Statistical mechanics beyond the Hopfield model: solvable problems in neural network theory.

We present four 'case study' examples of solvable problems in the theory of recurrent neural networks, which are relevant to our understanding of information processing in the brain, but which are also interesting from a purely statistical mechanical point of view, even at the level of simple models (which helps in stimulating interdisciplinary work). The examples concern issues in network dynamics, network connectivity, spike timing and synaptic plasticity.