mlsanityData to 14 Oct 2026

Topological Data Analysis for Neural Network Analysis: A Comprehensive Survey

arXiv 2312.05840 ↗First posted 10 Dec 2023cs.LG math.ATcited by 9

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Abstract (arXiv)

This survey provides a comprehensive exploration of applications of Topological Data Analysis (TDA) within neural network analysis. Using TDA tools such as persistent homology and Mapper, we delve into the intricate structures and behaviors of neural networks and their datasets. We discuss different strategies to obtain topological information from data and neural networks by means of TDA. Additionally, we review how topological information can be leveraged to analyze properties of neural networks, such as their generalization capacity or expressivity. We explore practical implications of deep learning, specifically focusing on areas like adversarial detection and model selection. Our survey organizes the examined works into four broad domains: 1. Characterization of neural network architectures; 2. Analysis of decision regions and boundaries; 3. Study of internal representations, activations, and parameters; 4. Exploration of training dynamics and loss functions. Within each category, we discuss several articles, offering background information to aid in understanding the various methodologies. We conclude with a synthesis of key insights gained from our study, accompanied by a discussion of challenges and potential advancements in the field.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 14 of its 148 references that are in the map. First posted on arXiv 10 Dec 2023.

Builds on

14 of 148 references.

References · 14

  1. 2014Explaining and Harnessing Adversarial Examplescited by 7,364
  2. 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,349
  3. 2013Auto-Encoding Variational Bayescited by 4,053
  4. 2015Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networkscited by 2,054
  5. 2018Towards a Definition of Disentangled Representationscited by 296
  6. 2020NAS-Bench-NLP: Neural Architecture Search Benchmark for Natural Language Processingcited by 60
  7. 2023Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networkscited by 43
  8. 2020NeurIPS 2020 Competition: Predicting Generalization in Deep Learningcited by 41
  9. 2022Algorithmic Determination of the Combinatorial Structure of the Linear Regions of ReLU Neural Networkscited by 22
  10. 2023On the Expressivity of Persistent Homology in Graph Learningcited by 19
  11. 2022An Introduction to Multiparameter Persistencecited by 16
  12. 2023Metric Space Magnitude and Generalisation in Neural Networkscited by 15
2 more
  1. 2022Predicting the generalization gap in neural networks using topological data analysiscited by 9
  2. 2023Disentanglement Learning via Topologycited by 4

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 1; 2026: 7.

9 papers.

  1. 2024TOAST: Transformer Optimization using Adaptive and Simple Transformationscited by 3
  2. 2026Topological Signatures of Grokkingcited by 2
  3. 2025Topology of Out-of-Distribution Examples in Deep Neural Networkscited by 1
  4. 2026Topology-Aware Layer Pruning for Large Vision-Language Modelscited by 0
  5. 2026Topology-Enhanced Alignment for Large Language Models: Trajectory Topology Loss and Topological Preference Optimizationcited by 0
  6. 2026How fine a change can moments see? A scale law for detecting distribution shift, with a kernel calibration rulecited by 0
  7. 2026Measuring Memory and Generalization as Separable Geometric Channels: The Topo^2 Frameworkcited by 0
  8. 2026Skeletal Prototypes on Iterative Nerve Expansionscited by 0
  9. 2026Looking Inside LLMs: Small-World Connectivity as a Signature of Reasoning Performancecited by 0