Synchronous vs asynchronous behavior of Hopfield's CAM neural net

The performance of Hopfield's neural net operating in synchronous and asynchronous modes is contrasted. Two interconnect matrices are considered: (1) the original Hopfield interconnect matrix; (2) the original Hopfield interconnect matrix with self-neural feedback. Specific attention is focused on techniques to maximize convergence rates and avoid steady-state oscillation. We identify two oscillation modes. Vertical oscillation occurs when the net's energy changes during each iteration. A neural net operated asynchronously cannot oscillate vertically. Synchronous operation, on the other hand, can change a net's energy either positively or negatively and vertical oscillation can occur. Horizontal oscillation occurs when the net alternates between two or more states of the same energy. Certain horizontal oscillations can be avoided by adopting appropriate thresholding rules. We demonstrate, for example, that when (1) the states of neurons with an input sum of zero are assigned the complement of their previous state, (2) the net is operated asynchronously, and (3) nonzero neural autoconnects are allowed, the net will not oscillate either vertically or horizontally.