mlsanityData to 7 Oct 2026

Topological Deep Learning: Classification Neural Networks

arXiv 2102.08354 ↗First posted 16 Feb 2021cs.LG math.AT stat.MLcited by 5

Not on the map. Why?

Abstract (arXiv)

Topological deep learning is a formalism that is aimed at introducing topological language to deep learning for the purpose of utilizing the minimal mathematical structures to formalize problems that arise in a generic deep learning problem. This is the first of a sequence of articles with the purpose of introducing and studying this formalism. In this article, we define and study the classification problem in machine learning in a topological setting. Using this topological framework, we show when the classification problem is possible or not possible in the context of neural networks. Finally, we demonstrate how our topological setting immediately illuminates aspects of this problem that are not as readily apparent using traditional tools.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 14 of its 35 references that are in the map. First posted on arXiv 16 Feb 2021.

Builds on

14 of 35 references.

References · 14

  1. 2016Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localizationcited by 6,690
  2. 2013Visualizing and Understanding Convolutional Networkscited by 2,278
  3. 2015Understanding Neural Networks Through Deep Visualizationcited by 332
  4. 2017The Expressive Power of Neural Networks: A View from the Widthcited by 318
  5. 2017Approximating Continuous Functions by ReLU Nets of Minimal Widthcited by 120
  6. 2017Deep Learning with Topological Signaturescited by 113
  7. 2020Topology of deep neural networkscited by 111
  8. 2019A Topology Layer for Machine Learningcited by 79
  9. 2018Geometric Understanding of Deep Learningcited by 41
  10. 2018Deep, Skinny Neural Networks are not Universal Approximatorscited by 37
  11. 2018Neural Networks Should Be Wide Enough to Learn Disconnected Decision Regionscited by 17
  12. 2016What can topology tell us about the neural code?cited by 6
2 more
  1. 2020A Topological Framework for Deep Learningcited by 5
  2. 2017Using Contour Trees in the Analysis and Visualization of Radio Astronomy Data Cubescited by 4

Built on by

Cited by year

Citing papers per year: 2023: 2; 2024: 3.

5 papers.

  1. 2024Demystifying Higher-Order Graph Neural Networkscited by 4
  2. 2024ICML Topological Deep Learning Challenge 2024: Beyond the Graph Domaincited by 3
  3. 2024Defining Neural Network Architecture through Polytope Structures of Datasetcited by 2
  4. 2023Estimating class separability of text embeddings with persistent homologycited by 1
  5. 2023Data Topology-Dependent Upper Bounds of Neural Network Widthscited by 1