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

• URL: http://arxiv.org/abs/2603.22317v1
• Date: Fri, 20 Mar 2026 06:09:01 GMT
• Title: Geometric Mixture-of-Experts with Curvature-Guided Adaptive Routing for Graph Representation Learning
• Abstract summary: We propose a Geometric Mixture-of-Experts framework (GeoMoE) to better accommodate multi-scale topological structures.<n>Specifically, we design a graph-aware gating network that assigns node-specific fusion weights to ensure interpretable and geometry-consistent routing.<n>Experiments on six benchmark datasets demonstrate that GeoMoE outperforms state-of-the-art baselines across diverse graph types.
• Score: 11.124702719919831
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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