Geometry-Constrained Kolmogorov-Arnold Networks: Learning Edge Geometry via Banach Duality
Kolmogorov-Arnold Networks (KANs) replace fixed activations in deep architectures with learnable univariate edge functions, making the choice of edge parametrisation central. Existing variants rely on fixed bases such as splines, polynomials, or Fourier features, which impose a function-space geometry before data are observed. We introduce geometry-constrained KANs, a family of edge activations derived from Banach duality maps in which the geometry itself is learned through a scalar exponent $p > 1$ per edge. This exponent controls the qualitative response: sub-Euclidean values produce sharp, threshold-like behaviour reminiscent of the $\ell_1$ (LASSO) geometry, $p = 2$ recovers the linea...
| Authors | K S Sesh Kumar |
|---|---|
| Primary category | cs.LG |
| Published | 26 August 2026 |
| Last updated at source | 26 August 2026 |
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