Statistical mechanics for neural networks with continuous-time dynamics

The authors summarize their current knowledge about the long-time behaviour of networks of graded response neurons with continuous-time dynamics. They demonstrate the workings of their previously developed statistical-mechanical approach to continuous-time dynamics by applying it to networks with various forms of synaptic organization (learning rules), and neural composition (neuron-types as encoded in gain functions), as well as to networks varying with respect to the ensemble of stored data (unbiased and low-activity patterns). They present phase diagrams and compute distributions of local fields for a variety of examples. Local field distributions are found to deviate from the Gaussian form obtained for stochastic neurons in the context of the replica approach. A solution to the low firing rates problems within the framework of nets of analogue neurons is also briefly discussed. Finally, the statistical-mechanical approach to the analysis of continuous-time dynamics is extended to include effects of fast stochastic noise.