6 citations · 9 across the 20 of their papers we have counts for
9 papers · 1 filter
Path Laplacian Encodings for Directed Graphs
Lydia Mezrag, Semih Cantürk, Michael Perlmutter +2
Directed graphs naturally model many real-world systems in which interactions are asymmetric, such as citation networks, web graphs, and information-flow networks. However, graph l…
Encoding the Euler Characteristic Transform
Nello Blaser, Odin Hoff Gardaa, Lars M. Salbu +2
The Euler Characteristic Curve (ECC) records the Euler characteristic of a linearly embedded cell complex as a function of filtration height in a given direction, and the Euler Cha…
A Centrality Measure Using Magnitude Homology
Nadja Häusermann, Bastian Rieck
The magnitude of a metric space constitutes an expressive invariant that subsumes numerous different geometrical-topological invariants. Building on recent advances in magnitude ho…
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,…
Have Graph -- Will Lift? The Case for Higher-Order Benchmarks
Bastian Rieck
After a somewhat rocky start, geometry and topology have established a foothold in machine learning. Message passing, either on graphs or higher-order complexes, is one of the main…
No Triangulation Without Representation: Generalization in Topological Deep Learning
Johannes S. Schmidt, Martin Carrasco, Ernst Röell +3
Despite an ever-increasing interest in topological deep learning models that target higher-order datasets, there is no consensus on how to evaluate such models. This is exacerbated…
Diversity Curves for Graph Representation Learning
Katharina Limbeck, Nadja Häusermann, Martin Carrasco +2
Graph-level representations are crucial tools for characterising structural differences between graphs. However, comparing graphs with different cardinalities, even when sampled fr…
Measuring Structure in Graph Benchmark Datasets Using Graph Invariants
Richard von Moos, Mathieu Alain, Bastian Rieck
Progress in graph learning is hindered by benchmark practices that conflate the contributions of node features and graph structure, making it hard to tell whether a model actually…
Geometry-Aware Simplicial Message Passing
Elena Xinyi Wang, Bastian Rieck
The Weisfeiler--Lehman (WL) test and its simplicial extension (SWL) characterize the combinatorial expressivity of message passing networks, but they are blind to geometry, i.e., m…