04225nam 22007335 450 991104915120332120260102120757.03-032-08283-810.1007/978-3-032-08283-1(CKB)44769872700041(MiAaPQ)EBC32470599(Au-PeEL)EBL32470599(DE-He213)978-3-032-08283-1(EXLCZ)994476987270004120260102d2026 u| 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierTopological Data Analysis for Neural Networks /by Rubén Ballester, Carles Casacuberta, Sergio Escalera1st ed. 2026.Cham :Springer Nature Switzerland :Imprint: Springer,2026.1 online resource (180 pages)SpringerBriefs in Computer Science,2191-57763-032-08282-X Chapter 1. Introduction -- Part I Fundamentals -- Chapter 2. Deep Learning -- Chapter 3. Topological Data Analysis -- Part II Interactions -- Chapter 4. Challenges in Deep Learning -- Chapter 5. Input and Output Spaces -- Chapter 6. Internal Representations and Activations -- Chapter 7. Training Dynamics and Loss Functions -- Chapter 8. Challenges, Future Directions, and Conclusions.This book offers a comprehensive presentation of methods from topological data analysis applied to the study of neural network structure and dynamics. Using topology-based tools such as persistent homology and the Mapper algorithm, the authors explore the intricate structures and behaviors of fully connected feedforward and convolutional neural networks. The authors discuss various strategies for extracting topological information from data and neural networks, synthesizing insights and results from over 40 research articles, including their own contributions to the study of activations in complete neural network graphs. Furthermore, they examine how this topological information can be leveraged to analyze properties of neural networks such as their generalization capacity or expressivity. Practical implications of the use of topological data analysis in deep learning are also discussed, with a focus on areas including adversarial detection and model selection. The authors conclude with a summary of key insights along with a discussion of current challenges and potential future developments in the field. This monograph is ideally suited for mathematicians with a background in topology who are interested in the applications of topological data analysis in artificial intelligence, as well as for computer scientists seeking to explore the practical use of topological tools in deep learning.SpringerBriefs in Computer Science,2191-5776Machine learningArtificial intelligenceArtificial intelligenceData processingNeural networks (Computer science)Computer scienceMathematicsTopologyMachine LearningArtificial IntelligenceData ScienceMathematical Models of Cognitive Processes and Neural NetworksMathematical Applications in Computer ScienceTopologyMachine learning.Artificial intelligence.Artificial intelligenceData processing.Neural networks (Computer science)Computer scienceMathematics.Topology.Machine Learning.Artificial Intelligence.Data Science.Mathematical Models of Cognitive Processes and Neural Networks.Mathematical Applications in Computer Science.Topology.006.31Ballester Rubén1886858Casacuberta Carles60354Escalera Sergio1886859MiAaPQMiAaPQMiAaPQBOOK9911049151203321Topological Data Analysis for Neural Networks4522435UNINA