A new neural network design called ER-KAN falls apart far less when its training data is noisy, exposing a weakness in a popular class of models that most papers had quietly avoided testing.
Kolmogorov-Arnold Networks (KANs) are a newer alternative to standard MLPs, and prior efficient-KAN papers, covering Chebyshev, wavelet, and radial-basis-function variants, were benchmarked almost entirely on clean data. When researchers instead corrupted training data with sigma=0.1 noise, ChebyKAN's test error jumped 10.6x and vanilla KAN's jumped 7.9x, versus just 1.7x for a standard MLP. Their own ER-KAN, built from shared Gaussian radial-basis-function bases, curriculum noise injection during training, and entropy-weighted regularization, rose only 1.4x, matching MLP accuracy at moderate noise with a mere 595 parameters. On a physics-informed neural network modeling a damped harmonic oscillator, ER-KAN beat MLP by 4.2x lower solution error, though on a tougher Burgers' equation PINN, every model tested, ER-KAN included, failed to converge.
KANs have been pitched as a leaner, more interpretable alternative to MLPs for scientific machine learning, where clean labeled data is often scarce and real measurements are messy. This paper is among the first to show that the clean-data benchmarking convention was masking a real fragility, and it proposes a simple "noise degradation ratio" metric that other KAN papers should start reporting.
The Burgers' equation failure is the honest part: a noise-robustness win on simpler problems does not mean an architecture is ready for harder nonlinear differential equations, and the authors say so rather than burying it.