GraphMoRE: Mitigating Topological Heterogeneity via Mixture of Riemannian Experts

TL;DR

GraphMoRE introduces a novel framework that uses a mixture of Riemannian experts with a gating mechanism to adaptively embed complex, heterogeneous graphs into personalized, mixed-curvature spaces, reducing distortion and improving representation quality.

Contribution

The paper proposes a new graph embedding method that dynamically selects and combines multiple Riemannian spaces to better capture diverse topological patterns in graphs.

Findings

Achieves lower embedding distortion on real-world and synthetic datasets.

Outperforms existing methods in modeling topological heterogeneity.

Demonstrates effectiveness in preserving complex graph structures.

Abstract

Real-world graphs have inherently complex and diverse topological patterns, known as topological heterogeneity. Most existing works learn graph representation in a single constant curvature space that is insufficient to match the complex geometric shapes, resulting in low-quality embeddings with high distortion. This also constitutes a critical challenge for graph foundation models, which are expected to uniformly handle a wide variety of diverse graph data. Recent studies have indicated that product manifold gains the possibility to address topological heterogeneity. However, the product manifold is still homogeneous, which is inadequate and inflexible for representing the mixed heterogeneous topology. In this paper, we propose a novel Graph Mixture of Riemannian Experts (GraphMoRE) framework to effectively tackle topological heterogeneity by personalized fine-grained topology geometry pattern preservation. Specifically, to minimize the embedding distortion, we propose a topology-aware gating mechanism to select the optimal embedding space for each node. By fusing the outputs of diverse Riemannian experts with learned gating weights, we construct personalized mixed curvature spaces for nodes, effectively embedding the graph into a heterogeneous manifold with varying curvatures at different points. Furthermore, to fairly measure pairwise distances between different embedding spaces, we present a concise and effective alignment strategy. Extensive experiments on real-world and synthetic datasets demonstrate that our method achieves superior performance with lower distortion, highlighting its potential for modeling complex graphs with topological heterogeneity, and providing a novel architectural perspective for graph foundation models.