Noise Robust Projection Rule for Hyperbolic Hopfield Neural Networks

A complex-valued Hopfield neural network (CHNN) is a multistate Hopfield model. Low noise tolerance is the main disadvantage of CHNNs. The hyperbolic Hopfield neural network (HHNN) is a noise robust multistate Hopfield model. In HHNNs employing the projection rule, noise tolerance rapidly worsened as the number of training patterns increased. This result was caused by the self-loops. The projection rule for CHNNs improves noise tolerance by removing the self-loops, however, that for HHNNs cannot remove them. In this brief, we extended the stability condition for the self-loops of HHNNs and modified the projection rule. Thus, the HHNNs had improved noise tolerance.