Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.07198 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914337885519872 |
|---|---|
| author | Bu, Tianci Wang, Chuanrui Ma, Hao Zheng, Haoren Lu, Xin Wu, Tailin |
| author_facet | Bu, Tianci Wang, Chuanrui Ma, Hao Zheng, Haoren Lu, Xin Wu, Tailin |
| contents | Generating graphs with hierarchical structures remains a fundamental challenge due to the limitations of Euclidean geometry in capturing exponential complexity. Here we introduce \textbf{GGBall}, a novel hyperbolic framework for graph generation that integrates geometric inductive biases with modern generative paradigms. GGBall combines a Hyperbolic Vector-Quantized Autoencoder (HVQVAE) with a Riemannian flow matching prior defined via closed-form geodesics. This design enables flow-based priors to model complex latent distributions, while vector quantization helps preserve the curvature-aware structure of the hyperbolic space. We further develop a suite of hyperbolic GNN and Transformer layers that operate entirely within the manifold, ensuring stability and scalability. Empirically, our model reduces degree MMD by over 75\% on Community-Small and over 40\% on Ego-Small compared to state-of-the-art baselines, demonstrating an improved ability to preserve topological hierarchies. These results highlight the potential of hyperbolic geometry as a powerful foundation for the generative modeling of complex, structured, and hierarchical data domains. Our code is available at \href{https://github.com/AI4Science-WestlakeU/GGBall}{here}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07198 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | GGBall: Graph Generative Model on Poincaré Ball Bu, Tianci Wang, Chuanrui Ma, Hao Zheng, Haoren Lu, Xin Wu, Tailin Machine Learning Generating graphs with hierarchical structures remains a fundamental challenge due to the limitations of Euclidean geometry in capturing exponential complexity. Here we introduce \textbf{GGBall}, a novel hyperbolic framework for graph generation that integrates geometric inductive biases with modern generative paradigms. GGBall combines a Hyperbolic Vector-Quantized Autoencoder (HVQVAE) with a Riemannian flow matching prior defined via closed-form geodesics. This design enables flow-based priors to model complex latent distributions, while vector quantization helps preserve the curvature-aware structure of the hyperbolic space. We further develop a suite of hyperbolic GNN and Transformer layers that operate entirely within the manifold, ensuring stability and scalability. Empirically, our model reduces degree MMD by over 75\% on Community-Small and over 40\% on Ego-Small compared to state-of-the-art baselines, demonstrating an improved ability to preserve topological hierarchies. These results highlight the potential of hyperbolic geometry as a powerful foundation for the generative modeling of complex, structured, and hierarchical data domains. Our code is available at \href{https://github.com/AI4Science-WestlakeU/GGBall}{here}. |
| title | GGBall: Graph Generative Model on Poincaré Ball |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2506.07198 |