Shuji Yatsuki

Associative ability of higher order neural networks

Higher order neural networks (HONNs) have been proposed as new systems. In this paper, we show some theoretical results on the associative ability of HONNs. Memory capacity of HONNs is much larger than that of the conventional neural networks. The capacity of auto-correlation associative memory is (/sup m//sub k/)/(2 log m), where m is the number of neurons and K is the order of connections.

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.

Statistical dynamics of associative memory for higher order neural networks

This paper describes dynamics of recalling process for associative memory in higher order neural networks by using the statistical method. As a result, it is shown that as dynamics of a pattern are not interfered with by the other patterns except the target pattern, the ability of associative memory in higher order neural networks is superior to that of the traditional model.

Associative memory of sequential patterns using higher order neural networks

This paper describes associative memory of sequential patterns using higher order neural networks with monotone and nonmonotone output functions. Specifically, it is shown in numerical simulation that the second order neural network with sigmoid output function is superior to the other model.

Higher Order Neurodynamics of Associative Memory for Sequential Patterns

This paper describes higher order neurodynamics of associative memory for sequential patterns using a statistical method. First, the statistical analysis of direct correlations between the cross talk noise terms for higher order neural networks is made. Further, it is shown that storage capacities for k = 1, 2 and 3 dimensional cases are 0.263n ,

Shift-Invariant Associative Memory Based on Homogeneous Neural Networks

0.207\binom{n}{2}

Dynamics of distance between patterns for higher order random neural networks

and

Some Properties on the Capability of Associative Memory for Higher Order Neural Networks

0.180\binom{n}{3}

On Some Dynamical Properties of Randomly Connected Higher Order Neural Networks

, respectively, where n is the number of neurons and

Some Characteristics of Higher Order Neural Networks with Decreasing Energy Functions (Special Section on Nonlinear Theory and its Applications)

\binom{n}{k}