Topological Data Analysis for Neural Networks
暫譯: 神經網絡的拓撲數據分析

Ballester, Rubén, Casacuberta, Carles, Escalera, Sergio

Topological Data Analysis for Neural Networks
  • 出版商: Springer
  • 出版日期: 2026-01-03
  • 售價: $2,470
  • 貴賓價: 9.5 折 $2,347
  • 語言: 英文
  • 頁數: 103
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 303208282X
  • ISBN-13: 9783032082824
  • 相關分類: DeepLearning

    • 海外代購書籍(需單獨結帳)

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商品描述

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.

商品描述(中文翻譯)

本書全面介紹了拓撲數據分析方法在神經網絡結構和動態研究中的應用。作者使用基於拓撲的工具，如持續同調（persistent homology）和Mapper算法，探討全連接前饋神經網絡和卷積神經網絡的複雜結構和行為。

作者討論了從數據和神經網絡中提取拓撲信息的各種策略，綜合了超過40篇研究文章的見解和結果，包括他們自己對完整神經網絡圖中激活的研究貢獻。此外，他們還研究了如何利用這些拓撲信息來分析神經網絡的特性，例如其泛化能力或表達能力。書中還討論了在深度學習中使用拓撲數據分析的實際應用，重點關注對抗檢測和模型選擇等領域。作者最後總結了關鍵見解，並討論了該領域當前的挑戰和未來的潛在發展。

這本專著非常適合具有拓撲背景的數學家，對拓撲數據分析在人工智慧中的應用感興趣，以及希望探索拓撲工具在深度學習中實際應用的計算機科學家。

作者簡介

Rubén Ballester is a PhD student in Topological Machine Learning at the Department of Mathematics and Computer Science of the University of Barcelona (UB). He received his bachelor's degrees in Mathematics and Computer Science from UB in 2021 and completed the Advanced Mathematics and Mathematical Engineering MSc at Universitat Politècnica de Catalunya (UPC) in 2022, achieving the highest master's degree GPA recognition. He has published articles on the connection between generalizations of neural networks and persistent homology and on the design of neural networks for topological domains. He won the Topological Deep Learning Challenge in the modality of combinatorial complexes, organized within the 2nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning at ICML 2023. In addition, he has actively contributed to the TopoX software suite for topological neural networks.

Carles Casacuberta is Full Professor of Geometry and Topology at the University of Barcelona (UB) since 2001. He earned his doctoral degree in 1988, specializing in algebraic topology. He has edited ten books and authored 55 research articles in areas such as homotopy theory, category theory, homological algebra, and more recently, topological data analysis. He serves on the editorial board of the Springer Universitext series and two research journals. Currently, he coordinates the Topological Machine Learning Seminar at UB and participates in several Horizon Europe projects focused on applications of artificial intelligence in biomedicine.

Sergio Escalera is Full Professor at the Department of Mathematics and Computer Science of the University of Barcelona. He is action editor of the Journal of Data-centric Machine Learning Research and IEEE Transactions on Pattern Analysis and Machine Intelligence. He is vice-president of ChaLearn Challenges in Machine Learning, leading ChaLearn Looking at People events. He is co-creator of the Codalab open source platform for challenge organization and co-founder of the NeurIPS competition and Datasets and Benchmarks tracks. He has published more than 400 research papers and participated in the organization of scientific events. His research interests include machine learning fundamentals, and inclusive and transparent analysis of humans from visual and multi-modal data by means of deep learning mechanisms.

作者簡介(中文翻譯)

Rubén Ballester 是巴塞隆納大學 (University of Barcelona, UB) 數學與計算機科學系的拓撲機器學習博士生。他於2021年獲得UB的數學和計算機科學學士學位，並於2022年在加泰羅尼亞理工大學 (Universitat Politècnica de Catalunya, UPC) 完成高級數學與數學工程碩士學位，並獲得最高碩士學位GPA的認可。他發表了有關神經網絡的廣義與持續同調之間聯繫的文章，以及針對拓撲領域的神經網絡設計的研究。他在2023年ICML的第二屆機器學習拓撲、代數與幾何年會中，贏得了拓撲深度學習挑戰賽的組合複合體類別。此外，他還積極參與拓撲神經網絡的TopoX軟體套件的貢獻。

Carles Casacuberta 自2001年以來擔任巴塞隆納大學 (UB) 幾何與拓撲的全職教授。他於1988年獲得博士學位，專攻代數拓撲。他編輯了十本書籍，並在同倫論、範疇論、同調代數等領域發表了55篇研究文章，最近則專注於拓撲數據分析。他擔任Springer Universitext系列和兩本研究期刊的編輯委員會成員。目前，他協調UB的拓撲機器學習研討會，並參與多個聚焦於人工智慧在生物醫學應用的Horizon Europe項目。

Sergio Escalera 是巴塞隆納大學數學與計算機科學系的全職教授。他是《數據中心機器學習研究期刊》(Journal of Data-centric Machine Learning Research) 和《IEEE模式分析與機器智慧期刊》(IEEE Transactions on Pattern Analysis and Machine Intelligence) 的行動編輯。他是ChaLearn機器學習挑戰的副總裁，負責領導ChaLearn Looking at People活動。他是Codalab開源平台的共同創建者，該平台用於挑戰組織，並且是NeurIPS競賽及數據集和基準追蹤的共同創辦人。他發表了超過400篇研究論文，並參與了科學活動的組織。他的研究興趣包括機器學習基礎，以及通過深度學習機制對視覺和多模態數據中的人類進行包容性和透明的分析。

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