用双曲空间生成有层级结构的图，比传统方法更准确。
GGBall: Graph Generative Model on Poincaré Ball
- 在双曲球面上构建生成模型，结合向量量化与流匹配
- 在两个数据集上度分布差异降低超75%和40%以上
- 适合处理具有层次结构的复杂网络数据
生成具有层级结构的图仍是一大挑战，因欧氏几何难以捕捉指数级复杂性。本文提出GGBall，一种新颖的双曲图生成框架，融合几何归纳偏置与现代生成范式。GGBall结合双曲向量量化自编码器（HVQVAE）与基于闭式测地线定义的黎曼流匹配先验，使流基先验能建模复杂潜在分布，同时向量量化有助于保持双曲空间的曲率感知结构。我们进一步设计了一套完全在流形内运作的双曲GNN与Transformer层，确保稳定性和可扩展性。实验表明，相比当前最优基线，模型在Community-Small上度分布MMD降低超过75%，在Ego-Small上降低超过40%，显著提升对拓扑层级的保持能力。结果表明双曲几何是生成复杂、结构化及层级数据的强大基础。代码已公开于https://github.com/AI4Science-WestlakeU/GGBall。
原文摘要 · Abstract (English)
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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