HYDRA：用于Kolmogorov-Arnold网络的双曲动态表示架构
HYDRA: Hyperbolic Dynamic Representation Architecture for Kolmogorov-Arnold Networks
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中文总结 AI 辅助
本文针对Kolmogorov-Arnold网络的参数冗余问题，提出双曲动态表示架构HYDRA，通过低秩原型块共享函数变换，在8个基准数据集上实现了更优的参数效率与预测性能。
中文摘要 AI 辅助
Kolmogorov-Arnold网络（KAN）通过将标量权重替换为可学习的单变量函数，提升了非线性函数逼近能力。然而，为每条连接分配独立函数会导致大量参数冗余，限制了其可扩展性与效率。为减少该冗余，我们提出HYperbolic Dynamic Representation Architecture（HYDRA），这是KAN的参数高效双曲扩展，将基于样条的函数学习与庞加莱球中的表示相结合。HYDRA将向量值输入映射到有界双曲潜空间，在切空间执行KAN式更新，并采用低秩原型块在隐藏维度间共享函数变换。所得双曲表示提供结构化径向坐标以作解释，而半径控制通过防止边界饱和提升训练稳定性。在8个基准数据集上的大量实验表明，HYDRA始终能达到有竞争力或更优的预测性能，同时提升参数效率与表示可解释性。
英文摘要
Kolmogorov-Arnold Networks (KANs) enhance nonlinear function approximation by replacing scalar weights with learnable univariate functions. However, assigning an independent function to every connection results in substantial parameter redundancy, limiting their scalability and efficiency. To reduce this redundancy, we introduce \textbf{HY}perbolic \textbf{D}ynamic \textbf{R}epresentation \textbf{A}rchitecture (HYDRA), a parameter-efficient hyperbolic extension of KAN that combines spline-based functional learning with representations in the Poincaré ball. HYDRA maps vector-valued inputs into a bounded hyperbolic latent space, performs KAN-style updates in tangent space, and employs a low-rank prototype block to share functional transformations across hidden dimensions. The resulting hyperbolic representations provide a structured radial coordinate for interpretation, while radius control improves training stability by preventing boundary saturation. Extensive experiments across eight benchmark datasets demonstrate that HYDRA consistently achieves competitive or superior predictive performance while improving parameter efficiency and representation interpretability.
