Recording from two neurons: second order stimulus reconstruction from spike trains and population coding

TL;DR

This study reconstructs visual stimuli from fly neuron spike trains, demonstrating that second order correlations improve accuracy, especially during specific events, and introduces a Gaussian-like approximation for complex correlation functions.

Contribution

The paper introduces a Gaussian-like representation for fourth order correlation functions, enabling effective second order stimulus reconstruction from neural spike trains.

Findings

Second order kernels contribute about 8% to rotational stimulus reconstruction.

Instant-dependent analysis shows up to 100% improvement with second order kernels during specific events.

Reconstruction of translational stimuli remains challenging with current methods.

Abstract

We study the reconstruction of visual stimuli from spike trains, recording simultaneously from the two H1 neurons located in the lobula plate of the fly Chrysomya megacephala. The fly views two types of stimuli, corresponding to rotational and translational displacements. If the reconstructed stimulus is to be represented by a Volterra series and correlations between spikes are to be taken into account, first order expansions are insufficient and we have to go to second order, at least. In this case higher order correlation functions have to be manipulated, whose size may become prohibitively large. We therefore develop a Gaussian-like representation for fourth order correlation functions, which works exceedingly well in the case of the fly. The reconstructions using this Gaussian-like representation are very similar to the reconstructions using the experimental correlation functions. The overall contribution to rotational stimulus reconstruction of the second order kernels - measured by a chi-squared averaged over the whole experiment - is only about 8% of the first order contribution. Yet if we introduce an instant-dependent chi-square to measure the contribution of second order kernels at special events, we observe an up to 100% improvement. As may be expected, for translational stimuli the reconstructions are rather poor. The Gaussian-like representation could be a valuable aid in population coding with large number of neurons.