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arXiv AI

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

RecKAN introduces a learnable recursive polynomial basis for Kolmogorov–Arnold Networks, replacing fixed bases like B-splines or Chebyshev polynomials. The basis is defined by a second‑order polynomial recurrence whose five coefficients are jointly learned with the network, enabling it to encompass classical families such as Chebyshev, Fibonacci, Pell, and Jacobsthal. Experiments across image, text, biomedical time‑series classification, and forecasting tasks show RecKAN outperforming parameter‑matched KAN baselines and achieving state‑of‑the‑art results on several benchmarks.

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arXiv AI
Oct 2

SW-KAN: Kolmogorov-Arnold Networks with Stieltjes-Wigert q-Orthogonal Polynomials

The paper introduces SW-KAN, a Kolmogorov‑Arnold Network that replaces traditional B‑spline activations with Stieltjes‑Wigert q‑orthogonal polynomials defined on the semi‑infinite domain (0, ∞). It addresses the domain mismatch between unbounded inputs and bounded polynomial bases by applying a smooth exponential‑of‑tanh mapping, and uses a numerically stable three‑term recurrence to evaluate polynomial expansions efficiently. Experiments on image classification and continuous function approximation show that SW‑KAN achieves better accuracy‑efficiency trade‑offs than existing polynomial KANs, especially in resource‑constrained scenarios with limited data or feature dimensionality.

By Amirhosein Azarpour, Seyyed Moein Kazemi
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arXiv Machine Learning
Oct 16

SUPN: Shallow Universal Polynomial Networks for Efficient Function Approximation

The paper introduces Shallow Universal Polynomial Networks (SUPNs), a single‑hidden‑layer architecture that replaces standard activations with learnable multivariate polynomials, thereby increasing expressivity per unit. SUPNs achieve universal approximation by either widening the network or increasing polynomial complexity, and the authors prove convergence rates and quasi‑optimal parameter choices. Empirical tests across a wide range of smooth, nonsmooth, and discontinuous functions in up to ten dimensions show that SUPNs often outperform deep neural networks and Kolmogorov‑Arnold networks in accuracy and variability while requiring fewer parameters and lower training cost.

By Zachary Morrow, Michael Penwarden, Brian Chen, Aurya Javeed, Akil Narayan, John D. Jakeman
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arXiv Machine Learning
3d ago

Tractable Inference with Kolmogorov-Arnold Networks

The paper introduces TOUCKANs, a variant of Kolmogorov–Arnold networks that use finite‑degree polynomial outer functions to create a decomposable sum–product structure. This design allows expectations, variances, and higher moments to be computed via deterministic recursions over one‑dimensional integrals, eliminating the need for costly Monte Carlo sampling even in high dimensions. Experiments on uniform and Gaussian benchmarks up to 50 dimensions show deterministic mean and variance errors below those of fixed‑budget Monte Carlo, and the method successfully enforces conservation laws and normalization constraints in physical simulations such as Cahn–Hilliard mass conservation and Schrödinger eigenpair computation.

By Juan Diego Toscano, Sascha Ranft, Zhiwei Gao, Li-Lian Wang, George Em Karniadakis
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Hugging Face Trending Papers
Jun 16

Monotonic Kolmogorov-Arnold Networks: A Theoretical and Empirical Study of Monotonicity as an Inductive Bias

Monotonicity has been a long-running architectural inductive bias for neural networks, motivated by tabular, scientific, and economic settings where outputs are known to respond monotonically to certain inputs. Existing approaches are MLP- or flow-based and lack per-edge functional transparency; the only Kolmogorov--Arnold Network (KAN) variant with monotonicity, MonoKAN, enforces the constraint only on a restricted parameter subset and requires a projection-style training procedure.

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