Geometric Mixture-of-Experts with Curvature-Guided Adaptive Routing for Graph Representation Learning

TL;DR

This paper introduces GeoMoE, a novel graph representation learning framework that adaptively combines multiple Riemannian spaces using curvature-guided routing, improving modeling of complex topologies.

Contribution

The paper proposes a geometric mixture-of-experts model utilizing Ollivier-Ricci Curvature for adaptive, interpretable routing across diverse Riemannian spaces in graph learning.

Findings

Outperforms state-of-the-art methods on six benchmark datasets

Effectively captures multi-scale topological structures

Demonstrates the importance of curvature-guided routing

Abstract

Graph-structured data typically exhibits complex topological heterogeneity, making it difficult to model accurately within a single Riemannian manifold. While emerging mixed-curvature methods attempt to capture such diversity, they often rely on implicit, task-driven routing that lacks fundamental geometric grounding. To address this challenge, we propose a Geometric Mixture-of-Experts framework (GeoMoE) that adaptively fuses node representations across diverse Riemannian spaces to better accommodate multi-scale topological structures. At its core, GeoMoE leverages Ollivier-Ricci Curvature (ORC) as an intrinsic geometric prior to orchestrate the collaboration of specialized experts. Specifically, we design a graph-aware gating network that assigns node-specific fusion weights, regularized by a curvature-guided alignment loss to ensure interpretable and geometry-consistent routing. Additionally, we introduce a curvature-aware contrastive objective that promotes geometric discriminability by constructing positive and negative pairs according to curvature consistency. Extensive experiments on six benchmark datasets demonstrate that GeoMoE outperforms state-of-the-art baselines across diverse graph types.