Helmut Bölcskei | DeepAI

DeepAI

Featured Co-authors

Shlomo Shamai
60 publications
Reinhard Heckel
38 publications
Alexander Jung
36 publications
Michael Tschannen
30 publications
Philipp Grohs
28 publications
Eirikur Agustsson
22 publications
Günther Koliander
12 publications
Erwin Riegler
7 publications
Thomas Wiatowski
7 publications
Dennis Elbrächter
6 publications
Aleksandar Stanić
5 publications

∙ 11/28/2022

Metric entropy of causal, discrete-time LTI systems

In [1] it is shown that recurrent neural networks (RNNs) can learn - in ...

Clemens Hutter, et al. ∙

∙ 11/24/2021

Lossy Compression of General Random Variables

This paper is concerned with the lossy compression of general random var...

Erwin Riegler, et al. ∙

∙ 07/26/2021

High-Dimensional Distribution Generation Through Deep Neural Networks

We show that every d-dimensional probability distribution of bounded sup...

Dmytro Perekrestenko, et al. ∙

∙ 05/06/2021

Metric Entropy Limits on Recurrent Neural Network Learning of Linear Dynamical Systems

One of the most influential results in neural network theory is the univ...

Clemens Hutter, et al. ∙

∙ 06/30/2020

Constructive Universal High-Dimensional Distribution Generation through Deep ReLU Networks

We present an explicit deep neural network construction that transforms ...

Dmytro Perekrestenko, et al. ∙

∙ 06/21/2020

Affine Symmetries and Neural Network Identifiability

We address the following question of neural network identifiability: Sup...

Verner Vlačić, et al. ∙

∙ 06/03/2020

Canonical Conditions for K/2 Degrees of Freedom

We present a necessary and sufficient condition for 1/2 degree of freedo...

Recep Gül, et al. ∙

∙ 06/11/2019

Neural network identifiability for a family of sigmoidal nonlinearities

This paper addresses the following question of neural network identifiab...

Verner Vlačić, et al. ∙

∙ 01/08/2019

Deep Neural Network Approximation Theory

Deep neural networks have become state-of-the-art technology for a wide ...

Philipp Grohs, et al. ∙

∙ 11/09/2018

Uncertainty relations and sparse signal recovery

This chapter provides a principled introduction to uncertainty relations...

Erwin Riegler, et al. ∙

∙ 06/05/2018

The universal approximation power of finite-width deep ReLU networks

We show that finite-width deep ReLU neural networks yield rate-distortio...

Dmytro Perekrestenko, et al. ∙

∙ 05/08/2018

Necessary Conditions for K/2 Degrees of Freedom

Stotz et al., 2016, reported a sufficient (injectivity) condition for ea...

Recep Gül, et al. ∙

∙ 04/24/2018

Rate-Distortion Theory for General Sets and Measures

This paper is concerned with a rate-distortion theory for sequences of i...

Erwin Riegler, et al. ∙

∙ 03/19/2018

Lossless Analog Compression

We establish the fundamental limits of lossless analog compression by co...

Giovanni Alberti, et al. ∙

∙ 07/10/2017

Topology Reduction in Deep Convolutional Feature Extraction Networks

Deep convolutional neural networks (CNNs) used in practice employ potent...

Thomas Wiatowski, et al. ∙

∙ 04/12/2017

Energy Propagation in Deep Convolutional Neural Networks

Many practical machine learning tasks employ very deep convolutional neu...

Thomas Wiatowski, et al. ∙

∙ 05/26/2016

Discrete Deep Feature Extraction: A Theory and New Architectures

First steps towards a mathematical theory of deep convolutional neural n...

Thomas Wiatowski, et al. ∙

∙ 04/29/2016

Deep Convolutional Neural Networks on Cartoon Functions

Wiatowski and Bölcskei, 2015, proved that deformation stability and vert...

Philipp Grohs, et al. ∙

∙ 12/19/2015

A Mathematical Theory of Deep Convolutional Neural Networks for Feature Extraction

Deep convolutional neural networks have led to breakthrough results in n...

Thomas Wiatowski, et al. ∙

∙ 04/21/2015

Deep Convolutional Neural Networks Based on Semi-Discrete Frames

Deep convolutional neural networks have led to breakthrough results in p...

Thomas Wiatowski, et al. ∙

∙ 04/20/2015

Nonparametric Nearest Neighbor Random Process Clustering

We consider the problem of clustering noisy finite-length observations o...

Michael Tschannen, et al. ∙

∙ 04/27/2014

Subspace clustering of dimensionality-reduced data

Subspace clustering refers to the problem of clustering unlabeled high-d...

Reinhard Heckel, et al. ∙

∙ 03/13/2014

Neighborhood Selection for Thresholding-based Subspace Clustering

Subspace clustering refers to the problem of clustering high-dimensional...

Reinhard Heckel, et al. ∙

∙ 11/13/2013

Compressive Nonparametric Graphical Model Selection For Time Series

We propose a method for inferring the conditional indepen- dence graph (...

Alexander Jung, et al. ∙

∙ 07/18/2013

Robust Subspace Clustering via Thresholding

The problem of clustering noisy and incompletely observed high-dimension...

Reinhard Heckel, et al. ∙

∙ 05/15/2013

Noisy Subspace Clustering via Thresholding

We consider the problem of clustering noisy high-dimensional data points...

Reinhard Heckel, et al. ∙

∙ 03/15/2013

Subspace Clustering via Thresholding and Spectral Clustering

We consider the problem of clustering a set of high-dimensional data poi...

Reinhard Heckel, et al. ∙