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This monograph presents a comprehensive account of methods from topological data analysis, such as persistent homology and Mapper graphs, applied to the study of neural network structure and dynamics. We describe various strategies for extracting topological information from data, and examine how such information can be used to analyze properties of neural networks, including their generalization capacity and expressivity. We also discuss practical implications of the usage of topological data analysis in deep learning applications, with a focus on adversarial detection and model selection. The monograph concludes with a discussion of current challenges and potential future developments in the field.

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Introduction

  • 章节

  • 发表日期：

    2026年

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  • Rubén Ballester,
  • Carles Casacuberta,
  • Sergio Escalera

摘要

This monograph presents a comprehensive account of methods from topological data analysis, such as persistent homology and Mapper graphs, applied to the study of neural network structure and dynamics. We describe various strategies for extracting topological information from data, and examine how such information can be used to analyze properties of neural networks, including their generalization capacity and expressivity. We also discuss practical implications of the usage of topological data analysis in deep learning applications, with a focus on adversarial detection and model selection. The monograph concludes with a discussion of current challenges and potential future developments in the field.