We present two learning mechanisms for networks of formal neurons analogous to Ising spin systems. The ‘‘projection rule’’ guarantees the errorless storage and retrieval of a set of information patterns: In other words, it allows us to compute the magnetic interactions so as to make a given set of states the ground states of the spin system (in zero external field). Several analytical results are derived for this rule; computer simulations and examples of applications to error correction are presented. Another learning mechanism, termed the ‘‘associating rule,’’ is also described; going beyond the memorization process, it allows us to design networks satisfying a set of dynamical constraints such as a given set of stable states and/or transitions and/or cycles. It provides a new tool to perform such functions as associations between information and concepts.

• Received 2 April 1986

DOI:https://doi.org/10.1103/PhysRevA.34.4217