Generative Embeddings of Brain Collective Dynamics Using Variational Autoencoders

We consider the problem of encoding pairwise correlations between coupled dynamical systems in a low-dimensional latent space based on few distinct observations. We use variational autoencoders (VAEs) 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 results in an embedding that encodes the repertoire of collective dynamics, as well as the topology of the underlying connectivity network. We first follow this approach to infer the trajectory of brain states measured from wakefulness to deep sleep from the two end points of this trajectory; then, we show that the same architecture was capable of representing the pairwise correlations of generic Landau-Stuart oscillators coupled by complex network topology.