Chapter 3 has been devoted to the modeling of the dynamics of neurons. The standard model we arrived at contains the main features which have been revealed by neuroelectrophysiology: the model considers neural nets as networks of probabilistic threshold binary automata. Real neural networks, however, are not mere automata networks. They display specific functions and the problem is to decide whether the standard model is able to show the same capabilities.

Memory is considered as one of the most prominent properties of real neural nets. Current experience shows that imprecise, truncated information is often sufficient to trigger the retrieval of full patterns. We correct misspelled names, we associate images or flavors with sounds and so on. It turns out that the formal nets display these memory properties if the synaptic efficacies are determined by the laws of classical conditioning which have been described in section 2.4. The synthesis in a single framework of observations of neurophysiology with observations of experimental psychology, to account for an emergent property of neuronal systems, is an achievement of the theory of neural networks.

The central idea behind the notion of conditioning is that of associativity. It has given rise to many theoretical developments, in particular to the building of simple models of associative memory which are called Hebbian models. The analysis of Hebbian models has been pushed rather far and a number of analytical results relating to Hebbian networks are gathered in this chapter. More refined models are treated in following chapters.