mlsanityData to 7 Oct 2026

Persistent Homology and the Upper Box Dimension

arXiv 1802.00533 ↗First posted 2 Feb 2018math.MG cs.CG math.ATcited by 15

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Abstract (arXiv)

We introduce a fractal dimension for a metric space defined in terms of the persistent homology of extremal subsets of that space. We exhibit hypotheses under which this dimension is comparable to the upper box dimension; in particular, the dimensions coincide for subsets of ℝ2 whose upper box dimension exceeds 1.5. These results are related to extremal questions about the number of persistent homology intervals of a set of n points in a metric space.

Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). First posted on arXiv 2 Feb 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 2; 2023: 4; 2024: 1; 2025: 4; 2026: 2.

15 papers.

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  1. 2023Intrinsic Dimension Estimation for Robust Detection of AI-Generated Textscited by 111
  2. 2021Intrinsic Dimension, Persistent Homology and Generalization in Neural Networkscited by 70
  3. 2023The Shape of Learning: Anisotropy and Intrinsic Dimensions in Transformer-Based Modelscited by 37
  4. 2023Generalization Bounds with Data-dependent Fractal Dimensionscited by 15
  5. 2023Metric Space Magnitude and Generalisation in Neural Networkscited by 15
  6. 2022Predicting the generalization gap in neural networks using topological data analysiscited by 9
  7. 2024On the Limitations of Fractal Dimension as a Measure of Generalizationcited by 5
  8. 2021Topology Applied to Machine Learning: From Global to Localcited by 4
  9. 2025Memorization in Language Models through the Lens of Intrinsic Dimensioncited by 3
  10. 2025T-REGS: Minimum Spanning Tree Regularization for Self-Supervised Learningcited by 2
  11. 2025When Personalization Tricks Detectors: The Feature-Inversion Trap in Machine-Generated Text Detectioncited by 1
  12. 2025Unveiling Intrinsic Dimension of Texts: from Academic Abstract to Creative Storycited by 1
3 more
  1. 2022On topological data analysis for structural dynamics: an introduction to persistent homologycited by 0
  2. 2026What Makes a Good Layer? Assessing the Layer-Wise Intrinsic Properties of Music Foundation Modelscited by 0
  3. 2026Linear Probing Provides Robust and Efficient Detection of Machine-Generated Textcited by 0