Pseudomemories of two‐dimensional multistate hopfield neural networks

Abstract

Complex-valued Hopfield neural networks (CVHNNs) are available for storage of multilevel data, such as gray-scale images. Such networks have low noise tolerance. This is a severe problem for their applications. To improve the noise tolerance, we have to study pseudomemories. In the case of one training pattern, CVHNNs have only rotated patterns as pseudomemories. There are many rotated patterns. This is considered the reason why CVHNNs have low noise tolerance. In the present paper, we investigate the pseudomemories of two-dimensional multistate Hopfield neural networks, including the complex-valued ones, with multiple training patterns. Computer simulations show that there are many pseudomemories other than the rotated patterns.

Dual‐numbered Hopfield neural networks

“…This problem becomes fatal in CHNNs and QHNNs. In CHNNs and QHNNs, the rotated patterns of training patterns are stored . It is referred to as rotational invariance.…”

Chaotic complex‐valued bipartite auto‐associative memory with a periodic activation function

“…A CAM can store multilevel data and has often been applied to the storage of grayscale images . A CAM has a difficulty with rotational invariance, which is to store both the training and rotated patterns . Rotational invariance produces many pseudomemories, and reduces the noise tolerance.…”