An analog integrated neural network capable of learning the Feigenbaum logistic map

A description is presented of the design and behavior of analog integrated circuits based on a digital neural network developed and used by A. Lapedes and R. Farber (Tech. Rep. LA-UR-87-26662, Los Alamos Nat. Lab., 1987) to learn the Feigenbaum logistic map. The analog circuits can operate in real time, orders of magnitude faster than the digital model, but it is shown that a direct analog implementation may not be as accurate as the original digital network. An analysis is also presented that shows that the inaccuracies arise not only, as expected, directly from the limited numerical precision of the analog circuit but also indirectly from parameter sensitivity, which is shown to be a problem for this type of neural network. To correct for these nonidealities the analog network includes an adaptive learning circuit. It is demonstrated that, in certain circumstances, the simple analog servomechanism suggested can replace the back-propagation learning algorithm used in digital neural networks