Titlebook: Statistical Mechanics of Neural Networks; Haiping Huang Book 2021 Higher Education Press 2021 Unsupervised Learning.Mean-field Theory.Cavi

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Mean-Field Model of Multi-layered Perceptron,rs has been proved to be a universal approximator [.]. However, compared with its achievement, the mechanism of deep networks is still challenging to understand. Redundancy is one of the characteristics of deep neural networks, which means that the deep network is robust under the removal perturbati

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Mean-Field Theory of Dimension Reduction,s no labels or rewards from the data, just by gradually creating better representations of the sensory inputs along a hierarchy of information flow to extract the intrinsic features hidden in the data. Both in the fields of artificial intelligence and neuroscience, the sensory inputs are physically

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Chaos Theory of Random Recurrent Neural Networks,utation principles underlying cognitive functions, e.g., working memory, decision-making and learning (Wulfram Gerstner et al. in Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition. Cambridge University Press, Cambridge, 2014 [.]). This is usually achieved by simulating a spi

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Statistical Mechanics of Random Matrices,network, which is related to phase transitions (e.g., in the Hopfield model), or dynamical modes in recurrent neural networks. The asymptotic properties of random matrices whose entries follow a pre-defined distribution can be connected to the thermodynamic behavior in statistical physics (Edwards a

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Perspectives,works), mainly focusing on an overview of main tools to deal with non-linearity intrinsic in neural computation, and detailed illustration of deep insights provided by physics analysis in a few typical examples (most of them were proposed by the authors’ own works). In Marr’s viewpoint [.], understa

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Book 2021 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 recu

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LUDE

Nishimori Line,ical inference problems [.,.,.,.]. Thus, this concept is an important theoretical perspective to understand the Bayesian learning process, one of the most popular paradigms in the deep learning era. Here, we introduce the basic knowledge about this concept first, and we leave more applications to later chapters of learning theory.

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