mlsanityData to 7 Oct 2026

Characterizing and Measuring the Similarity of Neural Networks with Persistent Homology

arXiv 2101.07752 ↗First posted 19 Jan 2021cs.LG math.ATcited by 8

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Abstract (arXiv)

Characterizing the structural properties of neural networks is crucial yet poorly understood, and there are no well-established similarity measures between networks. In this work, we observe that neural networks can be represented as abstract simplicial complex and analyzed using their topological 'fingerprints' via Persistent Homology (PH). We then describe a PH-based representation proposed for characterizing and measuring similarity of neural networks. We empirically show the effectiveness of this representation as a descriptor of different architectures in several datasets. This approach based on Topological Data Analysis is a step towards better understanding neural networks and serves as a useful similarity measure.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 22 of its 37 references that are in the map. First posted on arXiv 19 Jan 2021.

Builds on

22 of 37 references.

References · 22

  1. 2017Attention Is All You Needcited by 59,932
  2. 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,283
  3. 2019Similarity of Neural Network Representations Revisitedcited by 1,695
  4. 2015Persistence Images: A Stable Vector Representation of Persistent Homologycited by 235
  5. 2019A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homologycited by 134
  6. 2019Ripser: efficient computation of Vietoris-Rips persistence barcodescited by 115
  7. 2020Topology of deep neural networkscited by 111
  8. 2018Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topologycited by 73
  9. 2020giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Explorationcited by 55
  10. 2020Computing the Testing Error without a Testing Setcited by 54
  11. 2018On Characterizing the Capacity of Neural Networks using Algebraic Topologycited by 37
  12. 2019Persistence Homology of Networks: Methods and Applicationscited by 30
10 more
  1. 2020GPU-Accelerated Computation of Vietoris-Rips Persistence Barcodescited by 26
  2. 2018Functional Summaries of Persistence Diagramscited by 19
  3. 2018Topological Data Analysis of Decision Boundaries with Application to Model Selectioncited by 19
  4. 2019Impact of Fully Connected Layers on Performance of Convolutional Neural Networks for Image Classificationcited by 19
  5. 2019Topological Machine Learning with Persistence Indicator Functionscited by 11
  6. 2019Path homologies of deep feedforward networkscited by 6
  7. 2019Computing persistent homology of directed flag complexescited by 4
  8. 2019An empirical study of the relation between network architecture and complexitycited by 4
  9. 2019Capacity allocation analysis of neural networks: A tool for principled architecture designcited by 1
  10. 2020Some Geometrical and Topological Properties of DNNs' Decision Boundariescited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 0; 2023: 2; 2024: 1; 2025: 1; 2026: 2.

8 papers.

  1. 2023Generalization Bounds with Data-dependent Fractal Dimensionscited by 15
  2. 2021Persistent Homology Captures the Generalization of Neural Networks Without A Validation Setcited by 4
  3. 2023Estimating class separability of text embeddings with persistent homologycited by 1
  4. 2021Leveraging The Topological Consistencies of Learning in Deep Neural Networkscited by 0
  5. 2024Characterization of topological structures in different neural network architecturescited by 0
  6. 2025Persistent Topological Structures and Cohomological Flows as a Mathematical Framework for Brain-Inspired Representation Learningcited by 0
  7. 2026From Layers to Networks: Comparing Neural Representations via Diffusion Geometrycited by 0
  8. 2026TopoTuner: Topological Finetuning of Large Language Modelscited by 0