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Topological Approaches to Deep Learning

arXiv 1811.01122 ↗First posted 2 Nov 2018cs.LG cs.AI math.ATcited by 29

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Abstract (arXiv)

We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform. We apply this understanding to modify the computations so as to (a) speed up computations and (b) improve generalization from one data set of digits to another. One byproduct of the analysis is the production of a geometry on new sets of features on data sets of images, and use this observation to develop a methodology for constructing analogues of CNN's for many other geometries, including the graph structures constructed by topological data analysis.

Key facts. Cited by 29 papers in the map (data through 14 Oct 2026). First posted on arXiv 2 Nov 2018.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 8; 2022: 4; 2023: 7; 2024: 4; 2025: 4; 2026: 2.

29 papers.

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  1. 2021Z-GCNETs: Time Zigzags at Graph Convolutional Networks for Time Series Forecastingcited by 67
  2. 2023Topological Deep Learning: A Review of an Emerging Paradigmcited by 34
  3. 2021Topological Uncertainty: Monitoring trained neural networks through persistence of activation graphscited by 20
  4. 2021Activation Landscapes as a Topological Summary of Neural Network Performancecited by 18
  5. 2022Topology and geometry of data manifold in deep learningcited by 12
  6. 2024Tensor-view Topological Graph Neural Networkcited by 12
  7. 2022Predicting the generalization gap in neural networks using topological data analysiscited by 9
  8. 2021Topological Deep Learningcited by 6
  9. 2023Deep neural networks architectures from the perspective of manifold learningcited by 5
  10. 2022UGformer for Robust Left Atrium and Scar Segmentation Across Scannerscited by 3
  11. 2024Tensor-Fused Multi-View Graph Contrastive Learningcited by 3
  12. 2021Classification based on Topological Data Analysiscited by 2
17 more
  1. 2021Abstraction, Reasoning and Deep Learning: A Study of the "Look and Say" Sequencecited by 2
  2. 2022Zeroth-Order Topological Insights into Iterative Magnitude Pruningcited by 2
  3. 2023Topology Estimation of Simulated 4D Image Data by Combining Downscaling and Convolutional Neural Networkscited by 2
  4. 2023Spherical and Hyperbolic Toric Topology-Based Codes On Graph Embedding for Ising MRF Models: Classical and Quantum Topology Machine Learningcited by 1
  5. 2025TMetaNet: Topological Meta-Learning Framework for Dynamic Link Predictioncited by 1
  6. 2025Bayesian Topological Convolutional Neural Netscited by 1
  7. 2021From augmented microscopy to the topological transformer: a new approach in cell image analysis for Alzheimer's researchcited by 0
  8. 2021Leveraging The Topological Consistencies of Learning in Deep Neural Networkscited by 0
  9. 2023Decorrelating neurons using persistencecited by 0
  10. 2023Pool-Based Active Learning with Proper Topological Regionscited by 0
  11. 2023Topology-enhanced machine learning for speech signal processingcited by 0
  12. 2024Topology-Aware Exploration of Energy-Based Models Equilibrium: Toric QC-LDPC Codes and Hyperbolic MET QC-LDPC Codescited by 0
  13. 2024Towards an Algebraic Framework For Approximating Functions Using Neural Network Polynomialscited by 0
  14. 2025Topological Deep Learning for Speech Datacited by 0
  15. 2025Graph Lineages and Skeletal Graph Productscited by 0
  16. 2026Reparameterization through Coverings and Topological Weight Priorscited by 0
  17. 2026Graph Representation via Elements of Discrete Morse and Cobordism Theoriescited by 0