# Mesoscopic modeling of hidden spiking neurons

arXiv: https://arxiv.org/abs/2205.13493 · HTML: https://mlsanity.com/paper/2205.13493/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 106 references that are in the map.
- First posted on arXiv 26 May 2022.

## Builds on (most cited first, 16 of 16)

- [Flexible statistical inference for mechanistic models of neural dynamics](https://mlsanity.com/paper/1711.01861/) (2017)
- [Linear dynamical neural population models through nonlinear embeddings](https://mlsanity.com/paper/1605.08454/) (2016)
- [Learning interpretable continuous-time models of latent stochastic dynamical systems](https://mlsanity.com/paper/1902.04420/) (2019)
- [Tree-Structured Recurrent Switching Linear Dynamical Systems for Multi-Scale Modeling](https://mlsanity.com/paper/1811.12386/) (2018)
- [On Simplicity and Complexity in the Brave New World of Large-Scale Neuroscience](https://mlsanity.com/paper/1503.08779/) (2015)
- [Interpretable Nonlinear Dynamic Modeling of Neural Trajectories](https://mlsanity.com/paper/1608.06546/) (2016)
- [Fitting summary statistics of neural data with a differentiable spiking network simulator](https://mlsanity.com/paper/2106.10064/) (2021)
- [Metastable dynamics of neural circuits and networks](https://mlsanity.com/paper/2110.03025/) (2021)
- [Comparative Analysis of Viterbi Training and Maximum Likelihood Estimation for HMMs](https://mlsanity.com/paper/1312.4551/) (2013)
- [Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size](https://mlsanity.com/paper/1611.00294/) (2016)
- [Expectation-induced modulation of metastable activity underlies faster coding of sensory stimuli](https://mlsanity.com/paper/1710.02563/) (2017)
- [Mesoscopic population equations for spiking neural networks with synaptic short-term plasticity](https://mlsanity.com/paper/1812.09414/) (2018)
- [Cortical computations via metastable activity](https://mlsanity.com/paper/1906.07777/) (2019)
- [Inference of a mesoscopic population model from population spike trains](https://mlsanity.com/paper/1910.01618/) (2019)
- [Dynamics of multi-stable states during ongoing and evoked cortical activity](https://mlsanity.com/paper/1508.00165/) (2015)
- [Mind the Last Spike -- Firing Rate Models for Mesoscopic Populations of Spiking Neurons](https://mlsanity.com/paper/1909.10007/) (2019)

## Built on by (most cited first, 2 of 2)

- [Ternary Spike: Learning Ternary Spikes for Spiking Neural Networks](https://mlsanity.com/paper/2312.06372/) (2023)
- [ReverB-SNN: Reversing Bit of the Weight and Activation for Spiking Neural Networks](https://mlsanity.com/paper/2506.07720/) (2025)

## Abstract (arXiv)

Can we use spiking neural networks (SNN) as generative models of multi-neuronal recordings, while taking into account that most neurons are unobserved? Modeling the unobserved neurons with large pools of hidden spiking neurons leads to severely underconstrained problems that are hard to tackle with maximum likelihood estimation. In this work, we use coarse-graining and mean-field approximations to derive a bottom-up, neuronally-grounded latent variable model (neuLVM), where the activity of the unobserved neurons is reduced to a low-dimensional mesoscopic description. In contrast to previous latent variable models, neuLVM can be explicitly mapped to a recurrent, multi-population SNN, giving it a transparent biological interpretation. We show, on synthetic spike trains, that a few observed neurons are sufficient for neuLVM to perform efficient model inversion of large SNNs, in the sense that it can recover connectivity parameters, infer single-trial latent population activity, reproduce ongoing metastable dynamics, and generalize when subjected to perturbations mimicking photo-stimulation.