# Identification of recurrent dynamics in distributed neural populations

## TL;DR

This paper explores how linear models can capture brain activity dynamics and finds that considering noise and regime switching improves model accuracy.

## Contribution

The study introduces a scalable tensor-based approach to uncover recurrent dynamics in neural populations and highlights the importance of noise and regime switching.

## Key findings

- A low-rank tensor approach recovers attractor structures in stochastic neural models.
- Hierarchical clustering of dynamics is revealed using human brain connectivity simulations.
- Forecast time delay impacts the estimation of dynamic structure and temporal variability.

## Abstract

Large-scale recordings of neural activity over broad anatomical areas with high spatial and temporal resolution are increasingly common in modern experimental neuroscience. Recently, recurrent switching dynamical systems have been used to tackle the scale and complexity of these data. However, an important challenge remains in providing insights into the existence and structure of recurrent linear dynamics in neural time series data. Here we test a scalable approach to time-varying autoregression with low-rank tensors to recover the recurrent dynamics in stochastic neural mass models with multiple stable attractors. We demonstrate that the parsimonious representation of time-varying system matrices in terms of temporal modes can recover the attractor structure of simple systems via clustering. We then consider simulations based on a human brain connectivity matrix in high and low global connection strength regimes, and reveal the hierarchical clustering structure of the dynamics. Finally, we explain the impact of the forecast time delay on the estimation of the underlying rank and temporal variability of the time series dynamics. This study illustrates that prediction error minimization is not sufficient to recover meaningful dynamic structure and that it is crucial to account for the three key timescales arising from dynamics, noise processes, and attractor switching.

How can we make sense of the complex data we obtain from brain recordings? Linear systems are the most straightforward approach for describing brain dynamics. Many techniques have been developed that use sets of linear systems to predict and understand brain activity, including the discovery of recurrent linear dynamics. In this study, we use simulations of interacting neural populations to test whether linear recurrent dynamics are an appropriate description for noisy brain activity. Using a data-driven model, we uncover the neural dynamic structure and delineate the conditions under which there exist separate well-defined linear regimes. Moreover, we reveal the importance of looking beyond prediction error minimization in fitting linear models. We arrive at the seemingly paradoxical conclusion that accounting for the contributions of noise and regime switching is easier when predicting farther into the future. The insights and strategies we present will be helpful in making sense of complex brain data while minimizing bias in their interpretation.