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

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