On stability and associative recall of memories in attractor neural networks

Attractor neural networks such as the Hopfield model can be used to model associative memory. An efficient associative memory should be able to store a large number of patterns which must all be stable. We study in detail the meaning and definition of stability of network states. We reexamine the meanings of retrieval, recognition and recall and assign precise mathematical meanings to each of these terms. We also examine the relation between them and how they relate to memory capacity of the network. We have shown earlier in this journal that orthogonalization scheme provides an effective way of overcoming catastrophic interference that limits the memory capacity of the Hopfield model. It is not immediately apparent whether the improvement made by orthgonalization affects the processes of retrieval, recognition and recall equally. We show that this influence occurs to different degrees and hence affects the relations between them. We then show that the conditions for pattern stability can be split into a necessary condition (recognition) and a sufficient one (recall). We interpret in cognitive terms the information being stored in the Hopfield model and also after it is orthogonalized. We also study the alterations in the network dynamics of the Hopfield network upon the introduction of orthogonalization, and their effects on the efficiency of the network as an associative memory.