6 papers
Two fixed functions can approximate any continuous function using only addition and composition
Vugar Ismailov
We prove that two fixed univariate functions, namely, an arbitrary continuous non-affine function and a particular affine function, are sufficient to approximate continuous functio…
Universality of shallow and deep neural networks on non-Euclidean spaces
Vugar Ismailov
We study shallow and deep neural networks whose inputs range over a general topological space. The model is built from a prescribed family of continuous feature maps and reduces to…
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…
A note on the problem of straight-line interpolation by ridge functions
Azer Akhmedov, Vugar Ismailov
In this paper we discuss the problem of interpolation on straight lines by linear combinations of ridge functions with fixed directions. By using some geometry and/or systems of li…
On the Kurepa and inhomogeneous Cauchy functional equations
Rashid Aliev, Vugar Ismailov
It follows from de Bruijn's results that if a continuous or -th order continuously differentiable function is a solution of the Kurepa functional equation, then it can…