Convergence Of An Inverse Iteration Algorithm For Neural Networks

As a learning algorithm that is simple and useful, gradient algorithm has beenwidely used in training neural networks. The convergence of the gradient algorithm forfeed-forward neural networks has thoroughly studied. In this paper, we study the iter-ative inversion of neural networks. The following aspect of the algorithm are analyzedsystematically:1.The research status and application fields are reviewed. The basic definitions,structures and learning algorithms of neural networks, inverse problems and iterativeinversion of neural networks are introduced.2.The iterative inversion of neural networks has been used in solving problems inadaptive control, thanks to its good ability of information processing. In this paper, theconvergence of iterative inversion of neural networks has been studied. For two layersand three layers, some deterministic results have been gained: in the iterative process,the error function is proved to be monotone, and the gradient of the error function tendsto zero.3.The nonlinear equation has been solved by the iterative inversion of neuralnetworks. The results of the numerical experiment suggest that the error function tendsto 0 in finite steps and the algorithm has the characteristic of regularization. Thisilluminates that the algorithm is applicable to real problem.