6 citations · 9 across the 20 of their papers we have counts for
23 papers
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…
Graph Homomorphism Distortion: A structural (pseudo)-metric for attributed graphs
Martin Carrasco, Olga Zaghen, Kavir Sumaraj +2
A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing appr…
EmbedOR: Provable Cluster-Preserving Visualizations with Curvature-Based Stochastic Neighbor Embeddings
Tristan Luca Saidi, Abigail Hickok, Bastian Rieck +1
Stochastic Neighbor Embedding (SNE) algorithms like UMAP and tSNE often produce visualizations that do not preserve the geometry of noisy and high dimensional data. In particular,…
Low-dimensional embeddings of high-dimensional data
Cyril de Bodt, Alex Diaz-Papkovich, Michael Bleher +18
Large collections of high-dimensional data have become nearly ubiquitous across many academic fields and application domains, ranging from biology to the humanities. Since working…
Geometry-Aware Edge Pooling for Graph Neural Networks
Katharina Limbeck, Lydia Mezrag, Guy Wolf +1
Graph Neural Networks (GNNs) have shown significant success for graph-based tasks. Motivated by the prevalence of large datasets in real-world applications, pooling layers are cruc…
No Metric to Rule Them All: Toward Principled Evaluations of Graph-Learning Datasets
Corinna Coupette, Jeremy Wayland, Emily Simons +1
Benchmark datasets have proved pivotal to the success of graph learning, and good benchmark datasets are crucial to guide the development of the field. Recent research has highligh…
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…
Detecting Spatial Dependence in Transcriptomics Data using Vectorised Persistence Diagrams
Katharina Limbeck, Bastian Rieck
Evaluating spatial patterns in data is an integral task across various domains, including geostatistics, astronomy, and spatial tissue biology. The analysis of transcriptomics data…
Characterizing Physician Referral Networks with Ricci Curvature
Jeremy Wayland, Russel J. Funk, Bastian Rieck
Identifying (a) systemic barriers to quality healthcare access and (b) key indicators of care efficacy in the United States remains a significant challenge. To improve our understa…
Position: Topological Deep Learning is the New Frontier for Relational Learning
Theodore Papamarkou, Tolga Birdal, Michael Bronstein +19
Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models. This paper posits that TDL is the new fron…
Mapping the Multiverse of Latent Representations
Jeremy Wayland, Corinna Coupette, Bastian Rieck
Echoing recent calls to counter reliability and robustness concerns in machine learning via multiverse analysis, we present PRESTO, a principled framework for mapping the multivers…
Simplicial Representation Learning with Neural -Forms
Kelly Maggs, Celia Hacker, Bastian Rieck
Geometric deep learning extends deep learning to incorporate information about the geometry and topology data, especially in complex domains like graphs. Despite the popularity of…
Metric Space Magnitude for Evaluating the Diversity of Latent Representations
Katharina Limbeck, Rayna Andreeva, Rik Sarkar +1
The magnitude of a metric space is a novel invariant that provides a measure of the 'effective size' of a space across multiple scales, while also capturing numerous geometrical pr…
Topological Inductive Bias fosters Multiple Instance Learning in Data-Scarce Scenarios
Salome Kazeminia, Carsten Marr, Bastian Rieck
Multiple instance learning (MIL) is a framework for weakly supervised classification, where labels are assigned to sets of instances, i.e., bags, rather than to individual data poi…
Basic Analysis of Bin-Packing Heuristics
Bastian Rieck
The bin-packing problem continues to remain relevant in numerous application areas. This technical report discusses the empirical performance of different bin-packing heuristics fo…