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Infinite Dimensional Statistical Neural Manifold

Author: ChenXiongZhi
Tutor: CaiChangLin
School: Sichuan University
Course: Applied Mathematics
Keywords: And infinite dimensional statistical nerve manifold Dynamic subnet choice mechanism The statistical neural manifold Fisher information matrix And consistent empirical risk minimization reasoning principle Consistent with the natural gradient
CLC: TP183
Type: Master's thesis
Year: 2006
Downloads: 28
Quote: 0
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Abstract


Artificial neural network (ANN) is one of the most commonly used , capable of performing a series of artificial intelligence ( AI ) tool. Typically, a single artificial neural network may not be able to accurately and fully grasp the characteristics of a particular job , have been proposed Artificial Neural Network Ensemble ( [ 1 ] ) model - an integrated single artificial neural network of a certain number so that they can according to a certain mechanism given in the framework of the unified output . With the growth of the mathematical basis of in-depth study of the neural network model and the actual application needs statistics nerve manifold ( statistical Neural manifolds ) ( [ 2 ] , [ 3 ] ) model to examine the general class of neural network nature of the flow of information between the neural network dynamics . Recent neural network mathematics based on cutting-edge research interest to invest in the unity of the neural field theory ( [ 4 ] , [ 5 ] , [6] ) , in order given in the mathematical description of the behavior of large-scale neurons at the same time neural network statistical mathematical model . This work can be divided into three categories: one , the optimal network architecture and reasoning principles are the same [ 7 ] ; Second, the statistical the neural manifolds Fisher information matrix representation and calculation ; statistical model of neural network Uniform Mathematical Description of exploration . Specifically, this innovative work are: 1 ) the the three overall network topology, the network or Ensemble dynamic subnet selection mechanism , and gives the Ensemble has a unique , stable and statistically optimal output the combined weight of the necessary and sufficient condition . 2 ) gives the parameters MLP neural manifolds minutes fast matrix expression of the Fisher information matrix , given its Keyblock explicit expression and inverse . 3) Based on the sub- index of the S- type network (sub-exponential sigmoidal networks) ([8]) Vapnik-Chervonenkis dimension ( VC - dimension ) limited ( [ 8 ] , [9] ) , S- on the type MLP neural manifold consistent natural gradient algorithm . \4) the the infinite dimensional statistical nerve manifold model , all finite-dimensional neural manifold into a unified model .

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CLC: > Industrial Technology > Automation technology,computer technology > Automated basic theory > Artificial intelligence theory > Artificial Neural Networks and Computing
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