NIPS-3 Proceedings of the 1990 conference on Advances in neural information processing systems 3
Chaotic balanced state in a model of cortical circuits
Neural Computation
Spiking Neuron Models: An Introduction
Spiking Neuron Models: An Introduction
Dynamics of the firing probability of noisy integrate-and-fire neurons
Neural Computation
Integrate-and-fire neurons driven by correlated stochastic input
Neural Computation
Waves, bumps, and patterns in neural field theories
Biological Cybernetics
Spontaneous Dynamics of Asymmetric Random Recurrent Spiking Neural Networks
Neural Computation
Stationary Bumps in Networks of Spiking Neurons
Neural Computation
Noise in Integrate-and-Fire Neurons: From Stochastic Input to Escape Rates
Neural Computation
Stochastic dynamics of a finite-size spiking neural network
Neural Computation
Finite-size and correlation-induced effects in mean-field dynamics
Journal of Computational Neuroscience
Stochastic perturbation methods for spike-timing-dependent plasticity
Neural Computation
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Population rate or activity equations are the foundation of a common approach to modeling for neural networks. These equations provide mean field dynamics for the firing rate or activity of neurons within a network given some connectivity. The shortcoming of these equations is that they take into account only the average firing rate, while leaving out higher-order statistics like correlations between firing. A stochastic theory of neural networks that includes statistics at all orders was recently formulated. We describe how this theory yields a systematic extension to population rate equations by introducing equations for correlations and appropriate coupling terms. Each level of the approximation yields closed equations; they depend only on the mean and specific correlations of interest, without an ad hoc criterion for doing so. We show in an example of an all-to-all connected network how our system of generalized activity equations captures phenomena missed by the mean field rate equations alone.