GGBall: Graph Generative Model on Poincaré Ball

• URL: http://arxiv.org/abs/2506.07198v1
• Date: Sun, 08 Jun 2025 15:43:21 GMT
• Title: GGBall: Graph Generative Model on Poincaré Ball
• Authors: Tianci Bu, Chuanrui Wang, Hao Ma, Haoren Zheng, Xin Lu, Tailin Wu,
• Abstract summary: GGBall is a novel hyperbolic framework for graph generation that integrates geometric inductive biases with modern generative paradigms.<n>Our model reduces degree MMD by over 75% on Community-Small and over 40% on Ego-Small compared to state-of-the-art baselines.
• Score: 10.796246797823557
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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}.

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