The space of interactions in neural networks: Gardner's computation with the cavity method

Gardner's (1987,1988) computation of the number of N-bit patterns which can be stored in an optical neural network used as an associative memory is derived without replicas, using the cavity method. This allows for a unified presentation whatever the basic measure in the space of coupling constants, but above all it gives the clear physical content of the assumption of replica symmetry. TAP equations are also derived.