Generative Embeddings of Brain Collective Dynamics Using Variational Autoencoders.

Area of Science:

• Computational neuroscience
• Dynamical systems theory
• Machine learning

Background:

• Coupled dynamical systems exhibit complex behaviors relevant to brain states.
• Encoding these correlations in a low-dimensional space is challenging.
• Variational autoencoders (VAEs) offer a potential solution for dimensionality reduction.

Purpose of the Study:

• To encode pairwise correlations of coupled dynamical systems into a low-dimensional latent space.
• To utilize VAEs for embedding temporal correlations of nonlinear oscillators modeling brain states.
• To infer brain state trajectories and network topology from limited observations.

Main Methods:

• Employing variational autoencoders (VAEs) to embed temporal correlations.
• Training VAEs with samples from coupled nonlinear oscillators representing wake-sleep cycles.
• Analyzing the resulting two-dimensional manifold for encoded dynamics and network topology.

Main Results:

• A trained VAE successfully encoded collective dynamics and network topology.
• The VAE inferred brain state trajectories from wakefulness to deep sleep using endpoint data.
• The architecture also represented pairwise correlations in generic Landau-Stuart oscillators with complex network topology.

Conclusions:

• VAEs can effectively embed complex dynamics and network structures into low-dimensional spaces.
• This approach facilitates the inference of system states and connectivity from sparse data.
• The method is applicable to modeling brain states and other complex coupled systems.