Search Results for author: Michael Kohler

Found 10 papers, 1 papers with code

On the rate of convergence of an over-parametrized Transformer classifier learned by gradient descent

no code implementations28 Dec 2023 Michael Kohler, Adam Krzyzak

One of the most recent and fascinating breakthroughs in artificial intelligence is ChatGPT, a chatbot which can simulate human conversation.

Chatbot Language Modelling

Analysis of the expected $L_2$ error of an over-parametrized deep neural network estimate learned by gradient descent without regularization

no code implementations24 Nov 2023 Selina Drews, Michael Kohler

Recent results show that estimates defined by over-parametrized deep neural networks learned by applying gradient descent to a regularized empirical $L_2$ risk are universally consistent and achieve good rates of convergence.

regression

Analysis of convolutional neural network image classifiers in a rotationally symmetric model

no code implementations11 May 2022 Michael Kohler, Benjamin Walter

Convolutional neural network image classifiers are defined and the rate of convergence of the misclassification risk of the estimates towards the optimal misclassification risk is analyzed.

Image Classification

Estimation of a regression function on a manifold by fully connected deep neural networks

no code implementations20 Jul 2021 Michael Kohler, Sophie Langer, Ulrich Reif

Estimation of a regression function from independent and identically distributed data is considered.

regression

Uncertainty Quantification in Case of Imperfect Models: A Review

no code implementations17 Dec 2020 Sebastian Kersting, Michael Kohler

Uncertainty quantification of complex technical systems is often based on a computer model of the system.

Uncertainty Quantification

On the rate of convergence of fully connected very deep neural network regression estimates

no code implementations29 Aug 2019 Michael Kohler, Sophie Langer

Recent results in nonparametric regression show that deep learning, i. e., neural network estimates with many hidden layers, are able to circumvent the so-called curse of dimensionality in case that suitable restrictions on the structure of the regression function hold.

regression

Estimation of a function of low local dimensionality by deep neural networks

no code implementations29 Aug 2019 Michael Kohler, Adam Krzyzak, Sophie Langer

Consequently, the rate of convergence of the estimate does not depend on its input dimension $d$, but on its local dimension $d^*$ and the DNNs are able to circumvent the curse of dimensionality in case that $d^*$ is much smaller than $d$.

Dimensionality Reduction object-detection +4

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