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• W2034690675 abstract "The present paper is intended to summariz our rent knowledge about the long-time behaviour of nehwrks of graded response neurons with continuous- time dynamics. We demonstrate the workings of our previously developed statistical- mechanical approach to continuous-time dynamics by applying it to networks with various forms of synaptic organization (leaming 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). We 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 neumns in the wntexi of the replica approach. A solution to the low firing rates problem within the framework of nets of analogue neurons is also briefly discussed. Finally, the statisticalmechanical approach to the analysis of continuowtime dynamics is extended to include effects of fast stochastic noise. Detailed-balance solutions are shown to be unique and of canonical form, governed by Hamiltonians which exhibit a reciprocity relation between potential- dynamics and fuing-rate dynamics: for the potential-dynamics, the Hamiltonian is given by the Lyapounw function of the system-expressed in terms of the fuing rates-and it generates a Gibbs distribution over fuing-rate space. For the noisy firinerate dynamics, the same Lyapounov function-now expressed in terms of neural potentials-generates a Gibbs distribution Over the space of these potentials. As a consequence, the firing- rate dynamics will freeze in configurations saturating the neural input-xtput relations, whenever such saturation levels exist. Both types of stationary distribution are shown to exist only under unrealistic assumptions about the noise in the system." @default.
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• W2034690675 title "Statistical mechanics for neural networks with continuous-time dynamics" @default.
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• W2034690675 doi "https://doi.org/10.1088/0305-4470/26/4/012" @default.
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