PreprintCC BY-SA 4.0arXiv
Deep Learning of Topological Equivalence Classes
Abstract
We demonstrate an application of deep learning to the problem of identifying whether two generating vectors correspond to topologically equivalent finite group actions on Riemann surfaces, showing how architectures developed for semantic understanding have use for pure mathematical problems. In doing so we discuss how desired algebraic structure influences model design, and explore which structural properties of topological equivalence classes the model has successfully learnt.
Related
- A cardinal trichotomy for topological equivalence classes of countable trees
- Toscani-Fourier Distance on Probability Measures: Wasserstein Control, Topological Equivalence on Model Classes, and Duality
- Orbital equivalence classes of finite coverings of geodesic flows
- Functorial equivalence classes of 2-blocks of tame representation type
- Maximal regular subsemigroups containing the group of units of transformation semigroups that preserve a uniform equivalence relation with two classes
BibTeX
@misc{disneyhogg2026deep,
title = {{Deep Learning of Topological Equivalence Classes}},
author = {Linden Disney-Hogg and Max Zuev},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21981},
eprint = {2610.21981},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21981},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Deep Learning of Topological Equivalence Classes
AU - Linden Disney-Hogg
AU - Max Zuev
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21981
UR - https://arxiv.org/abs/2610.21981
AB - We demonstrate an application of deep learning to the problem of identifying whether two generating vectors correspond to topologically equivalent finite group actions on Riemann surfaces, showing how architectures developed for semantic understanding have use for pure mathematical problems. In doing so we discuss how desired algebraic structure influences model design, and explore which structural properties of topological equivalence classes the model has successfully learnt.
ER -