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This paper considers a structure of three-layer feedforward networks that approximate polynomial functions. The feedforward network has some system parameters such as the coupling coefficients and the biases. The structure of the feedforward network is determined by the system parameters. For any polynomial function, a simple calculation method of the parameters is proposed when the three-layer feedforward network sufficiently approximates the polynomial function. Moreover, it is shown that the obtained feedforward network smoothly approximates the polynomial function. [ABSTRACT FROM AUTHOR]

The main goal of this study is to elucidate the theoretical capability of the continuous time recurrent neural network. In this paper, we show that the approximation capability of the continuous time recurrent network can be extended to non-autonomous dynamical systems with external inputs. Moreover, if the dynamical system has an asymptotically stable periodic solution for a periodic external input, it is shown that the approximation can be extended to the global time interval. [ABSTRACT FROM AUTHOR]

In this paper, a generalised entropy based associative memory model will be proposed and applied to memory retrievals with analogue embedded vectors instead of the binary ones in order to compare with the conventional autoassociative model with a quadratic Lyapunov functionals. In the present approach, the updating dynamics will be constructed on the basis of the entropy minimization strategy which may be reduced asymptotically to the autocorrelation dynamics as a special case. From numerical results, it will be found that the presently proposed novel approach realizes the larger memory capacity even for the analogue memory retrievals in comparison with the autocorrelation model based on dynamics such as associatron according to the higher-order correlation involved in the proposed dynamics. [ABSTRACT FROM AUTHOR]

In this paper, an entropy based associative memory model will be proposed and applied to memory retrievals with an orthogonal learning model to compare with the conventional autoassociative model with a quadratic Lyapunov functionals. In the present approach, the updating dynamics will be constructed on the basis of the entropy minimization strategy which may be reduced asymptotically to the autocorrelation dynamics as a special case. From numerical results, it will be found that the presently proposed novel approach realizes the larger memory capacity in comparison with the autocorrelation model based on dynamics such as associatron according to the higher-order correlation involved in the proposed dynamics. [ABSTRACT FROM AUTHOR]