Inference on the Macroscopic Dynamics of Spiking Neurons

The process of inference on networks of spiking neurons is essential to decipher the underlying mechanisms of brain computation and function. In this study, we conduct inference on parameters and dynamics of a mean-field approximation, simplifying the interactions of neurons. Estimating parameters of this class of generative model allows one to predict the system's dynamics and responses under changing inputs and, indeed, changing parameters. We first assume a set of known state-space equations and address the problem of inferring the lumped parameters from observed time series. Crucially, we consider this problem in the setting of bistability, random fluctuations in system dynamics, and partial observations, in which some states are hidden. To identify the most efficient estimation or inversion scheme in this particular system identification, we benchmark against state-of-the-art optimization and Bayesian estimation algorithms, highlighting their strengths and weaknesses. Additionally, we explore how well the statistical relationships between parameters are maintained across different scales. We found that deep neural density estimators outperform other algorithms in the inversion scheme, despite potentially resulting in overestimated uncertainty and correlation between parameters. Nevertheless, this issue can be improved by incorporating time-delay embedding. We then eschew the mean-field approximation and employ deep neural ODEs on spiking neurons, illustrating prediction of system dynamics and vector fields from microscopic states. Overall, this study affords an opportunity to predict brain dynamics and responses to various perturbations or pharmacological interventions using deep neural networks.