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Life sciences · Preprint
arXiv · August 12, 2026
Posted before peer review. The findings may change or fail to hold.
HYDRA is a novel parameter-efficient hyperbolic extension of Kolmogorov-Arnold Networks reported to achieve competitive or superior performance on eight benchmark datasets while improving interpretability. This is an unrefereed preprint describing a computational method, not a peer-reviewed validation or clinical application study.
Preprint. Intervention: HYDRA (Hyperbolic Dynamic Representation Architecture): a parameter-efficient hyperbolic extension of KAN using spline-based functional learning in Poincaré ball with low-rank prototype block. Compared with: Kolmogorov-Arnold Networks (KAN) and unstated baseline methods.
HYDRA combines spline-based functional learning with Poincaré ball hyperbolic representations Demonstrates competitive or superior predictive performance across eight benchmark datasets Improves parameter efficiency and representation interpretability compared to baseline KAN
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This is an unrefereed preprint presenting a novel machine learning architecture with computational benchmarks but no clinical, biological, or peer-reviewed validation.
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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.
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