# ER-KANs: Efficient and Robust Kolmogorov-Arnold Networks for Data-Scarce Scientific Machine Learning

arXiv: https://arxiv.org/abs/2608.14773 · HTML: https://mlsanity.com/paper/2608.14773/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 19 references that are in the map.
- First posted on arXiv 14 Aug 2026.

## Builds on (most cited first, 6 of 6)

- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems](https://mlsanity.com/paper/2003.04919/) (2020)
- [A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks](https://mlsanity.com/paper/2406.02917/) (2024)

## Built on by (most cited first, 1 of 1)

- [Revalidation Beats Stateful Routing for Scientific Surrogates Under Distribution Shift](https://mlsanity.com/paper/2609.29715/) (2026)

## Abstract (arXiv)

The efficient-KAN literature---covering Chebyshev, wavelet, and radial-basis-function variants of the original Kolmogorov-Arnold Network---has been benchmarked almost entirely on clean data. We show that this choice conceals a large capability difference between architectures: ChebyKAN's test MSE (evaluated against clean ground truth) increases by a factor of 10.6x when training data is corrupted with sigma=0.1 noise, versus 7.9x for vanilla KAN, 1.7x for a standard MLP, and just 1.4x for our proposed ER-KAN. ER-KAN combines three design choices targeting the noisy, data-scarce setting: shared Gaussian RBF bases across all edges in a layer (providing locality and efficient parameterisation), curriculum noise injection during training (explicitly teaching noise robustness), and entropy-weighted adaptive regularisation (preventing overfitting at small N). The result is a 595-parameter network that matches MLP accuracy at moderate noise while degrading far more gracefully as noise grows. We evaluate on eight analytic functions (N in {50, 200, 500}, sigma in {0, 0.03, 0.1}), on a damped harmonic oscillator physics-informed neural network where ER-KAN achieves 4.2x lower solution MSE than MLP, and on a Burgers' equation PINN where all models fail to converge---a genuine limitation we report rather than suppress. We introduce the noise degradation ratio as a simple complementary metric and recommend it become a standard reporting requirement for efficient-KAN papers.