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By Bank W. Lee, Bing J. Sheu

This publication is designed to supply engineers and scientists with an advent to the sector of VLSI neurocomputing. it really is meant to be used on the graduate point, even if seniors would normally have all the required historical past wisdom. This booklet is written to help a semester path.

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Since the parameter GAP j represents the overlapped range of the i-th input current, two digital codes can be stable for a given input current when GAP j < 0 for every i as shown in Fig. 2. Therefore, the condition when the two digital codes cannot be local minima in the energy function for a given analog input value is GAP j ~ 0 for every i. ------_. u } (a) ) ------~-~-----. t } :-----_. u } ) (b) -------~------. u I 1,1 I Fig. 2 Calculation of a characteristic parameter GAP. (a) GAPi < O. (b) GAPi = O.

The energy function can be used to describe the macroscopic property of network dynamics. However, it is insufficient to explain such detailed behaviors of VLSI Hopfield circuits as the location of local 25 Chapter 2 VLSI Hopfield Networks minima, convergence speed, and required amplifier gain for proper network operation. 2 Existence of Local Minima Detailed properties of the local minima can be understood with the help of the following analysis method [7]. 6) . u. -I I j~. 7) . for each stable state can be cal- culated, I·I > I·I < - n 't" ~ jt:i j=l n 't" ~ jt:i j=l T IJ..

Of Solid-State Circuits, vol. SC-22, no. 3, pp. 317-321, June 1987. [17] H. P. Graf and P. deVegvar, "A CMOS implementation of a neural networlc. model," Proc. of the Stanford Advanced Research in VLSI Conference, pp. 351-362, Cambridge, MA: The MIT Chapter 1 Introduction 19 Press, 1987. [18] B. W. Lee and B. J. Sheu, "Design of a neural-based AID converter using modified Hopfield network," IEEE Jour. of Solid-State Circuits, vol. SC-24, no. 4, pp. 1129-1135, Aug. 1989. [19] Dahlquist, Bj~rck, and Anderson, Numerical Methods, pp.

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