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:2609.07240v1 Announce Type: new Abstract: Here we investigate the stability of the Kolmogorov--Arnold representation theorem (KART) under adversarial reparameterisations of the hidden layer for...
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:2408. 09112v2 Announce Type: replace Abstract: Reinforcement learning policies parametrized by deep neural networks have achieved strong performance for continuous control, yet even small input perturbations may lead to unpredictable behavior.
arXiv:2606. 19652v1 Announce Type: new Abstract: In this work, we introduce a training procedure for shallow neural networks that promotes robustness against adversarial attacks.
arXiv:2604. 25965v2 Announce Type: replace-cross Abstract: Deep learning models are widely deployed in safety-critical domains, but remain vulnerable to adversarial attacks.
The paper presents a unified framework for regularization-based robust reinforcement learning by deriving upper bounds on the performance gap between nominal and worst-case policies. These bounds are expressed as a regularization objective plus a KL-divergence penalty, explaining why KL penalties enhance robustness. The authors reformulate robust training as a constrained optimization problem, updating the Lagrange multiplier jointly with the policy to automatically tune regularization, and validate the approach with extensive adversarial evaluations on continuous control tasks.
arXiv:2505. 15497v3 Announce Type: replace Abstract: Neural networks hold great potential to act as approximate models of nonlinear dynamical systems, with the resulting neural approximations enabling verification and control of such systems.
arXiv:2406. 05670v3 Announce Type: replace Abstract: Modern machine learning pipelines leverage large amounts of public data, making it infeasible to guarantee data quality and leaving models open to poisoning and backdoor attacks.
arXiv:2502. 02260v2 Announce Type: replace Abstract: In the past decade, considerable research effort has been devoted to securing machine learning (ML) models that operate in adversarial settings.
PANDA is a scalable system that uses zero‑knowledge proofs to certify the robustness and fairness of neural networks without revealing their private parameters. Built on the CROWN robustness framework, PANDA introduces a novel algorithm for proving linear relaxation bounds on non‑linear activation layers, producing lightweight proofs. The system can generate proofs for networks with over 2.9 million parameters in just five minutes and verify them in ten seconds, scaling polynomially with network size and enabling verification of models four orders of magnitude larger than prior ZKP‑based approaches.
arXiv:2605. 10792v2 Announce Type: replace-cross Abstract: We propose an implicit neural formulation of optimal transport that eliminates adversarial min--max optimization and multi-network architectures commonly used in existing approaches.
arXiv:2606. 20325v1 Announce Type: new Abstract: Classical approximation theorems ask for a new neural network whenever the target accuracy is improved.