Stochastic resonance and finite resolution in a network of leaky integrate-and-fire neurons.

Abstract

This thesis is a study of stochastic resonance (SR) in a discrete implementation of a leaky integrate-and-fire (LIF) neuron network. The aim was to determine if SR can be realised in limited precision discrete systems implemented on digital hardware. How neuronal modelling connects with SR is discussed. Analysis techniques for noisy spike trains are described, ranging from rate coding, statistical measures, and signal processing measures like power spectrum and signal-to-noise ratio (SNR). The main problem in computing spike train power spectra is how to get equi-spaced sample amplitudes given the short duration of spikes relative to their frequency. Three different methods of computing the SNR of a spike train given its power spectrum are described. The main problem is how to separate the power at the frequencies of interest from the noise power as the spike train encodes both noise and the signal of interest. Two models of the LIF neuron were developed, one continuous and one discrete, and the results compared. The discrete model allowed variation of the precision of the simulation values allowing investigation of the effect of precision limitation on SR. The main difference between the two models lies in the evolution of the membrane potential. When both models are allowed to decay from a high start value in the absence of input, the discrete model does not completely discharge while the continuous model discharges to almost zero. The results of simulating the discrete model on an FPGA and the continuous model on a PC showed that SR can be realised in discrete low resolution digital systems. SR was found to be sensitive to the precision of the values in the simulations. For a single neuron, we find that SR increases between 10 bits and 12 bits resolution after which it saturates. For a feed-forward network with multiple input neurons and one output neuron, SR is stronger with more than 6 input neurons and it saturates at a higher resolution. We conclude that stochastic resonance can manifest in discrete systems though to a lesser extent compared to continuous systems.