Generative embeddings of brain collective dynamics using variational autoencoders

TL;DR

This paper demonstrates how variational autoencoders can embed complex brain dynamics and connectivity into a low-dimensional space, capturing the full range of collective behaviors during sleep-wake cycles.

Contribution

It introduces a novel VAE-based approach to encode and analyze pairwise correlations in coupled brain oscillators, revealing the topology of underlying networks.

Findings

VAE successfully embeds brain state trajectories into a 2D manifold.

The embedding captures the topology of the connectivity network.

The method generalizes to generic coupled oscillators with complex topology.

Abstract

We consider the problem of encoding pairwise correlations between coupled dynamical systems in a low-dimensional latent space based on few distinct observations. We used variational autoencoders (VAE) to embed temporal correlations between coupled nonlinear oscillators that model brain states in the wake-sleep cycle into a two-dimensional manifold. Training a VAE with samples generated using two different parameter combinations resulted in an embedding that represented the whole repertoire of collective dynamics, as well as the topology of the underlying connectivity network. We first followed this approach to infer the trajectory of brain states measured from wakefulness to deep sleep from the two endpoints of this trajectory; next, we showed that the same architecture was capable of representing the pairwise correlations of generic Landau-Stuart oscillators coupled by complex network topology