arXiv Machine Learning
Kolmogorov--Arnold stability for discontinuous functions
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arXiv Machine Learning
Sep 1
Kolmogorov--Arnold against bounded translations
The paper revisits the Kolmogorov–Arnold representation theorem (KART), which has gained renewed interest through its use in neural networks such as Kolmogorov–Arnold Networks (KANs). It addresses the open question of KART’s stability when the hidden layer is subjected to continuous adversarial perturbations, specifically bounded translations. The authors present a constructive proof of an approximate representation that uses fixed, piecewise‑linear inner functions and a single outer function that remains invariant across all summands, provided the maximum translation bound is known in advance.
arXiv AI
Aug 25
KAN-Robust-Bench: A Benchmark for Evaluating the Robustness of Kolmogorov-Arnold Networks
arXiv:2608.21488v1 Announce Type: cross Abstract: While machine learning models have demonstrated strong performance in many domains, these models have shown profound vulnerabilities when they are ex...
arXiv Machine Learning
Jun 18
On the Stability of the Jacobian Matrix in Deep Neural Networks
arXiv:2506. 08764v3 Announce Type: replace Abstract: Deep neural networks are known to suffer from exploding or vanishing gradients as depth increases, a phenomenon closely tied to the spectral behavior of the input-output Jacobian.
arXiv AI
Aug 13
Making Gaussian Kolmogorov-Arnold Networks Reliable and Accurate
arXiv:2604. 21174v3 Announce Type: replace-cross Abstract: Kolmogorov-Arnold Networks (KANs) replace fixed activations with learnable univariate edge functions whose behavior depends strongly on the chosen basis.
arXiv Machine Learning
Jun 26
Kolmogorov Arnold networks (KAN) for aerodynamic prediction: a comparison with MLPs and GNNs
arXiv:2606. 27126v1 Announce Type: new Abstract: Kolmogorov Arnold networks (KAN) have recently been introduced as a (deep) neural network architecture whose trainable parameters adapt the activation functions, instead of the coefficients of the affine transformations at the core of traditional architectures such as deep multilayer perceptrons (MLPs).
arXiv Machine Learning
Jul 21
Geometric origin of adversarial vulnerability in deep learning
arXiv:2509. 01235v2 Announce Type: replace Abstract: Balancing training accuracy and adversarial robustness has beeen a challenge since the birth of deep learning.