Statistical Mechanics of Neural Networks

Haiping Huang (Autor)

Buch | Hardcover

296 Seiten

2022 | 1st ed. 2021
Springer Verlag, Singapore
978-981-16-7569-0 (ISBN)

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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.

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.

Introduction.- Spin glass models and cavity method.- Variational mean-ﬁeld theory and belief propagation.- Monte Carlo simulation methods.- High-temperature expansion.- Nishimori line.- Random energy model.- Statistical mechanical theory of Hopﬁeld 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-ﬁeld theory of Ising Perceptron.- Mean-ﬁeld model of multi-layered Perceptron.- Mean-ﬁeld theory of dimension reduction.- Chaos theory of random recurrent neural networks.- Statistical mechanics of random matrices.- Perspectives.

Erscheinungsdatum	07.01.2022
Zusatzinfo	40 Illustrations, color; 22 Illustrations, black and white; XVIII, 296 p. 62 illus., 40 illus. in color.
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Chemie ► Physikalische Chemie
	Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
	Naturwissenschaften ► Physik / Astronomie ► Thermodynamik
Schlagworte	Cavity Method • Hopfield Model • Mean-field Theory • random matrices • Replica method • Restricted Boltzmann Machine • Unsupervised Learning
ISBN-10	981-16-7569-4 / 9811675694
ISBN-13	978-981-16-7569-0 / 9789811675690
Zustand	Neuware