Efficient Inference on a Network of Spiking Neurons using Deep Learning

The process of making inference on networks of spiking neurons is crucial to decipher the underlying mechanisms of neural computation. Mean-field theory simplifies the interactions between neurons to produce macroscopic network behavior, facilitating the study of information processing and computation within the brain. In this study, we perform inference on a mean-field model of spiking neurons to gain insight into likely parameter values, uniqueness and degeneracies, and also to explore how well the statistical relationship between parameters is maintained by traversing across scales. We benchmark against state-of-the-art optimization and Bayesian estimation algorithms to identify their strengths and weaknesses in our analysis. We show that when confronted with dynamical noise or in the case of missing data in the presence of bistability, generating probability distributions using deep neural density estimators outperforms other algorithms, such as adaptive Monte Carlo sampling. However, this class of deep generative models may result in an overestimation of uncertainty and correlation between parameters. Nevertheless, this issue can be improved by incorporating time-delay embedding. Moreover, we show that training deep Neural ODEs on spiking neurons enables the inference of system dynamics from microscopic states. In summary, this work demonstrates the enhanced accuracy and efficiency of inference on networks of spiking neurons when deep learning is harnessed to solve inverse problems in neural computation.