324 citations · 1.4k across the 135 of their papers we have counts for
11 papers · 1 filter
Analyzing Finite Neural Networks: Can We Trust Neural Tangent Kernel Theory?
Mariia Seleznova, Gitta Kutyniok
Neural Tangent Kernel (NTK) theory is widely used to study the dynamics of infinitely-wide deep neural networks (DNNs) under gradient descent. But do the results for infinitely-wid…
Quasi Monte Carlo Time-Frequency Analysis
Ron Levie, Haim Avron, Gitta Kutyniok
We study signal processing tasks in which the signal is mapped via some generalized time-frequency transform to a higher dimensional time-frequency space, processed there, and synt…
Analysis of simultaneous inpainting and geometric separation based on sparse decomposition
Van Tiep Do, Ron Levie, Gitta Kutyniok
Natural images are often the superposition of various parts of different geometric characteristics. For instance, an image might be a mixture of cartoon and texture structures. In…
Expressivity of Deep Neural Networks
Ingo Gühring, Mones Raslan, Gitta Kutyniok
In this review paper, we give a comprehensive overview of the large variety of approximation results for neural networks. Approximation rates for classical function spaces as well…
In-Distribution Interpretability for Challenging Modalities
Cosmas Heiß, Ron Levie, Cinjon Resnick +2
It is widely recognized that the predictions of deep neural networks are difficult to parse relative to simpler approaches. However, the development of methods to investigate the m…
The Restricted Isometry of ReLU Networks: Generalization through Norm Concentration
Alex Goeßmann, Gitta Kutyniok
While regression tasks aim at interpolating a relation on the entire input space, they often have to be solved with a limited amount of training data. Still, if the hypothesis func…
Real-time Localization Using Radio Maps
Çağkan Yapar, Ron Levie, Gitta Kutyniok +1
This paper deals with the problem of localization in a cellular network in a dense urban scenario. Global Navigation Satellite System typically performs poorly in urban environment…
tfShearlab: The TensorFlow Digital Shearlet Transform for Deep Learning
Héctor Andrade-Loarca, Gitta Kutyniok
The shearlet transform from applied harmonic analysis is currently the state of the art when analyzing multidimensional signals with anisotropic singularities. Its optimal sparse a…
Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks
Moritz Geist, Philipp Petersen, Mones Raslan +2
We perform a comprehensive numerical study of the effect of approximation-theoretical results for neural networks on practical learning problems in the context of numerical analysi…
Interval Neural Networks: Uncertainty Scores
Luis Oala, Cosmas Heiß, Jan Macdonald +3
We propose a fast, non-Bayesian method for producing uncertainty scores in the output of pre-trained deep neural networks (DNNs) using a data-driven interval propagating network. T…
Tensor network approaches for learning non-linear dynamical laws
A. Goeßmann, M. Götte, I. Roth +3
Given observations of a physical system, identifying the underlying non-linear governing equation is a fundamental task, necessary both for gaining understanding and generating det…