39 citations · 47 across the 9 of their papers we have counts for
9 papers
Graph Neural Networks Are Not Continuous Across Graph Resolutions
Christian Koke, Yuesong Shen, Abhishek Saroha +4
We show that contrary to conventional wisdom in the community, graph neural networks (GNNs) are not continuous with respect to all natural modes of graph convergence. As a result,…
Di-Graphs with tightly connected Clusters: Effective Graph Laplacians and Resolvent Convergence
Christian Koke
In this note, we study Laplacians on graphs for which connectivity within certain subgraphs tends to infinity. Our main focus are graphs sharing a common node set on which edge wei…
Large Coupling Convergence Beyond Definiteness
Christian Koke
We study convergence of operator families of the form towards an effective operator defined on , as the coupling constant tends to infinity. Crucially, w…
HoloNets: Spectral Convolutions do extend to Directed Graphs
Christian Koke, Daniel Cremers
Within the graph learning community, conventional wisdom dictates that spectral convolutional networks may only be deployed on undirected graphs: Only there could the existence of…
ResolvNet: A Graph Convolutional Network with multi-scale Consistency
Christian Koke, Abhishek Saroha, Yuesong Shen +2
It is by now a well known fact in the graph learning community that the presence of bottlenecks severely limits the ability of graph neural networks to propagate information over l…
Graph Scattering beyond Wavelet Shackles
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 calc…
Limitless stability for Graph Convolutional Networks
Christian Koke
This work establishes rigorous, novel and widely applicable stability guarantees and transferability bounds for graph convolutional networks -- without reference to any underlying…
Dirac equation on a square waveguide lattice with site-dependent coupling strengths and the gravitational Aharonov-Bohm effect
Christian Koke, Changsuk Noh, Dimitris G. Angelakis
The main objective of this work is to present a theoretical proposal for an implementation of the -dimensional Dirac equation in classical gravitational and electromagneti…
Dirac equation in 2-dimensional curved spacetime, particle creation, and coupled waveguide arrays
C. Koke, C. Noh, D. G. Angelakis
When quantum fields are coupled to gravitational fields, spontaneous particle creation may occur similarly to when they are coupled to external electromagnetic fields. Gravitationa…