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03/07/2023
Completion of Matrices with Low Description Complexity
We propose a theory for matrix completion that goes beyond the low-rank ...
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11/28/2022
Metric entropy of causal, discrete-time LTI systems
In [1] it is shown that recurrent neural networks (RNNs) can learn - in ...
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11/24/2021
Lossy Compression of General Random Variables
This paper is concerned with the lossy compression of general random var...
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07/26/2021
High-Dimensional Distribution Generation Through Deep Neural Networks
We show that every d-dimensional probability distribution of bounded sup...
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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...
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06/30/2020
Constructive Universal High-Dimensional Distribution Generation through Deep ReLU Networks
We present an explicit deep neural network construction that transforms ...
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06/21/2020
Affine Symmetries and Neural Network Identifiability
We address the following question of neural network identifiability: Sup...
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06/03/2020
Canonical Conditions for K/2 Degrees of Freedom
We present a necessary and sufficient condition for 1/2 degree of freedo...
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06/11/2019
Neural network identifiability for a family of sigmoidal nonlinearities
This paper addresses the following question of neural network identifiab...
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01/08/2019
Deep Neural Network Approximation Theory
Deep neural networks have become state-of-the-art technology for a wide ...
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11/09/2018
Uncertainty relations and sparse signal recovery
This chapter provides a principled introduction to uncertainty relations...
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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...
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05/08/2018
Necessary Conditions for K/2 Degrees of Freedom
Stotz et al., 2016, reported a sufficient (injectivity) condition for ea...
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04/24/2018
Rate-Distortion Theory for General Sets and Measures
This paper is concerned with a rate-distortion theory for sequences of i...
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03/19/2018
Lossless Analog Compression
We establish the fundamental limits of lossless analog compression by co...
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07/10/2017
Topology Reduction in Deep Convolutional Feature Extraction Networks
Deep convolutional neural networks (CNNs) used in practice employ potent...
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04/12/2017
Energy Propagation in Deep Convolutional Neural Networks
Many practical machine learning tasks employ very deep convolutional neu...
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05/26/2016
Discrete Deep Feature Extraction: A Theory and New Architectures
First steps towards a mathematical theory of deep convolutional neural n...
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04/29/2016
Deep Convolutional Neural Networks on Cartoon Functions
Wiatowski and Bölcskei, 2015, proved that deformation stability and vert...
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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...
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04/21/2015
Deep Convolutional Neural Networks Based on Semi-Discrete Frames
Deep convolutional neural networks have led to breakthrough results in p...
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04/20/2015
Nonparametric Nearest Neighbor Random Process Clustering
We consider the problem of clustering noisy finite-length observations o...
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04/27/2014
Subspace clustering of dimensionality-reduced data
Subspace clustering refers to the problem of clustering unlabeled high-d...
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03/13/2014
Neighborhood Selection for Thresholding-based Subspace Clustering
Subspace clustering refers to the problem of clustering high-dimensional...
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11/13/2013
Compressive Nonparametric Graphical Model Selection For Time Series
We propose a method for inferring the conditional indepen- dence graph (...
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07/18/2013
Robust Subspace Clustering via Thresholding
The problem of clustering noisy and incompletely observed high-dimension...
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05/15/2013
Noisy Subspace Clustering via Thresholding
We consider the problem of clustering noisy high-dimensional data points...
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03/15/2013