Multi-channel pattern reconstruction through $L$-directional associative memories

Abstract: We consider $L$-directional associative memories, composed of $L$ Hopfield networks, displaying imitative Hebbian intra-network interactions and anti-imitative Hebbian inter-network interactions, where couplings are built over a set of hidden binary patterns. We evaluate the model's performance in reconstructing the whole set of hidden binary patterns when provided with mixtures of noisy versions of these patterns. Our numerical results demonstrate the model's high effectiveness in the reconstruction task for structureless and structured datasets.