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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.
List of contents
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.
About the author
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.
