An analysis of the flows of neural networks with linear interconnections

The author analyzes the dynamic behavior of neural networks which consist of a set of sigmoid nonlinearities with linear interconnections, without assuming that the interconnections are symmetric or that there are no self-interactions. By eliminating these assumptions, the effects of imperfect implementation on the behavior of Hopfield networks can be studied. If one views the neural network as evolving on an n-dimensional hypercube, H=(0, 1)ⁿ. Thus, nearly complete solutions approach an equilibrium in a corner, irrespective of the initial condition. However, this might not be the correct equilibrium. As an illustration, the analog-to-digital converter proposed by Tank and Hopfield is analyzed using the methods developed