Dynamical properties of neural networks with product connections

Higher order neural networks with product connections which hold the weighted sum of products of input variables have been proposed as a new concept. In some applications, it is shown that they are more superior in ability than traditional neural networks. But, little is known about the fundamental property and possibility of these models. This paper describes some the dynamics properties, including the stability and dynamics of a distance between two states, of the neural networks using the statistical method for the case where the dynamics of traditional networks was shown. First, we show the qualitative properly of the dynamics of the networks by investigating their stability. Next, we show the dynamics of a distance between two states (input patterns). As a result, although more complex dynamics is realized in these networks, compared with the traditional ones, it is shown that the characteristics of both networks are similar