Statistical Mechanics of Neural Networks

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Sprache: Englisch

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Beschreibung

This book highlights a comprehensive introduction to the fundamental statistical mechanics underneath the inner workings of neural networks. The book discusses in details important concepts and techniques including the cavity method, the mean-field theory, replica techniques, the Nishimori condition, variational methods, the dynamical mean-field theory, unsupervised learning, associative memory models, perceptron models, the chaos theory of recurrent neural networks, and eigen-spectrums of neural networks, walking new learners through the theories and must-have skillsets to understand and use neural networks. The book focuses on quantitative frameworks of neural network models where the underlying mechanisms can be precisely isolated by physics of mathematical beauty and theoretical predictions. It is a good reference for students, researchers, and practitioners in the area of neural networks.

Über den Autor

Haiping Huang

Dr. Haiping Huang received his Ph.D. degree in theoretical physics from the Institute of Theoretical Physics, the Chinese Academy of Sciences. He works as an associate professor at the School of Physics, Sun Yat-sen University, China. His research interests include the origin of the computational hardness of the binary perceptron model, the theory of dimension reduction in deep neural networks, and inherent symmetry breaking in unsupervised learning. In 2021, he was awarded Excellent Young Scientists Fund by National Natural Science Foundation of China.

Zusammenfassung

Presents major theoretical tools for the analysis of neural networks

Provides concrete examples for the use of the theories in neural networks

Bridges old tools and frontiers in the theoretical development of neural networks

Inhaltsverzeichnis

Introduction.- Spin glass models and cavity method.- Variational mean-¿eld theory and belief propagation.- Monte Carlo simulation methods.- High-temperature expansion.- Nishimori line.- Random energy model.- Statistical mechanical theory of Hop¿eld model.- Replica symmetry and replica symmetry breaking.- Statistical mechanics of restricted Boltzmann machine.- Simplest model of unsupervised learning with binary synapses.- Inherent-symmetry breaking in unsupervised learning.- Mean-¿eld theory of Ising Perceptron.- Mean-¿eld model of multi-layered Perceptron.- Mean-¿eld theory of dimension reduction.- Chaos theory of random recurrent neural networks.- Statistical mechanics of random matrices.- Perspectives.

Erscheinungsjahr:	2023
Fachbereich:	Theoretische Physik
Genre:	Physik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xviii 296 S. 22 s/w Illustr. 40 farbige Illustr. 296 p. 62 illus. 40 illus. in color.
ISBN-13:	9789811675720
ISBN-10:	9811675724
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Huang, Haiping
Auflage:	1st ed. 2021
Hersteller:	Springer Singapore Springer Nature Singapore
Maße:	235 x 155 x 18 mm
Von/Mit:	Haiping Huang
Erscheinungsdatum:	06.01.2023
Gewicht:	0,482 kg

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