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This work introduces TopoBench, an open-source library designed to standardize benchmarking and accelerate research in topological deep learning (TDL). TopoBench decomposes TDL into a sequence of independent modules for data generation, loading, transforming and processing, as well as model training, optimization and evaluation. This modular organization provides flexibility for modifications and facilitates the adaptation and optimization of various TDL pipelines. A key feature of TopoBench is its support for transformations and lifting across topological domains. Mapping the topology and features of a graph to higher-order topological domains, such as simplicial and cell complexes, enables richer data representations and more fine-grained analyses. The applicability of TopoBench is demonstrated by benchmarking several TDL architectures across diverse tasks and datasets. 

Networks provide a powerful formalism for modeling complex sys- tems, by representing the underlying set of pairwise interactions. But much of the structure within these systems involves interac- tions that take place among more than two nodes at once — for example, communication within a group rather than person-to- person, collaboration among a team rather than a pair of co-authors, or biological interaction between a set of molecules rather than just two. We refer to these type of simultaneous interactions on sets of more than two nodes as higher-order interactions; they are ubiquitous, but the empirical study of them has lacked a general framework for evaluating higher-order models. Here we introduce such a framework, based on link prediction, a fundamental prob- lem in network analysis. The traditional link prediction problem seeks to predict the appearance of new links in a network, and here we adapt it to predict which (larger) sets of elements will have fu- ture interactions. We study the temporal evolution of 19 datasets from a variety of domains, and use our higher-order formulation of link prediction to assess the types of structural features that are most predictive of new multi-way interactions. Among our results, we find that different domains vary considerably in their distri- bution of higher-order structural parameters, and that the higher- order link prediction problem exhibits some fundamental differ- ences from traditional pairwise link prediction, with a greater role for local rather than long-range information in predicting the ap- pearance of new interactions.