Advantages of dilution in the connectivity of attractor networks in the brain

A fundamental question about brain function is why the connectivity in the cortex is diluted, in that neurons in a local region of the neocortex and in the CA3 part of the hippocampal cortex typically have a probability of having a synaptic connection between them that is less than 0.1. In both these types of cortex, there is evidence that the excitatory interconnections between neurons are associatively modifiable, and that the system supports attractor dynamics that enable memories to be stored, which are used in for example short-term memory and in episodic memory. The hypothesis proposed is that the diluted connectivity allows biological processes that set up synaptic connections between neurons to arrange for there to be only very rarely more than one synaptic connection between any pair of neurons. If probabilistically there were more than one connection between any two neurons, it is shown by simulation of an autoassociation attractor network that such connections would dominate the attractor states into which the network could enter and be stable, thus strongly reducing the memory capacity of the network (the number of memories that can be stored and correctly retrieved), below the normal large capacity for diluted connectivity. Diluted connectivity between neurons in the cortex thus has an important role in allowing high capacity of memory networks in the cortex, and helping to ensuring that the critical capacity is not reached at which overloading occurs leading to an impairment in the ability to retrieve any memories from the network. This intra-area diluted connectivity complements the diluted connectivity in the feedforward connections between cortical areas that helps the representations built by competitive learning to be stable.