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20202026
most citedLower bounds for artificial neural network approximations: A proof that shallow neural networks fail to overcome the curse of dimensionality

1 citations · 2 across the 5 of their papers we have counts for

collaborators

6 papers

math.OC2026

Landscape analysis for shallow neural networks: Complete classification of critical points for cubic activation and affine target functions

Shokhrukh Ibragimov, Ilkhom Mukhammadiev, Diyora Salimova

In this paper, we study the optimization landscape induced by the true loss for shallow polynomial neural networks (PNNs) with neurons on the hidden l…

math.OC2026

Unified convergence analysis for gradient descent optimization methods in the training of deep neural networks

Shokhrukh Ibragimov, Arnulf Jentzen

Gradient based optimization methods are nowadays the methods of choice for training deep neural networks (DNNs) in artificial intelligence (AI) systems. In practically relevant DNN…

cs.LG2025

On the logical skills of large language models: evaluations using arbitrarily complex first-order logic problems

Shokhrukh Ibragimov, Arnulf Jentzen, Benno Kuckuck

We present a method of generating first-order logic statements whose complexity can be controlled along multiple dimensions. We use this method to automatically create several data…

math.OC20221 cited

On the existence of infinitely many realization functions of non-global local minima in the training of artificial neural networks with ReLU activation

Shokhrukh Ibragimov, Arnulf Jentzen, Timo Kröger +1

Gradient descent (GD) type optimization schemes are the standard instruments to train fully connected feedforward artificial neural networks (ANNs) with rectified linear unit (ReLU…

math.NA20211 cited

Lower bounds for artificial neural network approximations: A proof that shallow neural networks fail to overcome the curse of dimensionality

Philipp Grohs, Shokhrukh Ibragimov, Arnulf Jentzen +1

Artificial neural networks (ANNs) have become a very powerful tool in the approximation of high-dimensional functions. Especially, deep ANNs, consisting of a large number of hidden…

math.CA2020

On a functional-differential equation with quasi-arithmetic mean value

Shokhrukh Ibragimov

In this paper we describe all differentiable functions satisfying the functional-differential equation \begin{equation*} [φ(y) - φ(x)]ψ'\bigl(h(x,y)\bigr…