利用李群结构设计新型双曲神经网络，提升层次数据建模效率
Cartan Networks: Group theoretical Hyperbolic Deep Learning
- 结合李群同态与保距微分同胚构建新架构
- 在多个基准数据集上展现良好性能
- 适合研究双曲几何与深度学习交叉的学者
双曲深度学习利用双曲空间的度量特性，高效表征层次化数据。本文聚焦双曲空间的可解李群结构，其源于对称空间的自然构造。该流形与李群的双重性质使我们提出一类新算法：将群同态与保距微分同胚交替使用。由此产生的算法称为卡坦网络（Cartan networks），在多个基准数据集上表现优异，并为双曲深度学习开辟了新架构方向。
原文摘要 · Abstract (English)
Hyperbolic deep learning leverages the metric properties of hyperbolic spaces to develop efficient and informative embeddings of hierarchical data. Here, we focus on the solvable group structure of hyperbolic spaces, which follows naturally from their construction as symmetric spaces. This dual nature of Lie group and Riemannian manifold allows us to propose a new class of hyperbolic deep learning algorithms where group homomorphisms are interleaved with metric-preserving diffeomorphisms. The resulting algorithms, which we call Cartan networks, show promising results on various benchmark data sets and open the way to a novel class of hyperbolic deep learning architectures.
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