Long term memory storage capacity of multiconnected neural networks.

Quantitative expressions of long-term memory storage capacities of complex neural network are derived. The networks are made of neurons connected by synapses of any order, of the axono-axonal type considered by Kandel et al. for example. The effect of link deletion possibly related to aging, is also considered. The central result of this study is that, within the framework of Hebb's laws, the number of stored bits is proportional to the number of synapses. The proportionality factor however, decreases when the order of involved synaptic contact increases. This tends to favor neural architectures with low-order synaptic connectivities. It is finally shown that the memory storage capacities can be optimized by a partition of the network into neuron clusters with size comparable with that observed for cortical microcolumns.