Neural Comput - A principled dimension-reduction method for the population density approach to modeling networks of neurons with synaptic dynamics.

Tópicos

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Resumo

The population density approach to neural network modeling has been utilized in a variety of contexts. The idea is to group many similar noisy neurons into populations and track the probability density function for each population that encompasses the proportion of neurons with a particular state rather than simulating individual neurons (i.e., Monte Carlo). It is commonly used for both analytic insight and as a time-saving computational tool. The main shortcoming of this method is that when realistic attributes are incorporated in the underlying neuron model, the dimension of the probability density function increases, leading to intractable equations or, at best, computationally intensive simulations. Thus, developing principled dimension-reduction methods is essential for the robustness of these powerful methods. As a more pragmatic tool, it would be of great value for the larger theoretical neuroscience community. For exposition of this method, we consider a single uncoupled population of leaky integrate-and-fire neurons receiving external excitatory synaptic input only. We present a dimension-reduction method that reduces a two-dimensional partial differential-integral equation to a computationally efficient one-dimensional system and gives qualitatively accurate results in both the steady-state and nonequilibrium regimes. The method, termed modified mean-field method, is based entirely on the governing equations and not on any auxiliary variables or parameters, and it does not require fine-tuning. The principles of the modified mean-field method have potential applicability to more realistic (i.e., higher-dimensional) neural networks.

Resumo Limpo

popul densiti approach neural network model util varieti context idea group mani similar noisi neuron popul track probabl densiti function popul encompass proport neuron particular state rather simul individu neuron ie mont carlo common use analyt insight timesav comput tool main shortcom method realist attribut incorpor under neuron model dimens probabl densiti function increas lead intract equat best comput intens simul thus develop principl dimensionreduct method essenti robust power method pragmat tool great valu larger theoret neurosci communiti exposit method consid singl uncoupl popul leaki integrateandfir neuron receiv extern excitatori synapt input present dimensionreduct method reduc twodimension partial differentialintegr equat comput effici onedimension system give qualit accur result steadyst nonequilibrium regim method term modifi meanfield method base entir govern equat auxiliari variabl paramet requir finetun principl modifi meanfield method potenti applic realist ie higherdimension neural network

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