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Sigmoid Generators for Neural Computing Using Piecewise Approximations
September 1996 (vol. 45 no. 9)
pp. 1045-1049

Abstract—A piecewise second order approximation scheme is proposed for computing the sigmoid function. The scheme provides high performance with low implementation cost; thus, it is suitable for hardwired cost effective neural emulators. It is shown that an implementation of the sigmoid generator outperforms, in both precision and speed, existing schemes using a bit serial pipelined implementation. The proposed generator requires one multiplication, no look-up table and no addition. It has been estimated that the sigmoid output is generated with a maximum computation delay of 21 bit serial machine cycles representing a speedup of 1.57 to 2.23 over other proposals.

[1] D.EE. Rumelhart and J.L. McClelland, Parallel Distributed Processing: Explorations in the Microstructure of Cognition, MIT Press, Cambridge, Mass., 1986.
[2] J. Holt and J. Hwang, "Finite Precision Error Analysis of Neural Network Hardware Implementations," IEEE Trans. Computers, vol. 42, no. 3, Mar. 1993.
[3] P. Murtagh and A.C. Tsoi, "Implementation Issues of Sigmoid Function and its Derivative for VLSI Digital Neural Networks," IEE Proc.-E, vol. 139, no.3, May 1992.
[4] D.J. Myers and G. Storti-Gajani, "Efficient Implementation of Piecewise Linear Activation Function for Digital VLSI Neural Networks," Electronics Letter, vol. 25, no. 24, pp. 1,662-1,663, Nov., 1989.
[5] C. Alippi and G. Storti-Gajani, "Simple Approximation of Sigmoidal Function: Realistic Design of Digital Neural Networks Capable of Learning," Proc. IEEE-ISCAS,Singapore, June11-14 1991.
[6] H.K. Kwan, "Digital Implementation Methods for Nonlinear Functions in Neural Networks," unpublished manuscript, 1993.
[7] M. Zhang, S. Vassiliadis, and J.G. Delgado-Frias, "Sigmoid Generators for Neural Computing Using Piecewise Approximations," TR 1-68340-44(1994)11, Dept. of Electrical Eng., Delft Univ. of Tech nology, Nov. 1994.

Index Terms:
Nonlinear function generators, sigmoid function, piecewise approximations, neural networks, hardware for twos complement notation, error analysis.
Ming Zhang, Stamatis Vassiliadis, José G. Delgado-Frias, "Sigmoid Generators for Neural Computing Using Piecewise Approximations," IEEE Transactions on Computers, vol. 45, no. 9, pp. 1045-1049, Sept. 1996, doi:10.1109/12.537127
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