ER-KAN: Robust Kolmogorov-Arnold Networks for Noisy, Data-Scarce Scientific ML

A recent publication on arXiv (2608.14773) presents ER-KAN, a robust and efficient adaptation of Kolmogorov-Arnold Networks (KANs) aimed at scientific machine learning, particularly in scenarios involving noisy and limited datasets. The study highlights that many current efficient-KAN models, such as Chebyshev, wavelet, and radial-basis-function types, have primarily been evaluated using clean data, obscuring their performance discrepancies in noisy conditions. When subjected to sigma=0.1 noise, ChebyKAN's test mean squared error (MSE) rises 10.6 times compared to the clean data, while vanilla KAN sees a 7.9x increase, a standard MLP shows a 1.7x rise, and ER-KAN only increases by 1.4x. ER-KAN employs three key strategies: shared Gaussian radial basis function (RBF) bases for efficient parameterization, curriculum noise injection during training for enhanced noise resilience, and entropy-weighted adaptive regularization to mitigate overfitting with small sample sizes (N). This results in a 595-parameter network that achieves MLP-level accuracy even in moderate noise conditions, making it a valuable tool for scientific fields where data is often limited and noisy. The full paper can be found on arXiv under the identifier 2608.14773.