Stability-Constrained Approximation in Spline KANs: Exact Layer Balancing and Budget-Compatible Saturation

arXiv:2609.17619 · stat.ML, cs.LG, cs.NA, math.NA · Submitted 2026-09-14 · Read on arXiv

stat.ML, cs.LG, cs.NA, math.NA

Submitted: 2026-09-14

Updated: 2026-09-14

Comments: 33 pages. Ancillary code reproduces the numerical constants of Appendix B. Complements arXiv:2604.26444, which constructs deep KAN representations with controlled layer-wise Lipschitz product; here the allocation of that product across layers is solved exactly, and the cost of preserving it under spline discretisation is bounded from both sides

Code: https://github.com/hippocratus/math

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Accuracy — 6× in this paper · explained in 1 episode
• Generalization — 2× in this paper · explained in 13 episodes
• Generalization Bounds — 2× in this paper · explained in 2 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Anisotropy — 1× in this paper · explained in 3 episodes
• Benchmark — 1× in this paper · explained in 2 episodes
• Sparsity — 1× in this paper · explained in 4 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Lower estimates for linear operators with smooth range
• Equi-normalization of Neural Networks
• Layer-wise Lipschitz-Product Control for Deep Kolmogorov--Arnold Network Representations of Compositionally Structured Functions
• Generalization Bounds and Model Complexity for Kolmogorov-Arnold Networks

Related papers

• Behavior of prediction performance metrics with rare events
• Optimal Estimation of Generic Dynamics by Path-Dependent Neural Jump ODEs
• A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors
• One Permutation Is All You Need: Fast, Deterministic Feature Importance and Model Stress-Testing
• Online Conformal Prediction for Non-Exchangeable Panel Data
• Deep Time-Series Forecasting in 10 Years: A Survey