Diagonal rotor Hopfield neural networks

Abstract

A complex-valued Hopfield neural network (CHNN) is a multistate Hopfield model and has been applied to the storage of image data. It has the weak noise tolerance due to the inherent property of rotational invariance. A hyperbolic-valued Hopfield neural network (HHNN) resolves rotational invariance and improves the noise tolerance. A rotor Hopfield neural network (RHNN) is an extension of CHNN and the weights are represented by matrices. It provides excellent noise tolerance by resolving the rotational invariance. However, an RHNN needs double weight parameters of a CHNN, unlike an HHNN. In this work, we propose a diagonal RHNN (DRHNN), which restricts the weights of RHNN to diagonal matrices and reduces the number of weight parameters. The number of weight parameters in a DRHNN, an HHNN, and a CHNN is same. In addition, a DRHNN resolves the rotational invariance and provides excellent noise tolerance like an RHNN.