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

Abstract

A Hopfield associative memory (HAM) can store binary data. A HAM has been extended to a complex-valued HAM (CHAM) which can store multi-level data. A CHAM has often been applied to the storage of grayscale images. A CHAM has a problem of rotational invariance, which makes many psuedomemories and reduces the noise tolerance. A chaotic CHAM can explore the stored patterns, though it recalls many pseudomemories. A complex-valued bipartite auto-associative memory (CBAAM) was proposed to improve the noise tolerance by solving rotational invariance. Since a CBAAM stores the reversed patterns, a chaotic CBAAM (CCBAAM) recalls both the training and reversed patterns. In order to solve this problem, a periodic activation function is introduced. A periodic activation function identifies the training and reversed patterns, so that a CCBAAM does not recall the reversed patterns. We evaluate our proposed CCBAAM by computer simulations.

Dual‐numbered Hopfield neural networks

“…Rotational invariance reduces noise tolerance. Several ideas have been proposed to avoid rotational invariance .…”