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

2026-03-20

AI Summary

This work addresses the challenge of modeling topological heterogeneity in graph data, which cannot be effectively captured within a single Riemannian manifold. To this end, we propose GeoMoE, a novel framework that, for the first time, leverages Ollivier–Ricci curvature as a geometric prior to guide a mixture-of-experts model in adaptively routing across Riemannian spaces of varying curvature, thereby enabling precise capture of multiscale graph topologies. Our approach introduces curvature-aware contrastive learning and a curvature-guided alignment loss, complemented by a graph-aware gating network that ensures geometric consistency and interpretability among experts. Extensive experiments on six benchmark graph datasets demonstrate that GeoMoE significantly outperforms current state-of-the-art methods, exhibiting strong generalization capabilities.

Technology Category

• Machine Learning: Mixture of Experts (MoE)
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• graph representation learning
• topological heterogeneity
• Riemannian manifold
• mixed-curvature
• geometric routing

Innovation

• Geometric Mixture-of-Experts
• Ollivier-Ricci Curvature
• Mixed-Curvature Representation
• Curvature-Guided Routing
• Riemannian Graph Learning