Analytic realization of polynomial functions by multilayerfeedforward neural networks

摘要

Summary form only given. An analytic method for constructingnpolynomial functions by multi layer feedforward neural networks has beenndeveloped. Because the polynomials consist of multiplication operationsnand linear weighted summations, if the multiplier can be constructed byna neural network, any polynomial function can be represented by a neuralnnetwork (a single unit already has the function of weighted summation).nAn attempt has been made to construct a neural network module with onenhidden layer that works as a multiplier. It was shown that thenmultiplier can be approximated by a neural network with four hiddennunits, with arbitrary accuracy on a bounded closed set