By Gustavo Deco, Dragan Obradovic
Neural networks offer a strong new know-how to version and keep an eye on nonlinear and complicated structures. during this publication, the authors current a close formula of neural networks from the information-theoretic perspective. They convey how this attitude offers new insights into the layout thought of neural networks. particularly they convey how those tools could be utilized to the subjects of supervised and unsupervised studying together with characteristic extraction, linear and non-linear self sustaining part research, and Boltzmann machines. Readers are assumed to have a easy knowing of neural networks, yet all of the proper innovations from info idea are conscientiously brought and defined. for this reason, readers from a number of assorted medical disciplines, particularly cognitive scientists, engineers, physicists, statisticians, and laptop scientists, will locate this to be a truly necessary advent to this topic.
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Extra resources for An Information-Theoretic Approach to Neural Computing
A neural network is deterministic if the architecture is defined by interconnected detenninistic neurons. The neural architecture is called stochastic if it is composed of stochastic units. 1. (a) Deterministic neuron. (b) Stochastic neuron. A second classification of architectures is defined by the type of connections between the neurons. Principally two types of architecture are defined: feedforward and recurrent. e. there is no backcoupling between neurons. 2 (a). The neurons are arranged in layers.
3 depicts two principal types of learning paradigms in neural modeling: supervised and unsupervised learning. e. the weight connections) of the neural model in order to match the behavior of a "teacher". During the learning process training examples are presented to the network. Each training example consists of an input pattern and an output pattern which plays the role of a teacher. Then, the learning algorithm changes the synapses in such a way that the difference between the neural network output and the teacher action is minimized.
Before the formulation of the theorem which defines the optimal W, the following auxiliary lemma is presented. 1 Let S be a N x M -matrix with I:S; M < N and rank (S) = M and let D be a N x N diagonal matrix. 23) where P is a N x M -matrix with orthonormal vectors in its columns, which spans the same space as the one spanned by the columns vectors of the matrix S. 24) such that R is a matrix with a particular structure. Its first M rows form an upper triangular matrix above the main diagonal while its remaining N - M rows contain elements equal to zero.