# Motif-aware Riemannian Graph Neural Network with Generative-Contrastive Learning

arXiv: https://arxiv.org/abs/2401.01232 · HTML: https://mlsanity.com/paper/2401.01232/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 45 references that are in the map.
- First posted on arXiv 2 Jan 2024.

## Builds on (most cited first, 27 of 27)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Riemannian Adaptive Optimization Methods](https://mlsanity.com/paper/1810.00760/) (2018)
- [GraphGAN: Graph Representation Learning with Generative Adversarial Nets](https://mlsanity.com/paper/1711.08267/) (2017)
- [Lorentzian Graph Convolutional Networks](https://mlsanity.com/paper/2104.07477/) (2021)
- [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)
- [Hyperbolic Variational Graph Neural Network for Modeling Dynamic Graphs](https://mlsanity.com/paper/2104.02228/) (2021)
- [Self-Supervised Continual Graph Learning in Adaptive Riemannian Spaces](https://mlsanity.com/paper/2211.17068/) (2022)
- [ACE-HGNN: Adaptive Curvature Exploration Hyperbolic Graph Neural Network](https://mlsanity.com/paper/2110.07888/) (2021)
- [A Self-supervised Riemannian GNN with Time Varying Curvature for Temporal Graph Learning](https://mlsanity.com/paper/2208.14073/) (2022)
- [Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approach](https://mlsanity.com/paper/2106.04941/) (2021)
- [Heterogeneous manifolds for curvature-aware graph embedding](https://mlsanity.com/paper/2202.01185/) (2022)
- [Hyperbolic Disk Embeddings for Directed Acyclic Graphs](https://mlsanity.com/paper/1902.04335/) (2019)
- [Contrastive Graph Clustering in Curvature Spaces](https://mlsanity.com/paper/2305.03555/) (2023)
- [Fully-Connected Network on Noncompact Symmetric Space and Ridgelet Transform based on Helgason-Fourier Analysis](https://mlsanity.com/paper/2203.01631/) (2022)
- [Random Laplacian Features for Learning with Hyperbolic Space](https://mlsanity.com/paper/2202.06854/) (2022)
- [Using Motif Transitions for Temporal Graph Generation](https://mlsanity.com/paper/2306.11190/) (2023)

## Built on by (most cited first, 23 of 23)

- [RiemannGFM: Learning a Graph Foundation Model from Riemannian Geometry](https://mlsanity.com/paper/2502.03251/) (2025)
- [LSEnet: Lorentz Structural Entropy Neural Network for Deep Graph Clustering](https://mlsanity.com/paper/2405.11801/) (2024)
- [Hyperbolic Geometric Latent Diffusion Model for Graph Generation](https://mlsanity.com/paper/2405.03188/) (2024)
- [Position: Beyond Euclidean -- Foundation Models Should Embrace Non-Euclidean Geometries](https://mlsanity.com/paper/2504.08896/) (2025)
- [Spiking Graph Neural Network on Riemannian Manifolds](https://mlsanity.com/paper/2410.17941/) (2024)
- [A Survey on Self-Supervised Graph Foundation Models: Knowledge-Based Perspective](https://mlsanity.com/paper/2403.16137/) (2024)
- [Deeper with Riemannian Geometry: Overcoming Oversmoothing and Oversquashing for Graph Foundation Models](https://mlsanity.com/paper/2510.17457/) (2025)
- [Multi-Domain Riemannian Graph Gluing for Building Graph Foundation Models](https://mlsanity.com/paper/2603.00618/) (2026)
- [DisRFM: Polar Riemannian Flow Matching for Structure-Preserving Graph Domain Adaptation](https://mlsanity.com/paper/2602.00656/) (2026)
- [R-ODE: Ricci Curvature Tells When You Will be Informed](https://mlsanity.com/paper/2405.17282/) (2024)
- [Toward a Unified Geometry Understanding: Riemannian Diffusion Framework for Graph Generation and Prediction](https://mlsanity.com/paper/2510.04522/) (2025)
- [Manifold GCN: Diffusion-based Convolutional Neural Network for Manifold-valued Graphs](https://mlsanity.com/paper/2401.14381/) (2024)
- [Leveraging Manifold Embeddings for Enhanced Graph Transformer Representations and Learning](https://mlsanity.com/paper/2507.07335/) (2025)
- [Riemannian Geometry Speaks Louder Than Words: From Graph Foundation Model to Next-Generation Graph Intelligence](https://mlsanity.com/paper/2603.21601/) (2026)
- [Alleviating Over-Smoothing via Aggregation over Compact Manifolds](https://mlsanity.com/paper/2407.19231/) (2024)
- [OpenGLT: A Comprehensive Benchmark of Graph Neural Networks for Graph-Level Tasks](https://mlsanity.com/paper/2501.00773/) (2025)
- [BEACON: A Benchmark for Efficient and Accurate Counting of Subgraphs](https://mlsanity.com/paper/2504.10948/) (2025)
- [A roadmap for curvature-based geometric data analysis and learning](https://mlsanity.com/paper/2510.22599/) (2025)
- [Deep Incomplete Multi-View Clustering via Hierarchical Imputation and Alignment](https://mlsanity.com/paper/2601.09051/) (2026)
- [Are Common Substructures Transferable? Riemannian Graph Foundation Model with Neural Vector Bundles](https://mlsanity.com/paper/2606.03270/) (2026)
- [Boundary Embedding Shaping with Adaptive Contrastive Learning for Graph Structural Disentanglement](https://mlsanity.com/paper/2606.20283/) (2026)
- [Link prediction on multi-relational graphs from an influence propagation perspective](https://mlsanity.com/paper/2608.05016/) (2026)
- [Learning Propagation Geometry from Message-Passing Feedback](https://mlsanity.com/paper/2609.34711/) (2026)

## Abstract (arXiv)

Graphs are typical non-Euclidean data of complex structures. In recent years, Riemannian graph representation learning has emerged as an exciting alternative to Euclidean ones. However, Riemannian methods are still in an early stage: most of them present a single curvature (radius) regardless of structural complexity, suffer from numerical instability due to the exponential/logarithmic map, and lack the ability to capture motif regularity. In light of the issues above, we propose the problem of Motif-aware Riemannian Graph Representation Learning, seeking a numerically stable encoder to capture motif regularity in a diverse-curvature manifold without labels. To this end, we present a novel Motif-aware Riemannian model with Generative-Contrastive learning (MotifRGC), which conducts a minmax game in Riemannian manifold in a self-supervised manner. First, we propose a new type of Riemannian GCN (D-GCN), in which we construct a diverse-curvature manifold by a product layer with the diversified factor, and replace the exponential/logarithmic map by a stable kernel layer. Second, we introduce a motif-aware Riemannian generative-contrastive learning to capture motif regularity in the constructed manifold and learn motif-aware node representation without external labels. Empirical results show the superiority of MofitRGC.