Helmut Bölcskei

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Professor of Electrical Engineering at ETH Zurich

High-Dimensional Distribution Generation Through Deep Neural Networks

We show that every d-dimensional probability distribution of bounded sup...
07/26/2021 ∙ by Dmytro Perekrestenko, et al. ∙ 249 ∙ share

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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...
05/06/2021 ∙ by Clemens Hutter, et al. ∙ 0 ∙ share

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Constructive Universal High-Dimensional Distribution Generation through Deep ReLU Networks

We present an explicit deep neural network construction that transforms ...
06/30/2020 ∙ by Dmytro Perekrestenko, et al. ∙ 1 ∙ share

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Affine Symmetries and Neural Network Identifiability

We address the following question of neural network identifiability: Sup...
06/21/2020 ∙ by Verner Vlačić, et al. ∙ 0 ∙ share

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Canonical Conditions for K/2 Degrees of Freedom

We present a necessary and sufficient condition for 1/2 degree of freedo...
06/03/2020 ∙ by Recep Gül, et al. ∙ 0 ∙ share

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Neural network identifiability for a family of sigmoidal nonlinearities

This paper addresses the following question of neural network identifiab...
06/11/2019 ∙ by Verner Vlačić, et al. ∙ 0 ∙ share

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Deep Neural Network Approximation Theory

Deep neural networks have become state-of-the-art technology for a wide ...
01/08/2019 ∙ by Philipp Grohs, et al. ∙ 1 ∙ share

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Uncertainty relations and sparse signal recovery

This chapter provides a principled introduction to uncertainty relations...
11/09/2018 ∙ by Erwin Riegler, et al. ∙ 0 ∙ share

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The universal approximation power of finite-width deep ReLU networks

We show that finite-width deep ReLU neural networks yield rate-distortio...
06/05/2018 ∙ by Dmytro Perekrestenko, et al. ∙ 1 ∙ share

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Necessary Conditions for K/2 Degrees of Freedom

Stotz et al., 2016, reported a sufficient (injectivity) condition for ea...
05/08/2018 ∙ by Recep Gül, et al. ∙ 0 ∙ share

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Rate-Distortion Theory for General Sets and Measures

This paper is concerned with a rate-distortion theory for sequences of i...
04/24/2018 ∙ by Erwin Riegler, et al. ∙ 0 ∙ share

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Lossless Analog Compression

We establish the fundamental limits of lossless analog compression by co...
03/19/2018 ∙ by Giovanni Alberti, et al. ∙ 0 ∙ share

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Topology Reduction in Deep Convolutional Feature Extraction Networks

Deep convolutional neural networks (CNNs) used in practice employ potent...
07/10/2017 ∙ by Thomas Wiatowski, et al. ∙ 0 ∙ share

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Energy Propagation in Deep Convolutional Neural Networks

Many practical machine learning tasks employ very deep convolutional neu...
04/12/2017 ∙ by Thomas Wiatowski, et al. ∙ 0 ∙ share

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Discrete Deep Feature Extraction: A Theory and New Architectures

First steps towards a mathematical theory of deep convolutional neural n...
05/26/2016 ∙ by Thomas Wiatowski, et al. ∙ 0 ∙ share

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Deep Convolutional Neural Networks on Cartoon Functions

Wiatowski and Bölcskei, 2015, proved that deformation stability and vert...
04/29/2016 ∙ by Philipp Grohs, et al. ∙ 0 ∙ share

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A Mathematical Theory of Deep Convolutional Neural Networks for Feature Extraction

Deep convolutional neural networks have led to breakthrough results in n...
12/19/2015 ∙ by Thomas Wiatowski, et al. ∙ 0 ∙ share

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Deep Convolutional Neural Networks Based on Semi-Discrete Frames

Deep convolutional neural networks have led to breakthrough results in p...
04/21/2015 ∙ by Thomas Wiatowski, et al. ∙ 0 ∙ share

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Nonparametric Nearest Neighbor Random Process Clustering

We consider the problem of clustering noisy finite-length observations o...
04/20/2015 ∙ by Michael Tschannen, et al. ∙ 0 ∙ share

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Subspace clustering of dimensionality-reduced data

Subspace clustering refers to the problem of clustering unlabeled high-d...
04/27/2014 ∙ by Reinhard Heckel, et al. ∙ 0 ∙ share

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Neighborhood Selection for Thresholding-based Subspace Clustering

Subspace clustering refers to the problem of clustering high-dimensional...
03/13/2014 ∙ by Reinhard Heckel, et al. ∙ 0 ∙ share

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Compressive Nonparametric Graphical Model Selection For Time Series

We propose a method for inferring the conditional indepen- dence graph (...
11/13/2013 ∙ by Alexander Jung, et al. ∙ 0 ∙ share

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Robust Subspace Clustering via Thresholding

The problem of clustering noisy and incompletely observed high-dimension...
07/18/2013 ∙ by Reinhard Heckel, et al. ∙ 0 ∙ share

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Noisy Subspace Clustering via Thresholding

We consider the problem of clustering noisy high-dimensional data points...
05/15/2013 ∙ by Reinhard Heckel, et al. ∙ 0 ∙ share

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Subspace Clustering via Thresholding and Spectral Clustering

We consider the problem of clustering a set of high-dimensional data poi...
03/15/2013 ∙ by Reinhard Heckel, et al. ∙ 0 ∙ share

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Helmut Bölcskei

Featured Co-authors

Shlomo Shamai

Alexander Jung

Reinhard Heckel

Michael Tschannen

Philipp Grohs

Eirikur Agustsson

Günther Koliander

Thomas Wiatowski

Erwin Riegler

Dennis Elbrächter

Dmytro Perekrestenko

High-Dimensional Distribution Generation Through Deep Neural Networks

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

Constructive Universal High-Dimensional Distribution Generation through Deep ReLU Networks

Affine Symmetries and Neural Network Identifiability

Canonical Conditions for K/2 Degrees of Freedom

Neural network identifiability for a family of sigmoidal nonlinearities

Deep Neural Network Approximation Theory

Uncertainty relations and sparse signal recovery

The universal approximation power of finite-width deep ReLU networks

Necessary Conditions for K/2 Degrees of Freedom

Rate-Distortion Theory for General Sets and Measures

Lossless Analog Compression

Topology Reduction in Deep Convolutional Feature Extraction Networks

Energy Propagation in Deep Convolutional Neural Networks

Discrete Deep Feature Extraction: A Theory and New Architectures

Deep Convolutional Neural Networks on Cartoon Functions

A Mathematical Theory of Deep Convolutional Neural Networks for Feature Extraction

Deep Convolutional Neural Networks Based on Semi-Discrete Frames

Nonparametric Nearest Neighbor Random Process Clustering

Subspace clustering of dimensionality-reduced data

Neighborhood Selection for Thresholding-based Subspace Clustering

Compressive Nonparametric Graphical Model Selection For Time Series

Robust Subspace Clustering via Thresholding

Noisy Subspace Clustering via Thresholding

Subspace Clustering via Thresholding and Spectral Clustering