Dynamical computations in networks of Poisson spiking neurons

Abstract

An important problem in computational neuroscience is how populations of neurons can perform computations. Many models of computation by neural networks are based on population firing rates, although precise spike timing has been shown to carry information. Recently, a novel framework proposed by Boerlin, Machens & Deneve 2013 described a method for embedding linear dynamics in a network of coupled leaky integrate-and-fire (LIF) neurons. Their model was based on the idea that the precise timing of each spike was determined by the neuron's contribution to a desired output; in this case to reducing the error between a target and the population estimate. The network, however, relied on significant amounts of noise in order to produce neural responses that were biologically realistic in variability and synchrony. Here, we show that this framework can be approached through a mapping of the LIF neurons to generalized linear model (GLM) neurons without a loss of accuracy. We present a study of the Boerlin et al. network and clarify several observed behaviors to provide motivation for the subsequent reformulation of the network with stochastic neurons. We then describe the GLM parameters and their implications on spike timing and precision in the behavior of the network. Finally, we show that the neuron can accurately reproduce the dynamics of the Boerlin et al. network and produces natural-looking spiking statistics. Our work unifies work on linear point process models with Poisson models, while simplifying and generalizing the current network and suggesting several exciting avenues for future research.