Stability-Constrained Approximation in Spline KANs: Exact Layer Balancing and Budget-Compatible Saturation
Deep spline superposition networks face a tension between approximation order and stability across depth. We study approximation under a hard layerwise Lipschitz budget, and organise it around two quantities: the factorisation stability complexity of a given deep factorisation, and the budget-compatible approximation complexity of a discretisation operator. First, we solve exactly the finite-depth diagonal balancing problem for a fixed chain of nonnegative envelope matrices: the optimal uniform layer budget equals $\|M_{L-1}\cdots M_0\|_{\infty\to\infty}^{1/L}$, attained by an explicit one-pass minimiser, for rectangular layers, with a complete treatment of degeneracies and non-attainment...
| Authors | Aleksander Tankman |
|---|---|
| Primary category | stat.ML |
| Published | 14 September 2026 |
| Last updated at source | 14 September 2026 |
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