9 citations · 20 across the 9 of their papers we have counts for
11 papers
Analysis of the rate of convergence of an over-parametrized convolutional neural network image classifier learned by gradient descent
Michael Kohler, Adam Krzyzak, Benjamin Walter
Image classification based on over-parametrized convolutional neural networks with a global average-pooling layer is considered. The weights of the network are learned by gradient…
Learning of deep convolutional network image classifiers via stochastic gradient descent and over-parametrization
Michael Kohler, Adam Krzyzak, Alisha Sänger
Image classification from independent and identically distributed random variables is considered. Image classifiers are defined which are based on a linear combination of deep conv…
On the rate of convergence of an over-parametrized Transformer classifier learned by gradient descent
Michael Kohler, Adam Krzyzak
One of the most recent and fascinating breakthroughs in artificial intelligence is ChatGPT, a chatbot which can simulate human conversation. ChatGPT is an instance of GPT4, which i…
Analysis of the rate of convergence of an over-parametrized deep neural network estimate learned by gradient descent
Michael Kohler, Adam Krzyzak
Estimation of a regression function from independent and identically distributed random variables is considered. The error with integration with respect to the design measure…
On the rate of convergence of a deep recurrent neural network estimate in a regression problem with dependent data
Michael Kohler, Adam Krzyzak
A regression problem with dependent data is considered. Regularity assumptions on the dependency of the data are introduced, and it is shown that under suitable structural assumpti…
On the rate of convergence of image classifiers based on convolutional neural networks
M. Kohler, A. Krzyzak, B. Walter
Image classifiers based on convolutional neural networks are defined, and the rate of convergence of the misclassification risk of the estimates towards the optimal misclassificati…
Over-parametrized deep neural networks do not generalize well
Michael Kohler, Adam Krzyzak
Recently it was shown in several papers that backpropagation is able to find the global minimum of the empirical risk on the training data using over-parametrized deep neural netwo…
Analysis of the rate of convergence of neural network regression estimates which are easy to implement
Alina Braun, Michael Kohler, Adam Krzyzak
Recent results in nonparametric regression show that for deep learning, i.e., for neural network estimates with many hidden layers, we are able to achieve good rates of convergence…
Estimation of a function of low local dimensionality by deep neural networks
Michael Kohler, Adam Krzyzak, Sophie Langer
Deep neural networks (DNNs) achieve impressive results for complicated tasks like object detection on images and speech recognition. Motivated by this practical success, there is n…
Discretization of quaternionic continuous wavelet transforms
A. Askari Hemmat, K. Thirulogasanthar, A. Krzyzak
A scheme to form a basis and a frame for a Hilbert space of quaternion valued square integrable function from a basis and a frame, respectively, of a Hilbert space of complex value…
An Affine Invariant -Nearest Neighbor Regression Estimate
Gérard Biau, Luc Devroye, Vida Dujmovic +1
We design a data-dependent metric in and use it to define the -nearest neighbors of a given point. Our metric is invariant under all affine transformations. We sho…