Work

Cup and Cap Topological Neural Network

Year: 2026

Type: preprint

Abstract: Topological Deep Learning (TDL) is designed to learn features associated not only with nodes but also with edges, triangles and higher dimensional simplices. However, most TDL approaches, being based on boundary operators and Hodge Laplacians, have the limitation that features and signals cannot be lifted or lowered across more than one dimension per layer. To overcome this limitation, in this work, we propose the adoption of the cup and cap products. Specifically, we formulate the Cup and Cap Topological Neural Network (CCNN), a topological deep learning architecture designed to learn node-based variables (or 0-cochains) by taking into account their many-body interactions (e.g. triangles) present in the data. We validate CCNN by assessing its performance on the TopoBench datasets, demonstrating its competitive performance with respect to other simplicial complex neural networks.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.03169

Authors: Niedostatek, Marta, Caralt, Ferran Hernandez, Wang, Runyue, Baccini, Federica, Giambagli, Lorenzo, Lió, Pietro, Bianconi, Ginestra

Institutions: Queen Mary University of London, University of Cambridge, Sapienza University of Rome, Freie Universität Berlin

Language: English

Topic: Topological and Geometric Data Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Queen Mary University of London, UK Research and Innovation, Biotechnology and Biological Sciences Research Council

OpenAlex ID: W7220436115

Cites: 9

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Related to: 10