mlsanityData to 14 Oct 2026

Topological Data Analysis of Decision Boundaries with Application to Model Selection

arXiv 1805.09949 ↗First posted 25 May 2018stat.ML cs.LGcited by 19

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Abstract (arXiv)

We propose the labeled vCech complex, the plain labeled Vietoris-Rips complex, and the locally scaled labeled Vietoris-Rips complex to perform persistent homology inference of decision boundaries in classification tasks. We provide theoretical conditions and analysis for recovering the homology of a decision boundary from samples. Our main objective is quantification of deep neural network complexity to enable matching of datasets to pre-trained models; we report results for experiments using MNIST, FashionMNIST, and CIFAR10.

Key facts. Cited by 19 papers in the map (data through 14 Oct 2026). First posted on arXiv 25 May 2018.

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Citing papers per year: 2021: 4; 2022: 5; 2023: 3; 2024: 3; 2025: 0; 2026: 4.

19 papers.

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  1. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 66
  2. 2021Topological Detection of Trojaned Neural Networkscited by 34
  3. 2021Topological Uncertainty: Monitoring trained neural networks through persistence of activation graphscited by 20
  4. 2022Topology and geometry of data manifold in deep learningcited by 12
  5. 2022Predicting the generalization gap in neural networks using topological data analysiscited by 9
  6. 2021Characterizing and Measuring the Similarity of Neural Networks with Persistent Homologycited by 8
  7. 2022HardVis: Visual Analytics to Handle Instance Hardness Using Undersampling and Oversampling Techniquescited by 5
  8. 2023Deep neural networks architectures from the perspective of manifold learningcited by 5
  9. 2023Unveiling the Hessian's Connection to the Decision Boundarycited by 5
  10. 2021Topology Applied to Machine Learning: From Global to Localcited by 4
  11. 2022Zeroth-Order Topological Insights into Iterative Magnitude Pruningcited by 2
  12. 2022Do Neural Networks Trained with Topological Features Learn Different Internal Representations?cited by 2
7 more
  1. 2024A Theoretical Study of Neural Network Expressive Power via Manifold Topologycited by 2
  2. 2023Addressing caveats of neural persistence with deep graph persistencecited by 1
  3. 2026Certified Topological Interaction in Neural Representations: Exact Tests and the Statistic They Requirecited by 1
  4. 2024Concept Boundary Vectorscited by 0
  5. 2026Understanding the geometry of deep learning with decision boundary volumecited by 0
  6. 2026Empirical Evidence for Simply Connected Decision Regions in Image Classifierscited by 0
  7. 2026Learning Transfers: Kan Extensions of Topological Invariants of Learned Representationscited by 0