Springer Proceedings in Mathematics & Statistics

Geometric Structures of Statistical Physics, Information Geometry, and Learning

SPIGL'20, Les Houches, France, July 27–31

Editors: Barbaresco, Frédéric, Nielsen, Frank (Eds.)

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  • 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
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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.

Table of contents (21 chapters)

Table of contents (21 chapters)
  • Structure des Systèmes Dynamiques Jean-Marie Souriau’s Book 50th Birthday

    Pages 3-11

    Saxcé, Géry (et al.)

  • Jean-Marie Souriau’s Symplectic Model of Statistical Physics: Seminal Papers on Lie Groups Thermodynamics - Quod Erat Demonstrandum

    Pages 12-50

    Barbaresco, Frédéric

  • Souriau-Casimir Lie Groups Thermodynamics and Machine Learning

    Pages 53-83

    Barbaresco, Frédéric

  • An Exponential Family on the Upper Half Plane and Its Conjugate Prior

    Pages 84-95

    Tojo, Koichi (et al.)

  • Wrapped Statistical Models on Manifolds: Motivations, The Case

    Pages 96-106

    Chevallier, Emmanuel (et al.)

Buy this book

eBook $169.00
price for USA in USD
  • ISBN 978-3-030-77957-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $219.99
price for USA in USD
  • ISBN 978-3-030-77956-6
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

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
Series Volume
361
Copyright
2021
Publisher
Springer International Publishing
Copyright Holder
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-77957-3
DOI
10.1007/978-3-030-77957-3
Hardcover ISBN
978-3-030-77956-6
Series ISSN
2194-1009
Edition Number
1
Number of Pages
XIII, 459
Number of Illustrations
24 b/w illustrations, 63 illustrations in colour
Topics