By Gustavo Deco, Dragan Obradovic
Neural networks offer a robust new expertise to version and keep watch over nonlinear and intricate platforms. during this publication, the authors current an in depth formula of neural networks from the information-theoretic standpoint. They express how this angle offers new insights into the layout thought of neural networks. specifically they convey how those tools could be utilized to the subjects of supervised and unsupervised studying together with characteristic extraction, linear and non-linear autonomous part research, and Boltzmann machines. Readers are assumed to have a simple realizing of neural networks, yet all of the appropriate innovations from info conception are conscientiously brought and defined. therefore, readers from numerous diversified clinical disciplines, significantly cognitive scientists, engineers, physicists, statisticians, and desktop scientists, will locate this to be a truly helpful advent to this topic.
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Extra info for An Information-Theoretic Approach to Neural Computing
41) with equality if and only if X and Yare independent. = H (X) The proof follows from the fact that 0:;:;; I (X; Y) - H (Xl Y) . 10: Independence bound on entropy Let Xi' X 2' ... , X k be random variables distributed according to the probability distribution p (xi' ... , x k ) . Then k H (Xi' X 2, ... , X k) :;:;; l i=1 with equality if and only if all Xi are independent. e, k k LH(XiIXi _ l , .. 43) i=I o This theorem provides the generalization of the non-negativity of the generalized multidimensional mutual information defined as: I (XI;'" ;Xk ) = K~ (xI' ..
11]). 6 presents an example of unsupervised learning. 4 Feedforward Networks: Backpropagation This section presents an example of a well known and frequently used learning algorithm for feedforward deterministic neural networks called backpropagation. 4. 4. Deterministic feedforward backpropagation neural network. The first layer represents the input data ~f of dimension n for the training example a. Elements of the Theory of Neural Networks 29 The second layer is a layer of m hidden neurons with activation functions given by the function ( .
E. Ym = max (Yj) . e. Llw·. -w .. )8. 27) where 11 is a learning constant and 0nm is the Kronecker delta function. In this way the synapse updates encourage specialization of certain neurons to "win" certain input patterns without the direction of a teacher. In the next chapter we will see several variants of this heuristic paradigm that will be derived by incorporating information theoretic concepts and will extract the statistics of the environment. 29]. Hebb's results have motivated a number of artificial learning paradigms such as the one presented in the previous section.
An Information-Theoretic Approach to Neural Computing by Gustavo Deco, Dragan Obradovic