324 citations · 1.4k across the 135 of their papers we have counts for
14 papers · 1 filter
Dataset of Pathloss and ToA Radio Maps With Localization Application
Çağkan Yapar, Ron Levie, Gitta Kutyniok +1
In this article, we present a collection of radio map datasets in dense urban setting, which we generated and made publicly available. The datasets include simulated pathloss/recei…
Turing meets Moore-Penrose: Computing the Pseudoinverse on Turing Machines
Holger Boche, Adalbert Fono, Gitta Kutyniok
The pseudoinverse of a matrix, a generalized notion of the inverse, is of fundamental importance in linear algebra and, thereby, in many different fields. Despite its proven existe…
Complexity Blowup for Solutions of the Laplace and the Diffusion Equation
Aras Bacho, Holger Boche, Gitta Kutyniok
In this paper, we investigate the computational complexity of solutions to the Laplace and the diffusion equation. We show that for a certain class of initial-boundary value proble…
Unveiling the Sampling Density in Non-Uniform Geometric Graphs
Raffaele Paolino, Aleksandar Bojchevski, Stephan Günnemann +2
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…
Explaining Image Classifiers with Multiscale Directional Image Representation
Stefan Kolek, Robert Windesheim, Hector Andrade Loarca +2
Image classifiers are known to be difficult to interpret and therefore require explanation methods to understand their decisions. We present ShearletX, a novel mask explanation met…
Symbolic Recovery of Differential Equations: The Identifiability Problem
Philipp Scholl, Aras Bacho, Holger Boche +1
Symbolic recovery of differential equations is the ambitious attempt at automating the derivation of governing equations with the use of machine learning techniques. In contrast to…
Memorization-Dilation: Modeling Neural Collapse Under Label Noise
Duc Anh Nguyen, Ron Levie, Julian Lienen +2
The notion of neural collapse refers to several emergent phenomena that have been empirically observed across various canonical classification problems. During the terminal phase o…
OOD Link Prediction Generalization Capabilities of Message-Passing GNNs in Larger Test Graphs
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-…
Inverse Problems Are Solvable on Real Number Signal Processing Hardware
Holger Boche, Adalbert Fono, Gitta Kutyniok
Despite the success of Deep Learning (DL) serious reliability issues such as non-robustness persist. An interesting aspect is, whether these problems arise due to insufficient tool…
The Mathematics of Artificial Intelligence
Gitta Kutyniok
We currently witness the spectacular success of artificial intelligence in both science and public life. However, the development of a rigorous mathematical foundation is still at…
LocUNet: Fast Urban Positioning Using Radio Maps and Deep Learning
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 Systems (GNSS) typically perform poorly in urban envi…
Limitations of Deep Learning for Inverse Problems on Digital Hardware
Holger Boche, Adalbert Fono, Gitta Kutyniok
Deep neural networks have seen tremendous success over the last years. Since the training is performed on digital hardware, in this paper, we analyze what actually can be computed…
Generalization Analysis of Message Passing Neural Networks on Large Random Graphs
Sohir Maskey, Ron Levie, Yunseok Lee +1
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, a…
Neural Tangent Kernel Beyond the Infinite-Width Limit: Effects of Depth and Initialization
Mariia Seleznova, Gitta Kutyniok
Neural Tangent Kernel (NTK) is widely used to analyze overparametrized neural networks due to the famous result by Jacot et al. (2018): in the infinite-width limit, the NTK is dete…