这篇论文提出HYDRA，给KAN“减负”，参数更省还不掉点，双曲空间让表示更可解释。做KAN相关研究的可以看看。
Kolmogorov-Arnold网络（KAN）用可学习单变量函数替换标量权重以增强非线性逼近，但每个连接独立函数导致参数冗余。HYDRA将输入映射到Poincaré球的双曲空间，在切空间执行KAN更新，并用低秩原型块跨隐藏维共享函数变换。在八个基准数据集上，HYDRA在保持竞争性或更优预测性能的同时，提高了参数效率和表示可解释性。
HYDRA: Hyperbolic Dynamic Representation Architecture for Kolmogorov-Arnold Networks
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.