17 papers
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…
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…
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,…
TOAST: Transformer Optimization using Adaptive and Simple Transformations
Irene Cannistraci, Simone Antonelli, Emanuele Palumbo +4
Foundation models achieve state-of-the-art performance across different tasks, but their size and computational demands raise concerns about accessibility and sustainability. Exist…
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…