RecKAN: Kolmogorov-Arnold Networks with a Learnable Recursive Polynomial Basis
Kolmogorov--Arnold Networks (KANs) replace the fixed scalar weights of a standard network with learnable univariate functions on each edge, but existing variants still fix the \emph{basis} that those functions are built from: B-splines, Chebyshev polynomials, wavelets, or Jacobi polynomials, and learn only the combination weights over it. We introduce RecKAN, which instead defines the basis itself by a second order polynomial recurrence, $R_{n+1}(x) = (ax^2+bx+c)R_n(x) + (dx+e)R_{n-1}(x)$, whose five coefficients are learned jointly with the network. We show this recurrence recovers several classical polynomial families including both kinds of Chebyshev polynomials, Fibonacci, Pell, and J...
| Authors | Amirhosein Azarpour |
|---|---|
| Primary category | cs.LG |
| Published | 1 September 2026 |
| Last updated at source | 1 September 2026 |
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