# FMGNN: Fused Manifold Graph Neural Network

arXiv: https://arxiv.org/abs/2304.01081 · HTML: https://mlsanity.com/paper/2304.01081/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 41 references that are in the map.
- First posted on arXiv 3 Apr 2023.

## Builds on (most cited first, 24 of 24)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Constant Curvature Graph Convolutional Networks](https://mlsanity.com/paper/1911.05076/) (2019)
- [Embedding Text in Hyperbolic Spaces](https://mlsanity.com/paper/1806.04313/) (2018)
- [Graph Geometry Interaction Learning](https://mlsanity.com/paper/2010.12135/) (2020)
- [A Hyperbolic-to-Hyperbolic Graph Convolutional Network](https://mlsanity.com/paper/2104.06942/) (2021)
- [Spherical Text Embedding](https://mlsanity.com/paper/1911.01196/) (2019)
- [Small-GAN: Speeding Up GAN Training Using Core-sets](https://mlsanity.com/paper/1910.13540/) (2019)
- [From One Point to A Manifold: Knowledge Graph Embedding For Precise Link Prediction](https://mlsanity.com/paper/1512.04792/) (2015)
- [Geometry Interaction Knowledge Graph Embeddings](https://mlsanity.com/paper/2206.12418/) (2022)
- [Neighborhood Growth Determines Geometric Priors for Relational Representation Learning](https://mlsanity.com/paper/1910.05565/) (2019)
- [Scalable k-Means Clustering via Lightweight Coresets](https://mlsanity.com/paper/1702.08248/) (2017)
- [The k-PDTM : a coreset for robust geometric inference](https://mlsanity.com/paper/1801.10346/) (2018)

## Built on by (most cited first, 2 of 2)

- [Curve Your Attention: Mixed-Curvature Transformers for Graph Representation Learning](https://mlsanity.com/paper/2309.04082/) (2023)
- [Manifold GCN: Diffusion-based Convolutional Neural Network for Manifold-valued Graphs](https://mlsanity.com/paper/2401.14381/) (2024)

## Abstract (arXiv)

Graph representation learning has been widely studied and demonstrated effectiveness in various graph tasks. Most existing works embed graph data in the Euclidean space, while recent works extend the embedding models to hyperbolic or spherical spaces to achieve better performance on graphs with complex structures, such as hierarchical or ring structures. Fusing the embedding from different manifolds can further take advantage of the embedding capabilities over different graph structures. However, existing embedding fusion methods mostly focus on concatenating or summing up the output embeddings, without considering interacting and aligning the embeddings of the same vertices on different manifolds, which can lead to distortion and impression in the final fusion results. Besides, it is also challenging to fuse the embeddings of the same vertices from different coordinate systems. In face of these challenges, we propose the Fused Manifold Graph Neural Network (FMGNN), a novel GNN architecture that embeds graphs into different Riemannian manifolds with interaction and alignment among these manifolds during training and fuses the vertex embeddings through the distances on different manifolds between vertices and selected landmarks, geometric coresets. Our experiments demonstrate that FMGNN yields superior performance over strong baselines on the benchmarks of node classification and link prediction tasks.