Dynamics of distance between patterns for higher order random neural networks

Higher order neural networks which hold the weighted sum of products of input variables, have been proposed as a new concept. In some applications using them, it is shown that they are superior in ability to the traditional neural networks. But, little is known about the fundamental property and possibility of these models. In the previous paper, we have shown dynamical properties, dynamics of the activities for states, for higher order random neural networks (HORNNs) with the digital {-1,1}-, {0,1}- and the analog {-1,1}-, {0,1}-models. This paper describes dynamics of a distance between two states in full detail for HORNNs with the digital {0,1}-model using a statistical method. Further, comparison between the digital {-1,1}- and {0,1}-models is made