Kolmogorov–Arnold Networks: A Spline-Based Alternative to Multilayer Perceptrons for Function Approximation

Multilayer perceptrons (MLPs) have been the default building block of deep learning for more than three decades, yet their fixed nodal non-linearities and purely linear edge weights limit both their parameter efficiency and their interpretability. This paper reviews and empirically examines Kolmogorov–Arnold Networks (KANs), a recently proposed architecture that reverses this design: every edge carries a learnable univariate function, typically parameterized by a spline-like basis, while nodes perform only summation. KANs are grounded in the Kolmogorov–Arnold representation theorem, which guarantees that any continuous multivariate function can be written as a finite composition of continuous univariate functions. We formalize the KAN layer, describe a Chebyshev-polynomial instantiation of the learnable edge functions, and report a controlled experiment in which a compact KAN and a conventional MLP are trained to approximate a smooth, non-additively-separable two-dimensional function. With roughly one-quarter of the trainable parameters of the MLP, the KAN achieves lower training and test mean-squared error, and its individual edge functions can be visualized directly, offering a route toward more transparent models. We discuss the practical trade-offs of the approach, including training cost and sensitivity to basis choice, and outline directions for combining KANs with other novel deep learning algorithms.

کلیدواژه ها:

Kolmogorov–Arnold Networks ، spline-based neural networks ، function approximation ، interpretable deep learning ، novel neural network architectures.