RecKAN: Kolmogorov-Arnold Networks with a Learnable Recursive Polynomial Basis
Quick summary
arXiv:2609.01729v1 Announce Type: cross Abstract: 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 ne
Key takeaways
- arXiv:2609.01729v1 Announce Type: cross Abstract: 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 ne
Why it matters
The importance of “RecKAN: Kolmogorov-Arnold Networks with a Learnable Recursive Polynomial Basis” will be measured by what changes in practice. User behavior, access conditions, verifiable performance and responsible-use outcomes are the signals worth following.
Member comments