On monotone spline approximation
SIAM Journal on Mathematical Analysis
Fundamentals of Artificial Neural Networks
Fundamentals of Artificial Neural Networks
Some new results on neural network approximation
Neural Networks
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This paper proposes a new way of digital hardware implementation of nonlinear activation functions in feed-forward neural networks. The basic idea of this new realization is that the nonlinear functions can be implemented using a matrix-vector multiplication. Recently a new approach was proposed for the realization of matrix-vector multiplications which approach can also be applied for implementing the nonlinear functions if the nonlinear functions are approximated by simple basis functions. The paper proposes to use B-spline basis functions to the approximate nonlinear sigmoidal functions, it shows that this approximation fulfills the general requirements on the activation functions, presents the details of the proposed hardware implementation, and gives a summary of an extensive study about the effects of B-spline nonlinear function realization on the size and the trainability of feed-forward neural networks.