aiqbench analysis
This paper introduces ER-KAN, an efficient Kolmogorov-Arnold Network architecture specifically designed to maintain robustness in noisy, data-scarce scientific machine learning environments. By integrating shared Gaussian RBF bases with curriculum noise injection and adaptive regularisation, the model demonstrates superior stability compared to vanilla KANs and standard MLPs when training data is corrupted. The authors also highlight a critical limitation where all tested models fail to converge on certain physics-informed tasks like Burgers' equation PINNs, advocating for new metrics that honestly report degradation under noise rather than just clean-data performance.
ER-KANs: Efficient and Robust Kolmogorov-Arnold Networks for Data-Scarce Scientific Machine Learning
arXiv:2608.14773v1 Announce Type: new Abstract: 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.
Abstract: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.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
I.2.6; G.1.2; I.5.1
arXiv:2608.14773 [cs.LG]
(or arXiv:2608.14773v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2608.14773 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 309 words
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