120 citations · 295 across the 23 of their papers we have counts for
5 papers · 1 filter
Topological DeepONets and a generalization of the Chen-Chen operator approximation theorem
Vugar Ismailov
Deep Operator Networks (DeepONets) provide a branch-trunk neural architecture for approximating nonlinear operators acting between function spaces. In the classical operator approx…
Addressing common misinterpretations of KART and UAT in neural network literature
Vugar Ismailov
This note addresses the Kolmogorov-Arnold Representation Theorem (KART) and the Universal Approximation Theorem (UAT), focusing on their frequent misinterpretations found in the ne…
Measure theoretic results for approximation by neural networks with limited weights
Vugar Ismailov, Ekrem Savas
In this paper, we study approximation properties of single hidden layer neural networks with weights varying on finitely many directions and thresholds from an open interval. We ob…
Approximation error of single hidden layer neural networks with fixed weights
Vugar Ismailov
This paper provides an explicit formula for the approximation error of single hidden layer neural networks with two fixed weights.
A three layer neural network can represent any multivariate function
Vugar Ismailov
In 1987, Hecht-Nielsen showed that any continuous multivariate function can be implemented by a certain type three-layer neural network. This result was very much discussed in neur…