Topological features of spike trains in recurrent spiking neural networks that are trained to generate spatiotemporal patterns

Abstract

In this study, we focus on training recurrent spiking neural networks to generate spatiotemporal patterns in the form of closed two-dimensional trajectories. Spike trains in the trained networks are examined in terms of their dissimilarity using the Victor-Purpura distance. We apply algebraic topology methods to the matrices obtained by rank-ordering the entries of the distance matrices, specifically calculating the persistence barcodes and Betti curves. By comparing the features of different types of output patterns, we uncover the complex relations between low-dimensional target signals and the underlying multidimensional spike trains.

Keywords: persistent homology; reservoir computing; spike metrics; spiking neural network; supervised learning; target spatiotemporal pattern.