Geometric Structures of Statistical Physics, Information Geometry, and Learning

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

Häftad, Engelska, 2022

AvFrédéric Barbaresco,Frank Nielsen,Frederic Barbaresco

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Machine learning and artificial intelligence increasingly use methodological tools rooted in 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.

Produktinformation

Utgivningsdatum2022-06-28
Mått155 x 235 x 26 mm
Vikt715 g
FormatHäftad
SpråkEngelska
SerieSpringer Proceedings in Mathematics & Statistics
Antal sidor459
Upplaga22001
FörlagSpringer Nature Switzerland AG
ISBN9783030779597

Tillhör följande kategorier

Fysik inom Naturvetenskap och teknik
Matematisk statistik inom Naturvetenskap och teknik
Systemvetenskap och AI inom Data och IT
Artificiell intelligens inom Data och IT

PART 1: Tribute to Jean-Marie Souriau seminal works: G. de Saxcé and C.-M. Marle, Structure des Systèmes Dynamiques.- Jean-Marie Souriau’s book 50th birthday.- F. Barbaresco, Jean-Marie Souriau’s Symplectic Model of Statistical Physics : Seminal papers on Lie Groups Thermodynamics - Quod Erat Demonstrandum.- PART 2: Lie Group Geometry & Diffeological Model of Statistical Physics and Information Geometry: F. Barbaresco - Souriau-Casimir Lie Groups Thermodynamics & Machine Learning.- K. Tojo and T. Yoshino, An exponential family on the upper half plane and its conjugate prior.- E. Chevallier and N. Guigui, Wrapped statistical models on manifolds: motivations, the case SE(n), and generalization to symmetric spaces.- G. de Saxcé, Galilean Thermodynamics of Continua.- H. Vân Lê and A. Tuzhilin, Nonparametric estimations and the diffeological Fisher metric.- PART 3: Advanced Geometrical Models of Statistical Manifolds in Information Geometry: J.-P. Francoise, Information Geometry and Integrable Hamiltonian Systems.- M. N. Boyom, Relevant Differential topology in statistical manifolds.- G. Pistone, A lecture about the use of Orlicz Spaces in Information Geometry.- F. Nielsen and G. Hadjeres, Quasiconvex Jensen divergences and quasiconvex Bregman divergences.- PART 4: Geometric Structures of Mechanics, Thermodynamics & Inference for Learning: F. Gay-Balmaz and H. Yoshimura, Dirac Structures and Variational Formulation of Thermodynamics for Open Systems.- A. A. Simoes, D. Martín de Diego, M. L. Valcázar and Manuel de León, The geometry of some thermodynamic systems.- F. Chinesta, E. Cueto, M. Grmela, B. Mioya, M. Pavelka and M. Sipka, Learning Physics from Data: a Thermodynamic Interpretation.- Z. Terze, V. Pandža, M. Andrić and D. Zlatar, Computational dynamics of reduced coupled multibody-fluid system in Lie group setting.- F. Masi, I. Stefanou, P. Vannucci and V. Maffi-Berthier, Material modeling via Thermodynamics-based Artificial Neural Networks.- K. Grosvenor, Information Geometry and Quantum Fields.- PART 5: Hamiltonian Monte Carlo, HMC Sampling and Learning on Manifolds: A. Barp, The Geometric Integration of Measure-Preserving Flows for Sampling and Hamiltonian Monte Carlo.- A. Fradi, I. Adouani and C. Samir, Bayesian inference on local distributions of functions and multidimensional curves with spherical HMC sampling.- S. Huntsman, Sampling and Statistical Physics via Symmetry.- T. Gerald, H. Zaatiti and H. Hajri, A Practical hands-on for learning Graph Data Communities on Manifolds.