCGP), a group-theoretic augmentation method that enriches node features through Schreier-coset embeddings without altering the input graph topology. SCGP embeds bottleneck-free connectivity patterns into a compact feature space, improving long-range message passing while maintaining computational efficiency. Empirical evaluations across standard node and graph classification benchmarks demonstrate that SCGP achieves performance comparable to, or exceeding, expander graph and rewired GNN baselines. Furthermore, SCGP exhibits particular advantages in processing hierarchical and modular graph structures, offering reduced inference latency, improved scalability, and a low memory footprint, making it suitable for real-time and resource-constrained applications.