# Addressing common misinterpretations of KART and UAT in neural network literature

arXiv: https://arxiv.org/abs/2408.16389 · HTML: https://mlsanity.com/paper/2408.16389/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 31 references that are in the map.
- First posted on arXiv 29 Aug 2024.

## Builds on (most cited first, 16 of 16)

- [Approximating Continuous Functions by ReLU Nets of Minimal Width](https://mlsanity.com/paper/1710.11278/) (2017)
- [Wav-KAN: Wavelet Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.12832/) (2024)
- [Minimum Width for Universal Approximation](https://mlsanity.com/paper/2006.08859/) (2020)
- [GKAN: Graph Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.06470/) (2024)
- [KAGNNs: Kolmogorov-Arnold Networks meet Graph Learning](https://mlsanity.com/paper/2406.18380/) (2024)
- [Deep, Skinny Neural Networks are not Universal Approximators](https://mlsanity.com/paper/1810.00393/) (2018)
- [Kolmogorov-Arnold Graph Neural Networks](https://mlsanity.com/paper/2406.18354/) (2024)
- [Achieve the Minimum Width of Neural Networks for Universal Approximation](https://mlsanity.com/paper/2209.11395/) (2022)
- [Approximation capability of two hidden layer feedforward neural networks with fixed weights](https://mlsanity.com/paper/2101.09181/) (2021)
- [Predictive Modeling of Flexible EHD Pumps using Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.07488/) (2024)
- [On the Kolmogorov neural networks](https://mlsanity.com/paper/2311.00049/) (2023)
- [Kolmogorov-Arnold Networks (KAN) for Time Series Classification and Robust Analysis](https://mlsanity.com/paper/2408.07314/) (2024)
- [Initial Investigation of Kolmogorov-Arnold Networks (KANs) as Feature Extractors for IMU Based Human Activity Recognition](https://mlsanity.com/paper/2406.11914/) (2024)
- [A single hidden layer feedforward network with only one neuron in the hidden layer can approximate any univariate function](https://mlsanity.com/paper/1601.00013/) (2015)
- [Minimum number of neurons in fully connected layers of a given neural network (the first approximation)](https://mlsanity.com/paper/2405.14147/) (2024)
- [Approximation error of single hidden layer neural networks with fixed weights](https://mlsanity.com/paper/2202.03289/) (2022)

## Built on by (most cited first, 9 of 9)

- [FC-KAN: Function Combinations in Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2409.01763/) (2024)
- [SechKAN: Kolmogorov-Arnold Networks with Hyperbolic Secant Functions](https://mlsanity.com/paper/2607.18290/) (2026)
- [Polynomial, trigonometric, and tropical activations](https://mlsanity.com/paper/2502.01247/) (2025)
- [Universality of shallow and deep neural networks on non-Euclidean spaces](https://mlsanity.com/paper/2602.23381/) (2026)
- [Kolmogorov Arnold networks (KAN) for aerodynamic prediction: a comparison with MLPs and GNNs](https://mlsanity.com/paper/2606.27126/) (2026)
- [Quantum Kolmogorov--Arnold representation theorem for continuous unitary-valued maps](https://mlsanity.com/paper/2607.03187/) (2026)
- [Kolmogorov--Arnold against bounded translations](https://mlsanity.com/paper/2608.30710/) (2026)
- [Kolmogorov--Arnold stability for discontinuous functions](https://mlsanity.com/paper/2609.07240/) (2026)
- [Evaluating the Effectiveness of SechKAN on 1D Data](https://mlsanity.com/paper/2609.25876/) (2026)

## Abstract (arXiv)

This note addresses the Kolmogorov-Arnold Representation Theorem (KART) and the Universal Approximation Theorem (UAT), focusing on their frequent misinterpretations found in the neural network literature. Our remarks aim to support a more accurate understanding of KART and UAT among neural network specialists. In addition, we explore the minimal number of neurons required for universal approximation, showing that the same number of neurons needed for exact representation of functions in KART-based networks also suffices for standard multilayer perceptrons in the context of approximation.