Topological exploration of artificial neuronal network dynamics

TL;DR

This paper introduces a novel algebraic topology-based method using persistent homology to classify neural network dynamics from spike train data, outperforming traditional approaches and generalizing across different networks.

Contribution

The authors develop a topological approach for classifying neural network regimes, providing a new tool that captures global network properties beyond traditional statistical methods.

Findings

Topological features effectively classify network dynamics.

Machine learning models trained on these features generalize well.

Combining multiple spike-train distances improves classification accuracy.

Abstract

One of the paramount challenges in neuroscience is to understand the dynamics of individual neurons and how they give rise to network dynamics when interconnected. Historically, researchers have resorted to graph theory, statistics, and statistical mechanics to describe the spatiotemporal structure of such network dynamics. Our novel approach employs tools from algebraic topology to characterize the global properties of network structure and dynamics. We propose a method based on persistent homology to automatically classify network dynamics using topological features of spaces built from various spike-train distances. We investigate the efficacy of our method by simulating activity in three small artificial neural networks with different sets of parameters, giving rise to dynamics that can be classified into four regimes. We then compute three measures of spike train similarity and use persistent homology to extract topological features that are fundamentally different from those used in traditional methods. Our results show that a machine learning classifier trained on these features can accurately predict the regime of the network it was trained on and also generalize to other networks that were not presented during training. Moreover, we demonstrate that using features extracted from multiple spike-train distances systematically improves the performance of our method.