Search Results for author: Gitta Kutyniok

Found 43 papers, 13 papers with code

Graph Scattering beyond Wavelet Shackles

no code implementations26 Jan 2023 Christian Koke, Gitta Kutyniok

This work develops a flexible and mathematically sound framework for the design and analysis of graph scattering networks with variable branching ratios and generic functional calculus filters.

Graph Classification

Computability of Optimizers

no code implementations15 Jan 2023 Yunseok Lee, Holger Boche, Gitta Kutyniok

Optimization problems are a staple of today's scientific and technical landscape.

Explaining Image Classifiers with Multiscale Directional Image Representation

no code implementations22 Nov 2022 Stefan Kolek, Robert Windesheim, Hector Andrade Loarca, Gitta Kutyniok, Ron Levie

However, the smoothness of a mask limits its ability to separate fine-detail patterns, that are relevant for the classifier, from nearby nuisance patterns, that do not affect the classifier.

Dataset of Pathloss and ToA Radio Maps With Localization Application

no code implementations18 Nov 2022 Çağkan Yapar, Ron Levie, Gitta Kutyniok, Giuseppe Caire

In this article, we present a collection of radio map datasets in dense urban setting, which we generated and made publicly available.

Well-definedness of Physical Law Learning: The Uniqueness Problem

1 code implementation15 Oct 2022 Philipp Scholl, Aras Bacho, Holger Boche, Gitta Kutyniok

Finally, we provide extensive numerical experiments showing that our algorithms in combination with common approaches for learning physical laws indeed allow to guarantee that a unique governing differential equation is learnt, without assuming any knowledge about the function, thereby ensuring reliability.

Unveiling the Sampling Density in Non-Uniform Geometric Graphs

no code implementations15 Oct 2022 Raffaele Paolino, Aleksandar Bojchevski, Stephan Günnemann, Gitta Kutyniok, Ron Levie

A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.

Memorization-Dilation: Modeling Neural Collapse Under Label Noise

1 code implementation11 Jun 2022 Duc Anh Nguyen, Ron Levie, Julian Lienen, Gitta Kutyniok, Eyke Hüllermeier

The notion of neural collapse refers to several emergent phenomena that have been empirically observed across various canonical classification problems.


OOD Link Prediction Generalization Capabilities of Message-Passing GNNs in Larger Test Graphs

no code implementations30 May 2022 Yangze Zhou, Gitta Kutyniok, Bruno Ribeiro

This work provides the first theoretical study on the ability of graph Message Passing Neural Networks (gMPNNs) -- such as Graph Neural Networks (GNNs) -- to perform inductive out-of-distribution (OOD) link prediction tasks, where deployment (test) graph sizes are larger than training graphs.

Link Prediction

Inverse Problems Are Solvable on Real Number Signal Processing Hardware

no code implementations5 Apr 2022 Holger Boche, Adalbert Fono, Gitta Kutyniok

In this work, we show that real number computing in the framework of BSS machines does enable the algorithmic solvability of finite dimensional inverse problems.

The Mathematics of Artificial Intelligence

no code implementations16 Mar 2022 Gitta Kutyniok

We currently witness the spectacular success of artificial intelligence in both science and public life.

Limitations of Deep Learning for Inverse Problems on Digital Hardware

no code implementations28 Feb 2022 Holger Boche, Adalbert Fono, Gitta Kutyniok

In fact, our result even holds for Borel-Turing computability., i. e., there does not exist an algorithm which performs the training of a neural network on digital hardware for any given accuracy.

LocUNet: Fast Urban Positioning Using Radio Maps and Deep Learning

1 code implementation1 Feb 2022 Çağkan Yapar, Ron Levie, Gitta Kutyniok, Giuseppe Caire

We present LocUNet: A deep learning method for localization, based merely on Received Signal Strength (RSS) from Base Stations (BSs), which does not require any increase in computation complexity at the user devices with respect to the device standard operations, unlike methods that rely on time of arrival or angle of arrival information.

Neural Tangent Kernel Beyond the Infinite-Width Limit: Effects of Depth and Initialization

1 code implementation1 Feb 2022 Mariia Seleznova, Gitta Kutyniok

We derive exact expressions for the NTK dispersion in the infinite-depth-and-width limit in all three phases and conclude that the NTK variability grows exponentially with depth at the EOC and in the chaotic phase but not in the ordered phase.

Generalization Analysis of Message Passing Neural Networks on Large Random Graphs

no code implementations1 Feb 2022 Sohir Maskey, Ron Levie, Yunseok Lee, Gitta Kutyniok

Message passing neural networks (MPNN) have seen a steep rise in popularity since their introduction as generalizations of convolutional neural networks to graph-structured data, and are now considered state-of-the-art tools for solving a large variety of graph-focused problems.

Graph Classification

A Rate-Distortion Framework for Explaining Black-box Model Decisions

no code implementations12 Oct 2021 Stefan Kolek, Duc Anh Nguyen, Ron Levie, Joan Bruna, Gitta Kutyniok

We present the Rate-Distortion Explanation (RDE) framework, a mathematically well-founded method for explaining black-box model decisions.

Physical Simulations

Cartoon Explanations of Image Classifiers

1 code implementation7 Oct 2021 Stefan Kolek, Duc Anh Nguyen, Ron Levie, Joan Bruna, Gitta Kutyniok

We present CartoonX (Cartoon Explanation), a novel model-agnostic explanation method tailored towards image classifiers and based on the rate-distortion explanation (RDE) framework.

Transferability of Graph Neural Networks: an Extended Graphon Approach

no code implementations21 Sep 2021 Sohir Maskey, Ron Levie, Gitta Kutyniok

Our main contributions can be summarized as follows: 1) we prove that any fixed GCNN with continuous filters is transferable under graphs that approximate the same graphon, 2) we prove transferability for graphs that approximate unbounded graphon shift operators, which are defined in this paper, and, 3) we obtain non-asymptotic approximation results, proving linear stability of GCNNs.

Deep Microlocal Reconstruction for Limited-Angle Tomography

no code implementations12 Aug 2021 Héctor Andrade-Loarca, Gitta Kutyniok, Ozan Öktem, Philipp Petersen

We present a deep learning-based algorithm to jointly solve a reconstruction problem and a wavefront set extraction problem in tomographic imaging.

Real-time Outdoor Localization Using Radio Maps: A Deep Learning Approach

1 code implementation23 Jun 2021 Çağkan Yapar, Ron Levie, Gitta Kutyniok, Giuseppe Caire

Global Navigation Satellite Systems typically perform poorly in urban environments, where the likelihood of line-of-sight conditions between the devices and the satellites is low, and thus alternative localization methods are required for good accuracy.

Analyzing Finite Neural Networks: Can We Trust Neural Tangent Kernel Theory?

no code implementations8 Dec 2020 Mariia Seleznova, Gitta Kutyniok

We find out that whether a network is in the NTK regime depends on the hyperparameters of random initialization and the network's depth.

Expressivity of Deep Neural Networks

no code implementations9 Jul 2020 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.

The Restricted Isometry of ReLU Networks: Generalization through Norm Concentration

no code implementations1 Jul 2020 Alex Goeßmann, Gitta Kutyniok

In case of the NeuRIP event, we then provide bounds on the expected risk, which hold for networks in any sublevel set of the empirical risk.

In-Distribution Interpretability for Challenging Modalities

no code implementations1 Jul 2020 Cosmas Heiß, Ron Levie, Cinjon Resnick, Gitta Kutyniok, Joan Bruna

It is widely recognized that the predictions of deep neural networks are difficult to parse relative to simpler approaches.

Physical Simulations

Real-time Localization Using Radio Maps

no code implementations9 Jun 2020 Çağkan Yapar, Ron Levie, Gitta Kutyniok, Giuseppe Caire

Using the approximations of the pathloss functions of all base stations and the reported signal strengths, we are able to extract a very accurate approximation of the location of the user.

Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks

1 code implementation25 Apr 2020 Moritz Geist, Philipp Petersen, Mones Raslan, Reinhold Schneider, Gitta Kutyniok

Here, approximation theory predicts that the performance of the model should depend only very mildly on the dimension of the parameter space and is determined by the intrinsic dimension of the solution manifold of the parametric partial differential equation.

Interval Neural Networks: Uncertainty Scores

1 code implementation25 Mar 2020 Luis Oala, Cosmas Heiß, Jan Macdonald, Maximilian März, Wojciech Samek, Gitta Kutyniok

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.

Image Reconstruction

RadioUNet: Fast Radio Map Estimation with Convolutional Neural Networks

1 code implementation17 Nov 2019 Ron Levie, Çağkan Yapar, Gitta Kutyniok, Giuseppe Caire

In this paper we propose a highly efficient and very accurate deep learning method for estimating the propagation pathloss from a point $x$ (transmitter location) to any point $y$ on a planar domain.

Association Scheduling

Transferability of Spectral Graph Convolutional Neural Networks

no code implementations30 Jul 2019 Ron Levie, Wei Huang, Lorenzo Bucci, Michael M. Bronstein, Gitta Kutyniok

Transferability, which is a certain type of generalization capability, can be loosely defined as follows: if two graphs describe the same phenomenon, then a single filter or ConvNet should have similar repercussions on both graphs.

A Rate-Distortion Framework for Explaining Neural Network Decisions

2 code implementations27 May 2019 Jan Macdonald, Stephan Wäldchen, Sascha Hauch, Gitta Kutyniok

We formalise the widespread idea of interpreting neural network decisions as an explicit optimisation problem in a rate-distortion framework.

General Classification Image Classification

A Theoretical Analysis of Deep Neural Networks and Parametric PDEs

no code implementations31 Mar 2019 Gitta Kutyniok, Philipp Petersen, Mones Raslan, Reinhold Schneider

We derive upper bounds on the complexity of ReLU neural networks approximating the solution maps of parametric partial differential equations.

Error bounds for approximations with deep ReLU neural networks in $W^{s,p}$ norms

no code implementations21 Feb 2019 Ingo Gühring, Gitta Kutyniok, Philipp Petersen

We analyze approximation rates of deep ReLU neural networks for Sobolev-regular functions with respect to weaker Sobolev norms.

On the Transferability of Spectral Graph Filters

no code implementations29 Jan 2019 Ron Levie, Elvin Isufi, Gitta Kutyniok

For filters in this space, the perturbation in the filter is bounded by a constant times the perturbation in the graph, and filters in the Cayley smoothness space are thus termed linearly stable.

Extraction of digital wavefront sets using applied harmonic analysis and deep neural networks

1 code implementation5 Jan 2019 Héctor Andrade-Loarca, Gitta Kutyniok, Ozan Öktem, Philipp Petersen

Microlocal analysis provides deep insight into singularity structures and is often crucial for solving inverse problems, predominately, in imaging sciences.

The Mismatch Principle: The Generalized Lasso Under Large Model Uncertainties

no code implementations20 Aug 2018 Martin Genzel, Gitta Kutyniok

We study the estimation capacity of the generalized Lasso, i. e., least squares minimization combined with a (convex) structural constraint.

Learning Theory Variable Selection

Optimal Approximation with Sparsely Connected Deep Neural Networks

no code implementations4 May 2017 Helmut Bölcskei, Philipp Grohs, Gitta Kutyniok, Philipp Petersen

Specifically, all function classes that are optimally approximated by a general class of representation systems---so-called \emph{affine systems}---can be approximated by deep neural networks with minimal connectivity and memory requirements.

Shearlet-based compressed sensing for fast 3D cardiac MR imaging using iterative reweighting

no code implementations1 May 2017 Jackie Ma, Maximilian März, Stephanie Funk, Jeanette Schulz-Menger, Gitta Kutyniok, Tobias Schaeffter, Christoph Kolbitsch

High-resolution three-dimensional (3D) cardiovascular magnetic resonance (CMR) is a valuable medical imaging technique, but its widespread application in clinical practice is hampered by long acquisition times.

Anatomy Image Reconstruction

A Mathematical Framework for Feature Selection from Real-World Data with Non-Linear Observations

no code implementations31 Aug 2016 Martin Genzel, Gitta Kutyniok

In this paper, we study the challenge of feature selection based on a relatively small collection of sample pairs $\{(x_i, y_i)\}_{1 \leq i \leq m}$.

Variable Selection

A Haar Wavelet-Based Perceptual Similarity Index for Image Quality Assessment

1 code implementation20 Jul 2016 Rafael Reisenhofer, Sebastian Bosse, Gitta Kutyniok, Thomas Wiegand

In most practical situations, the compression or transmission of images and videos creates distortions that will eventually be perceived by a human observer.

Denoising Image Quality Assessment +2

Sparse Proteomics Analysis - A compressed sensing-based approach for feature selection and classification of high-dimensional proteomics mass spectrometry data

no code implementations11 Jun 2015 Tim Conrad, Martin Genzel, Nada Cvetkovic, Niklas Wulkow, Alexander Leichtle, Jan Vybiral, Gitta Kutyniok, Christof Schütte

Results: We present a new algorithm, Sparse Proteomics Analysis (SPA), based on the theory of compressed sensing that allows us to identify a minimal discriminating set of features from mass spectrometry data-sets.

General Classification

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