Noise-Robust Projection Rule for Rotor and Matrix-Valued Hopfield Neural Networks

A complex-valued Hopfield neural network (CHNN) has weak noise tolerance due to rotational invariance. Some alternatives of CHNN, such as a rotor Hopfield neural network (RHNN) and a matrix-valued Hopfield neural network (MHNN), resolve rotational invariance and improve the noise tolerance. However, the RHNN and MHNN with projection rules have a different problem of self-feedbacks. If the self-feedbacks are reduced, the noise tolerance is expected to be improved further. For reduction in the self-feedbacks, the noise-robust projection rules are introduced. The stability conditions are extended, and the self-feedbacks are reduced based on the extended stability conditions. Computer simulations support that the noise tolerance is improved. In particular, the noise tolerance is more robust against an increase in the number of training patterns.