Cup and Cap Topological Neural Network
Abstract
Topological Deep Learning (TDL) is designed to learn features associated with higher-dimensional simplices including not only nodes but also edges, triangles and so on. 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, revealing its competitiveness with respect to other simplicial complex neural networks.
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BibTeX
@misc{niedostatek2026topological,
title = {{Cup and Cap Topological Neural Network}},
author = {Marta Niedostatek and Ferran Hernandez Caralt and Runyue Wang and Federica Baccini and Lorenzo Giambagli and Pietro Lió and Ginestra Bianconi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03169},
eprint = {2610.03169},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03169},
}
RIS
TY - UNPB
TI - Cup and Cap Topological Neural Network
AU - Marta Niedostatek
AU - Ferran Hernandez Caralt
AU - Runyue Wang
AU - Federica Baccini
AU - Lorenzo Giambagli
AU - Pietro Lió
AU - Ginestra Bianconi
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03169
UR - https://arxiv.org/abs/2610.03169
AB - Topological Deep Learning (TDL) is designed to learn features associated with higher-dimensional simplices including not only nodes but also edges, triangles and so on. 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, revealing its competitiveness with respect to other simplicial complex neural networks.
ER -