Publications (17)
Distilling Influences to Mitigate Prediction Churn in Graph Neural Networks
Andreas Roth, Thomas Liebig
Models with similar performances exhibit significant disagreement in the predictions of individual samples, referred to as prediction churn. Our work explores this phenomenon in gr…
A Retarded Mean-Field Approach for Interacting Fiber Structures
Raul Borsche, Axel Klar, Christian Nessler +2
We consider an interacting system of one-dimensional structures modelling fibers with fiber-fiber interaction in a fiber lay-down process. The resulting microscopic system is inves…
Rank Collapse Causes Over-Smoothing and Over-Correlation in Graph Neural Networks
Andreas Roth, Thomas Liebig
Our study reveals new theoretical insights into over-smoothing and feature over-correlation in graph neural networks. Specifically, we demonstrate that with increased depth, node r…
First-order quarter- and mixed-moment realizability theory and Kershaw closures for a Fokker-Planck equation in two space dimensions
Florian Schneider, Jochen Kall, Andreas Roth
Mixed-moment models, introduced before for one space dimension, are a modification of the method of moments applied to a (linear) kinetic equation, by choosing mixtures of differen…
Quantum Spin Hall Insulator State in HgTe Quantum Wells
Markus Koenig, Steffen Wiedmann, Christoph Bruene +5
Recent theory predicted that the Quantum Spin Hall Effect, a fundamentally novel quantum state of matter that exists at zero external magnetic field, may be realized in HgTe/(Hg,Cd…
What Can We Learn From MIMO Graph Convolutions?
Andreas Roth, Thomas Liebig
Most graph neural networks (GNNs) utilize approximations of the general graph convolution derived in the graph Fourier domain. While GNNs are typically applied in the multi-input m…
Instantaneous control of interacting particle systems in the mean-field limit
Martin Burger, Rene Pinnau, Claudia Totzeck +2
Controlling large particle systems in collective dynamics by a few agents is a subject of high practical importance, e.g., in evacuation dynamics. In this paper we study an instant…
Curvature-based Pooling within Graph Neural Networks
Cedric Sanders, Andreas Roth, Thomas Liebig
Over-squashing and over-smoothing are two critical issues, that limit the capabilities of graph neural networks (GNNs). While over-smoothing eliminates the differences between node…
Simplifying the Theory on Over-Smoothing
Andreas Roth
Graph convolutions have gained popularity due to their ability to efficiently operate on data with an irregular geometric structure. However, graph convolutions cause over-smoothin…
Medley2K: A Dataset of Medley Transitions
Lukas Faber, Sandro Luck, Damian Pascual +3
The automatic generation of medleys, i.e., musical pieces formed by different songs concatenated via smooth transitions, is not well studied in the current literature. To facilitat…
Spin polarization of the quantum spin Hall edge states
Christoph Brüne, Andreas Roth, Hartmut Buhmann +5
While the helical character of the edge channels responsible for charge transport in the quantum spin Hall regime of a two-dimensional topological insulator is by now well establis…
Controlling a self-organizing system of individuals guided by a few external agents -- particle description and mean-field limit
Martin Burger, René Pinnau, Andreas Roth +2
Optimal control of large particle systems with collective dynamics by few agents is a subject of high practical importance (e.g. in evacuation dynamics), but still limited mathemat…
Nonlocal edge state transport in the quantum spin Hall state
Andreas Roth, Christoph Bruene, Hartmut Buhmann +4
We present direct experimental evidence for nonlocal transport in HgTe quantum wells in the quantum spin Hall regime, in the absence of any external magnetic field. The data conclu…
Towards Understanding and Avoiding Limitations of Convolutions on Graphs
Andreas Roth
While message-passing neural networks (MPNNs) have shown promising results, their real-world impact remains limited. Although various limitations have been identified, their theore…
Transforming PageRank into an Infinite-Depth Graph Neural Network
Andreas Roth, Thomas Liebig
Popular graph neural networks are shallow models, despite the success of very deep architectures in other application domains of deep learning. This reduces the modeling capacity a…
Forecasting Unobserved Node States with spatio-temporal Graph Neural Networks
Andreas Roth, Thomas Liebig
Forecasting future states of sensors is key to solving tasks like weather prediction, route planning, and many others when dealing with networks of sensors. But complete spatial co…
Preventing Representational Rank Collapse in MPNNs by Splitting the Computational Graph
Andreas Roth, Franka Bause, Nils M. Kriege +1
The ability of message-passing neural networks (MPNNs) to fit complex functions over graphs is limited as most graph convolutions amplify the same signal across all feature channel…