Approximate Projection Expression of Nonlinear Artificial Intelligent Systems Based on Matrix Operator Polynomial Approximations

摘要

Firstly about an extended filter bank where input and output signal are matrix operators, we introduce a theory developed by Kida that shows the equivalence relation established between the optimum operator signal approximation which minimizes all the upper limit measures of error at the same time and the operator signal approximation based on the concept of pseudo inverse matrix which minimizes square average norm of the error. Secondly, based on a new concept of Kullback Leibler divergence extended to operator signals, we present a new scanning type approximation of operator signals that guarantees similar optimum performance in the above approximation. Thirdly, about a nonlinear operator in an artificial intelligence system represented by deep learning, we prove that there is an operator matrix polynomial approximation that the upper limit of error is approximately smaller than a given positive number epsilon. Finally, we prove that the above operator matrix polynomial approximation of the nonlinear operator in the artificial intelligence system is reduced to a linear combination of the input operator and the output operator. As a consequence, under some number of trials, we show that there is a possibility of controlling and guiding those artificial intelligence nonlinear operator systems to undesirable direction. And, in order to prevent bad use of words in an artificial intelligence chat system, we point out the necessity of introducing "the prior check and censorship" of "words to use" in these artificial intelligence chat systems.