KANs need curvature: penalties for compositional smoothness
Kolmogorov-Arnold networks (KANs) offer a potent combination of accuracy and interpretability, thanks to their compositions of learnable univariate activation functions. However, the activations of well-fitting KANs tend to exhibit pathologically high-curvature oscillations, making them difficult to interpret, and standard regularization penalties do not prevent this. Here we derive a basis-agnostic curvature penalty and show that penalized models can maintain accuracy while achieving substantially smoother activations. Accounting for how function composition shapes curvature, we prove an upper bound on the full model's curvature relative to the curvature penalty, and use this to motivate...
| Authors | James Bagrow |
|---|---|
| Primary category | cs.LG |
| Published | 4 May 2026 |
| Last updated at source | 4 May 2026 |
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