mlsanityData to 7 Oct 2026

Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology

arXiv 1812.09764 ↗First posted 23 Dec 2018cs.LG math.AT stat.MLcited by 73

Not on the map. Why?

Abstract (arXiv)

While many approaches to make neural networks more fathomable have been proposed, they are restricted to interrogating the network with input data. Measures for characterizing and monitoring structural properties, however, have not been developed. In this work, we propose neural persistence, a complexity measure for neural network architectures based on topological data analysis on weighted stratified graphs. To demonstrate the usefulness of our approach, we show that neural persistence reflects best practices developed in the deep learning community such as dropout and batch normalization. Moreover, we derive a neural persistence-based stopping criterion that shortens the training process while achieving comparable accuracies as early stopping based on validation loss.

Key facts. Cited by 73 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 Dec 2018.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 13; 2022: 12; 2023: 15; 2024: 9; 2025: 7; 2026: 17.

73 papers.

Sort:

By area:

  1. 2021Intrinsic Dimension, Persistent Homology and Generalization in Neural Networkscited by 70
  2. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 65
  3. 2021Artificial Text Detection via Examining the Topology of Attention Mapscited by 49
  4. 2021Topological Detection of Trojaned Neural Networkscited by 34
  5. 2023Topological Deep Learning: A Review of an Emerging Paradigmcited by 34
  6. 2021Topological Uncertainty: Monitoring trained neural networks through persistence of activation graphscited by 20
  7. 2021Activation Landscapes as a Topological Summary of Neural Network Performancecited by 17
  8. 2021A survey on shape-constraint deep learning for medical image segmentationcited by 15
  9. 2023Generalization Bounds with Data-dependent Fractal Dimensionscited by 15
  10. 2023Metric Space Magnitude and Generalisation in Neural Networkscited by 15
  11. 2026Learning Global Hypothesis Space for Enhancing Synergistic Reasoning Chaincited by 15
  12. 2022Topology and geometry of data manifold in deep learningcited by 12
38 more
  1. 2024Persistent Topological Features in Large Language Modelscited by 11
  2. 2022Experimental Observations of the Topology of Convolutional Neural Network Activationscited by 10
  3. 2023ReLU Neural Networks, Polyhedral Decompositions, and Persistent Homologcited by 10
  4. 2021Topological Measurement of Deep Neural Networks Using Persistent Homologycited by 9
  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. 2022Approximating Persistent Homology for Large Datasetscited by 8
  8. 2023Selecting which Dense Retriever to use for Zero-Shot Searchcited by 7
  9. 2021Quantitative Performance Assessment of CNN Units via Topological Entropy Calculationcited by 6
  10. 2022BERTops: Studying BERT Representations under a Topological Lenscited by 5
  11. 2022FONDUE: an algorithm to find the optimal dimensionality of the latent representations of variational autoencoderscited by 5
  12. 2023Deep neural networks architectures from the perspective of manifold learningcited by 5
  13. 2023On Characterizing the Evolution of Embedding Space of Neural Networks using Algebraic Topologycited by 5
  14. 2024Mapping the Multiverse of Latent Representationscited by 5
  15. 2022Deep Architecture Connectivity Matters for Its Convergence: A Fine-Grained Analysiscited by 4
  16. 2022Internal Representations of Vision Models Through the Lens of Frames on Data Manifoldscited by 3
  17. 2023Singular value decomposition based matrix surgerycited by 3
  18. 2023Persistent Homology for High-dimensional Data Based on Spectral Methodscited by 3
  19. 2026Representation Geometry as a Diagnostic for Out-of-Distribution Robustnesscited by 3
  20. 2021A Multi-parameter Persistence Framework for Mathematical Morphologycited by 2
  21. 2021Neural Network Layer Algebra: A Framework to Measure Capacity and Compression in Deep Learningcited by 2
  22. 2022Functional Network: A Novel Framework for Interpretability of Deep Neural Networkscited by 2
  23. 2022Zeroth-Order Topological Insights into Iterative Magnitude Pruningcited by 2
  24. 2022Do Neural Networks Trained with Topological Features Learn Different Internal Representations?cited by 2
  25. 2023Understanding Sparse Neural Networks from their Topology via Multipartite Graph Representationscited by 2
  26. 2024Mixup Barcodes: Quantifying Geometric-Topological Interactions between Point Cloudscited by 2
  27. 2024A Theoretical Study of Neural Network Expressive Power via Manifold Topologycited by 2
  28. 2021Leveraging the Graph Structure of Neural Network Training Dynamicscited by 1
  29. 2022Betti numbers of attention graphs is all you really needcited by 1
  30. 2023Can Persistent Homology provide an efficient alternative for Evaluation of Knowledge Graph Completion Methods?cited by 1
  31. 2023Estimating class separability of text embeddings with persistent homologycited by 1
  32. 2023Addressing caveats of neural persistence with deep graph persistencecited by 1
  33. 2024Functional connectomes of neural networkscited by 1
  34. 2025Topology of Out-of-Distribution Examples in Deep Neural Networkscited by 1
  35. 2025Topology-Aware CLIP Few-Shot Learningcited by 1
  36. 2025Geometric Analysis of Neural Regression Collapse via Intrinsic Dimensioncited by 1
  37. 2025HOLE: Homological Observation of Latent Embeddings for Neural Network Interpretabilitycited by 1
  38. 2026A Persistent Homology Design Space for 3D Point Cloud Deep Learningcited by 1

50 most cited of 73 All 73 (JSON)