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RecKAN: Kolmogorov-Arnold Networks with a Learnable Recursive Polynomial Basis — arXiv:2609.01729

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.01729
License (as archived): CC0-1.0
Archived: 2026-10-17T03:26:48.542Z
SHA-256 of the archived text: 5d4de3f7916bd7ce08ab0461658eb178e1473f4237de9fd9f74b48567f8dbcbc
Stable URL of this page: https://metraipolis.com/documento/dc_508ef24eb511

How to cite

RecKAN: Kolmogorov-Arnold Networks with a Learnable Recursive Polynomial Basis — arXiv:2609.01729 — arXiv (en), https://arxiv.org/abs/2609.01729 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_508ef24eb511 (Metraipolis archive dc_508ef24eb511, sha256 5d4de3f7916bd7ce08ab0461658eb178e1473f4237de9fd9f74b48567f8dbcbc)

BibTeX

@misc{dc508ef24eb511,
  title = {RecKAN: Kolmogorov-Arnold Networks with a Learnable Recursive Polynomial Basis — arXiv:2609.01729},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.01729},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_508ef24eb511; sha256 5d4de3f7916bd7ce08ab0461658eb178e1473f4237de9fd9f74b48567f8dbcbc},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.01729. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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 Jacobsthal polynomials as special cases, and prove that its degree grows linearly in $n$ exactly on the sub-family containing all of them, giving a concrete sense in which the learned basis can move beyond any fixed classical choice. Across multiple benchmark datasets spanning image, text, biomedical time series classification, and time series forecasting, RecKAN outperforms three parameter-matched KAN baselines (Chebyshev, Jacobi, and spline based) on all classification tasks and achieves the lowest MSE on the ETTh1 forecasting benchmark. Additionally, when used as a classifier head with a convolutional backbone, RecKAN achieves higher accuracy than standard MLP heads on Fashion MNIST, CIFAR-10, and SVHN. On a synthetic function fitting benchmark it tracks a sharply oscillatory target that a parameter comparable MLP under fits. We further show that the learned recurrence coefficients are interpretable: on the task requiring the most local structure, training moves the basis away from the linear degree growth regime that contains every classical family we identify, consistent with our theoretical analysis of what that structural shift enables.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-03 in cs.AI).
Categorie arXiv: Machine Learning (cs.LG) ; Artificial Intelligence (cs.AI).
Pagina del lavoro: https://arxiv.org/abs/2609.01729 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T03:13:12.474Z dalla pagina https://arxiv.org/catchup/cs.AI/2026-09-03?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).