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