Liu et al. (2024) name and structurally base a new neural-network architecture, Kolmogorov-Arnold Networks, directly on the 1957 Kolmogorov-Arnold representation theorem

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A 2024 paper by a team from MIT, Caltech, and Northeastern — Ziming Liu, Yixuan Wang, Sachin Vaidya, Fabian Ruehle, James Halverson, Marin Soljačić, Thomas Y. Hou, and Max Tegmark — states directly: "We propose a promising alternative to MLPs, called Kolmogorov-Arnold Networks (KANs)." The multi-layer perceptron (MLP) is the standard building block of deep learning, built from fixed nonlinear activation functions on nodes and learned linear weights on edges. KANs invert this: they replace the fixed node activations with learnable spline functions placed on the edges, directly following the compositional form of the Kolmogorov-Arnold representation theorem — the pair of 1957 results by Andrey Kolmogorov and his student Vladimir Arnold (Arnold's reduction to functions of two variables resolving Hilbert's 13th problem, and Kolmogorov's strengthening to single-variable functions plus addition), cited as one theorem: any continuous multivariate function decomposes into a finite composition of continuous single-variable functions and addition. The paper was accepted at ICLR 2025, and the name "Kolmogorov-Arnold Networks" is the authors' own, not a later popularization.

The paper's framing places KANs as a direct structural rival to the MLP rather than a niche variant, arguing the architecture offers advantages in accuracy and interpretability for certain scientific-computing and function-fitting tasks. This gives the 67-year-old pure-mathematics theorem a named, actively-developed descendant family in modern AI, with subsequent variants (e.g. KAN 2.0, TKAN) following within roughly a year of publication (noted in the source capture but not independently verified here).