Efficient Inference on a Network of Spiking Neurons using Deep Learning

Abstract

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.

Simulation-based inference on virtual brain models of disorders

“…Although, we have shown that this non-parametric approach is able to accurately estimate the spatial map of epileptogenicity across whole-brain areas, it required a reparameterization over model configuration space to facilitate efficient exploration of the posterior distribution in terms of computational time and convergence diagnostics (Jha et al 2022). In the presence of metastability in the state space (see figures 1 and S1), MCMC methods require either more computational cost or intricately designed sampling strategies (Gabrié et al 2022, Jha et al 2022, Baldy et al 2023, whereas SBI allows for efficient Bayesian estimation without the access to the full knowledge on the state space representation of a system (Baldy et al 2024). Note that we used the data features derived from only firing rates, while the information related to membrane potential activities was treated as missing data (i.e.…”

“…SBI (Cranmer et al 2020, Boelts et al 2022 or likelihood-free inference (Papamakarios et al 2019b sidesteps problems with MCMC sampling such as geometrical issues (Betancourt et al 2014, Betancourt 2016, immense computational cost (Baldy et al 2024), and algorithm sequentiality entirely: SBI uses the generative model to map samples from the prior (i.e background knowledge) to a corresponding set of low dimensional data features, and then it takes a maximum likelihood estimate of a Bayesian regression of model parameters on data features. In practice, to ensure the resulting approximate posterior density is sufficiently expressive, these methods employ deep neural networks to parametrize or construct directly the approximated density (Greenberg et al 2019.…”