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

arXiv: https://arxiv.org/abs/2603.22317 · HTML: https://mlsanity.com/paper/2603.22317/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in MoE for time series and graphs, one of 12 directions in Mixture-of-experts.
- Builds on 13 of its 66 references that are in the map.
- First posted on arXiv 20 Mar 2026.

## Placed in

- Mixture-of-experts / [MoE for time series and graphs](https://mlsanity.com/moe/moe-for-time-series-and-graphs/)

## Builds on (most cited first, 13 of 13)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Wiki-CS: A Wikipedia-Based Benchmark for Graph Neural Networks](https://mlsanity.com/paper/2007.02901/) (2020)
- [DeepSphere: a graph-based spherical CNN](https://mlsanity.com/paper/2012.15000/) (2020)
- [ACMP: Allen-Cahn Message Passing with Attractive and Repulsive Forces for Graph Neural Networks](https://mlsanity.com/paper/2206.05437/) (2022)
- [Node-wise Filtering in Graph Neural Networks: A Mixture of Experts Approach](https://mlsanity.com/paper/2406.03464/) (2024)
- [Graph Classification by Mixture of Diverse Experts](https://mlsanity.com/paper/2103.15622/) (2021)
- [Graph Pooling via Ricci Flow](https://mlsanity.com/paper/2407.04236/) (2024)
- [Spectro-Riemannian Graph Neural Networks](https://mlsanity.com/paper/2502.00401/) (2025)
- [Local-Curvature-Aware Knowledge Graph Embedding: An Extended Ricci Flow Approach](https://mlsanity.com/paper/2512.07332/) (2025)

## Built on by (most cited first, 1 of 1)

- [CliffSearch: Structured Agentic Co-Evolution over Theory and Code for Scientific Algorithm Discovery](https://mlsanity.com/paper/2604.01210/) (2026)

## Abstract (arXiv)

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.