1 citations · 1 across the 5 of their papers we have counts for
6 papers
Learning Coherent Representations: A Topological Approach to Interpretability
Sigurd Gaukstad, Melvin Vaupel, Valdemar Kargård Olsen +2
Deep neural networks learn representations where individual features often lack interpretable meaning; a single neuron may activate for scattered, unrelated inputs. We introduce co…
Dowker's theorem for higher-order relations
Vin de Silva, Chad Giusti, Vladimir Itskov +5
Given a relation between two sets, Dowker's Theorem (1952) states that the homology groups of two associated simplicial complexes, now known as Dowker comp…
The bifiltration of a relation and extended Dowker duality
Melvin Vaupel, Benjamin Dunn
We explain how homotopical information of two composeable relations can be organized in two simplicial categories that augment the relations row and column complexes. We show that…
ICLR 2022 Challenge for Computational Geometry and Topology: Design and Results
Adele Myers, Saiteja Utpala, Shubham Talbar +25
This paper presents the computational challenge on differential geometry and topology that was hosted within the ICLR 2022 workshop ``Geometric and Topological Representation Learn…
Reeb complexes and topological persistence
Melvin Vaupel, Erik Hermansen, Paul Trygsland
We introduce Reeb complexes in order to capture how generators of homology flow along sections of a real valued continuous function. This intuition suggests a close relation of Ree…
Section complexes of simplicial height functions
Melvin Vaupel, Erik Hermansen, Paul Trygsland
A theory of sections of simplicial height functions is developed. At the core of this theory lies the section complex, which is assembled from higher section spaces. The latter enc…