Topological Deep Learning: A Review of an Emerging Paradigm

Fuente: arXiv
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Main Authors: Zia, Ali, Khamis, Abdelwahed, Nichols, James, Hayder, Zeeshan, Rolland, Vivien, Petersson, Lars
Format: Preprint
Published: 2023
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author Zia, Ali
Khamis, Abdelwahed
Nichols, James
Hayder, Zeeshan
Rolland, Vivien
Petersson, Lars
author_facet Zia, Ali
Khamis, Abdelwahed
Nichols, James
Hayder, Zeeshan
Rolland, Vivien
Petersson, Lars
contents Topological data analysis (TDA) provides insight into data shape. The summaries obtained by these methods are principled global descriptions of multi-dimensional data whilst exhibiting stable properties such as robustness to deformation and noise. Such properties are desirable in deep learning pipelines but they are typically obtained using non-TDA strategies. This is partly caused by the difficulty of combining TDA constructs (e.g. barcode and persistence diagrams) with current deep learning algorithms. Fortunately, we are now witnessing a growth of deep learning applications embracing topologically-guided components. In this survey, we review the nascent field of topological deep learning by first revisiting the core concepts of TDA. We then explore how the use of TDA techniques has evolved over time to support deep learning frameworks, and how they can be integrated into different aspects of deep learning. Furthermore, we touch on TDA usage for analyzing existing deep models; deep topological analytics. Finally, we discuss the challenges and future prospects of topological deep learning.
format Preprint
id arxiv_https___arxiv_org_abs_2302_03836
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Topological Deep Learning: A Review of an Emerging Paradigm
Zia, Ali
Khamis, Abdelwahed
Nichols, James
Hayder, Zeeshan
Rolland, Vivien
Petersson, Lars
Machine Learning
Artificial Intelligence
Topological data analysis (TDA) provides insight into data shape. The summaries obtained by these methods are principled global descriptions of multi-dimensional data whilst exhibiting stable properties such as robustness to deformation and noise. Such properties are desirable in deep learning pipelines but they are typically obtained using non-TDA strategies. This is partly caused by the difficulty of combining TDA constructs (e.g. barcode and persistence diagrams) with current deep learning algorithms. Fortunately, we are now witnessing a growth of deep learning applications embracing topologically-guided components. In this survey, we review the nascent field of topological deep learning by first revisiting the core concepts of TDA. We then explore how the use of TDA techniques has evolved over time to support deep learning frameworks, and how they can be integrated into different aspects of deep learning. Furthermore, we touch on TDA usage for analyzing existing deep models; deep topological analytics. Finally, we discuss the challenges and future prospects of topological deep learning.
title Topological Deep Learning: A Review of an Emerging Paradigm
topic Machine Learning
Artificial Intelligence
url https://arxiv.org/abs/2302.03836