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.
By Sviatoslav V. Dzhenzher
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...
By Mohammad Meymani, Roozbeh Razavi-Far
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.
By Benjamin Dadoun, Soufiane Hayou, Hanan Salam, Mohamed El Amine Seddik, Pierre Youssef
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.
By Amir Noorizadegan, Sifan Wang, Leevan Ling
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).
By Miguel Jaraiz, Fermin Gutierrez, Pablo Yeste, Miguel S\'anchez-Dom\'inguez, Eusebio Valero, Gonzalo Rubio, Lucas Lacasa
arXiv:2509. 01235v2 Announce Type: replace Abstract: Balancing training accuracy and adversarial robustness has beeen a challenge since the birth of deep learning.
By Yixiong Ren, Wenkang Du, Jianhui Zhou, Haiping Huang
arXiv:2606. 14708v1 Announce Type: cross Abstract: Data-driven machine learning approaches have become increasingly attractive for nonlinear system identification, but standard models often fail to preserve the underlying physical structure and remain difficult to interpret, especially when no analytical model is available.
By Achraf El Messaoudi (UMLP, ENSMM, FEMTO-ST), Karim Cherifi (UMLP, ENSMM, FEMTO-ST), Yann Le Gorrec (UMLP, ENSMM, FEMTO-ST), Yongxin Wu (UMLP, ENSMM, FEMTO-ST)
arXiv:2607. 16329v1 Announce Type: cross Abstract: Lipschitz continuity is a fundamental property of neural networks that characterizes their sensitivity to input perturbations.
By R\'ois\'in Luo, James McDermott, Colm O'Riordan
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). This architecture builds on the Kolmogorov-Arnold theorem, which endows it with universal approximation properties.
arXiv:2604. 25965v2 Announce Type: replace-cross Abstract: Deep learning models are widely deployed in safety-critical domains, but remain vulnerable to adversarial attacks.
By Yuxuan Hou
The paper introduces a method for constructing L-Lipschitz deep residual networks (ResNets) using a Linear Matrix Inequality (LMI) framework. By reformulating the ResNet architecture as a pseudo-tridiagonal LMI and applying the Gershgorin circle theorem, the authors derive closed‑form constraints on network parameters that guarantee Lipschitz continuity. The work also presents a compositional framework for handling recursive systems in hierarchical architectures, while noting that the Gershgorin-based approximations can over‑constrain the system, reducing expressive capacity.
By Marius F. R. Juston, William R. Norris, Dustin Nottage, Ahmet Soylemezoglu
arXiv:2606. 09820v1 Announce Type: cross Abstract: We generalize the universal approximation theorem for functional input neural networks (FNN) to differentiable maps by including the approximation of the derivatives.
By Philipp Schmocker, Josef Teichmann