Models and analysis of a stochastic neural source coder

Abstract

Information transfer in neurons takes place through action potentials (spikes) which are metabolically expensive. A neural coding approach was developed by Johnson et al. (2016) that is optimal, high-fidelity, energy-efficient and well matches the experimental spiking behavior of real neurons. This coder, called a neural source-coder, uses an adaptive threshold to internally reconstruct the stimulus. The spikes are timed to minimize coding error. These spikes are generated by a deterministic firing rule. However, some random variability in spike timing is observed in real data. It seems reasonable to account for the variability by adding a stochastic component to the deterministic model.

Previously, the source-coding neuron used a constant threshold for generating spikes, while the stochastic neural encoder uses a partially randomized threshold. In this thesis we explore this random component and its success in explaining and recreating experimentally obtained spike-train statistics (from P-type electrosensory afferents of weakly electric fish). We also take a close look at the growth in variance of inter-spike intervals (ISIs) and the deviation of the stochastic source-coding neuron from an ideal DC-block system with infinite memory. The stochastic source-coding neuron model was able to achieve very accurate reconstructions of P-type weakly electric fish spike-time statistics (inter-spike interval histograms, serial correlation coefficients) with a very simple model consisting of only four free tuning parameters. We were also able to demonstrate a markedly slower growth in variance consistent with experimental data but which Poisson spike trains fail to capture. We were also able to derive mathematical correspondence for the observed experimental behavior such as the SCC trends, the rate of growth in variance of the ISIs and the power spectrum of the spike trains at low frequencies. The simulations back the mathematical findings illustrating the success of the model at creating statistically accurate and realistic spike trains.