Overview
- Provides new geometric foundations of inference in machine learning based on statistical physics
- Deepens mathematical physics models with new insights from statistical machine learning
- Combines numerical schemes from geometric integrators in physics with intrinsic machine learning inference
Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 361)
Included in the following conference series:
Conference proceedings info: SPIGL 2020.
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About this book
Machine learning and artificial intelligence increasingly use methodological tools rooted in statistical physics. Conversely, limitations and pitfalls encountered in AI question the very foundations of statistical physics. This interplay between AI and statistical physics has been attested since the birth of AI, and principles underpinning statistical physics can shed new light on the conceptual basis of AI. During the last fifty years, statistical physics has been investigated through new geometric structures allowing covariant formalization of the thermodynamics. Inference methods in machine learning have begun to adapt these new geometric structures to process data in more abstract representation spaces.
This volume collects selected contributions on the interplay of statistical physics and artificial intelligence. The aim is to provide a constructive dialogue around a common foundation to allow the establishment of new principles and laws governing these two disciplines in a unified manner. The contributions were presented at the workshop on the Joint Structures and Common Foundation of Statistical Physics, Information Geometry and Inference for Learning which was held in Les Houches in July 2020. The various theoretical approaches are discussed in the context of potential applications in cognitive systems, machine learning, signal processing.
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Table of contents (21 papers)
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Front Matter
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Part I: Tribute to Jean-Marie Souriau Seminal Works
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Front Matter
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Part II: Lie Group Geometry and Diffeological Model of Statistical Physics and Information Geometry
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Front Matter
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Part III: Advanced Geometrical Models of Statistical Manifolds in Information Geometry
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Front Matter
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Part IV: Geometric Structures of Mechanics, Thermodynamics and Inference for Learning
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Front Matter
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Other volumes
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Geometric Structures of Statistical Physics, Information Geometry, and Learning
Editors and Affiliations
Bibliographic Information
Book Title: Geometric Structures of Statistical Physics, Information Geometry, and Learning
Book Subtitle: SPIGL'20, Les Houches, France, July 27–31
Editors: Frédéric Barbaresco, Frank Nielsen
Series Title: Springer Proceedings in Mathematics & Statistics
DOI: https://doi.org/10.1007/978-3-030-77957-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-77956-6Published: 27 June 2021
Softcover ISBN: 978-3-030-77959-7Published: 28 June 2022
eBook ISBN: 978-3-030-77957-3Published: 27 June 2021
Series ISSN: 2194-1009
Series E-ISSN: 2194-1017
Edition Number: 1
Number of Pages: XIII, 459
Number of Illustrations: 24 b/w illustrations, 63 illustrations in colour
Topics: Mathematical Applications in Computer Science, Artificial Intelligence, Theoretical, Mathematical and Computational Physics, Statistical Theory and Methods