Audun Myers

Mathilde Papillon, Mustafa Hajij, Helen Jenne et al.

This paper presents the computational challenge on topological deep learning that was hosted within the ICML 2023 Workshop on Topology and Geometry in Machine Learning. The competition asked participants to provide open-source implementations of topological neural networks from the literature by contributing to the python packages TopoNetX (data processing) and TopoModelX (deep learning). The challenge attracted twenty-eight qualifying submissions in its two-month duration. This paper describes the design of the challenge and summarizes its main findings.

Audun Myers, Firas A. Khasawneh, Elizabeth Munch

One of the most important problems arising in time series analysis is that of bifurcation, or change point detection. That is, given a collection of time series over a varying parameter, when has the structure of the underlying dynamical system changed? For this task, we turn to the field of topological data analysis (TDA), which encodes information about the shape and structure of data. The idea of utilizing tools from TDA for signal processing tasks, known as topological signal processing (TSP), has gained much attention in recent years, largely through a standard pipeline that computes the persistent homology of the point cloud generated by the Takens' embedding. However, this procedure is limited by computation time since the simplicial complex generated in this case is large, but also has a great deal of redundant data. For this reason, we turn to a more recent method for encoding the structure of the attractor, which constructs an ordinal partition network (OPN) representing information about when the dynamical system has passed between certain regions of state space. The result is a weighted graph whose structure encodes information about the underlying attractor. Our previous work began to find ways to package the information of the OPN in a manner that is amenable to TDA; however, that work only used the network structure and did nothing to encode the additional weighting information. In this paper, we take the next step: building a pipeline to analyze the weighted OPN with TDA and showing that this framework provides more resilience to noise or perturbations in the system and improves the accuracy of the dynamic state detection.

Guillermo Bernárdez, Lev Telyatnikov, Marco Montagna et al.

This paper describes the 2nd edition of the ICML Topological Deep Learning Challenge that was hosted within the ICML 2024 ELLIS Workshop on Geometry-grounded Representation Learning and Generative Modeling (GRaM). The challenge focused on the problem of representing data in different discrete topological domains in order to bridge the gap between Topological Deep Learning (TDL) and other types of structured datasets (e.g. point clouds, graphs). Specifically, participants were asked to design and implement topological liftings, i.e. mappings between different data structures and topological domains --like hypergraphs, or simplicial/cell/combinatorial complexes. The challenge received 52 submissions satisfying all the requirements. This paper introduces the main scope of the challenge, and summarizes the main results and findings.