Geometric Mixture-of-Experts with Curvature-Guided Adaptive Routing for Graph Representation Learning
arXiv:2603.22317v1 Announce Type: new 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
arXiv:2603.22317v1 Announce Type: new 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.
Executive Summary
The article proposes a novel Geometric Mixture-of-Experts framework (GeoMoE) to address the challenges of graph representation learning. GeoMoE leverages Ollivier-Ricci Curvature (ORC) as an intrinsic geometric prior to adaptively fuse node representations across diverse Riemannian spaces. The framework incorporates a graph-aware gating network and a curvature-aware contrastive objective to ensure geometry-consistent routing and promote geometric discriminability. Extensive experiments demonstrate that GeoMoE outperforms state-of-the-art baselines across diverse graph types. The proposed approach has the potential to improve the accuracy and interpretability of graph representation learning, particularly for complex topological structures.
Key Points
- ▸ GeoMoE leverages ORC as an intrinsic geometric prior for adaptive fusion of node representations.
- ▸ The framework incorporates a graph-aware gating network and a curvature-aware contrastive objective.
- ▸ GeoMoE outperforms state-of-the-art baselines across diverse graph types.
Merits
Strength in Geometric Fundamentals
GeoMoE builds upon a strong foundation of geometric principles, leveraging ORC to ensure geometry-consistent routing and promote geometric discriminability.
Flexibility and Adaptability
The framework's adaptive nature enables it to accommodate diverse Riemannian spaces and multi-scale topological structures.
Demerits
Computational Complexity
The framework's reliance on a graph-aware gating network and a curvature-aware contrastive objective may increase computational complexity, particularly for large-scale graphs.
Scalability
The framework's performance may degrade for extremely large-scale graphs, requiring further optimization and scalability enhancements.
Expert Commentary
While GeoMoE demonstrates promising results, further investigation into its scalability and computational complexity is necessary. Additionally, exploring the framework's potential applications in other domains, such as computer vision and natural language processing, could lead to innovative breakthroughs. The incorporation of geometric principles and adaptive fusion mechanisms in GeoMoE highlights the importance of geometric fundamentals in machine learning and graph representation learning.
Recommendations
- ✓ future research should focus on optimizing the framework's computational complexity and scalability, particularly for large-scale graphs.
- ✓ the framework's potential applications in other domains, such as computer vision and natural language processing, should be explored to uncover new and innovative uses for GeoMoE.
Sources
Original: arXiv - cs.LG
