Associative memory networks, fault-tolerance and coding theory

The binary-couplings neural network used as an associative memory is studied under the effects of synaptic damage. The model of damage is to flip synapses (J_ij→-J_ij) randomly with a probability λ. A simple model based on a network with constant stabilities is proposed that allows the calculation of the storage properties of the damaged networks. The networks are fault-tolerant at low storage densities, the fraction of bit-errors in the stored patterns being finite but very small up to high concentrations of flipped synapses. Results are compared with some standard error-correcting codes, some implications for coding-theory are discussed