Topological exploration of artificial neuronal network dynamics

Author:

Bardin Jean-Baptiste1,Spreemann Gard1,Hess Kathryn1

Affiliation:

1. Laboratory for Topology and Neuroscience, Brain Mind Institute, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

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.

Funder

Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

Publisher

MIT Press - Journals

Subject

Applied Mathematics,Artificial Intelligence,Computer Science Applications,General Neuroscience

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