LEADER 04225nam 22007335 450 001 9911049151203321 005 20260102120757.0 010 $a3-032-08283-8 024 7 $a10.1007/978-3-032-08283-1 035 $a(CKB)44769872700041 035 $a(MiAaPQ)EBC32470599 035 $a(Au-PeEL)EBL32470599 035 $a(DE-He213)978-3-032-08283-1 035 $a(EXLCZ)9944769872700041 100 $a20260102d2026 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTopological Data Analysis for Neural Networks /$fby Rubén Ballester, Carles Casacuberta, Sergio Escalera 205 $a1st ed. 2026. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2026. 215 $a1 online resource (180 pages) 225 1 $aSpringerBriefs in Computer Science,$x2191-5776 311 08$a3-032-08282-X 327 $aChapter 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. 330 $aThis book offers a comprehensive presentation of methods from topological data analysis applied to the study of neural network structure and dynamics. Using topology-based tools such as persistent homology and the Mapper algorithm, the authors explore the intricate structures and behaviors of fully connected feedforward and convolutional neural networks. The authors discuss various strategies for extracting topological information from data and neural networks, synthesizing insights and results from over 40 research articles, including their own contributions to the study of activations in complete neural network graphs. Furthermore, they examine how this topological information can be leveraged to analyze properties of neural networks such as their generalization capacity or expressivity. Practical implications of the use of topological data analysis in deep learning are also discussed, with a focus on areas including adversarial detection and model selection. The authors conclude with a summary of key insights along with a discussion of current challenges and potential future developments in the field. This monograph is ideally suited for mathematicians with a background in topology who are interested in the applications of topological data analysis in artificial intelligence, as well as for computer scientists seeking to explore the practical use of topological tools in deep learning. 410 0$aSpringerBriefs in Computer Science,$x2191-5776 606 $aMachine learning 606 $aArtificial intelligence 606 $aArtificial intelligence$xData processing 606 $aNeural networks (Computer science) 606 $aComputer science$xMathematics 606 $aTopology 606 $aMachine Learning 606 $aArtificial Intelligence 606 $aData Science 606 $aMathematical Models of Cognitive Processes and Neural Networks 606 $aMathematical Applications in Computer Science 606 $aTopology 615 0$aMachine learning. 615 0$aArtificial intelligence. 615 0$aArtificial intelligence$xData processing. 615 0$aNeural networks (Computer science) 615 0$aComputer science$xMathematics. 615 0$aTopology. 615 14$aMachine Learning. 615 24$aArtificial Intelligence. 615 24$aData Science. 615 24$aMathematical Models of Cognitive Processes and Neural Networks. 615 24$aMathematical Applications in Computer Science. 615 24$aTopology. 676 $a006.31 700 $aBallester$b Rubén$01886858 701 $aCasacuberta$b Carles$060354 701 $aEscalera$b Sergio$01886859 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911049151203321 996 $aTopological Data Analysis for Neural Networks$94522435 997 $aUNINA