Latent fields lead to emergence of scaling in simulated neurons*

Understanding activity of large populations of neurons is difficult due to the combinatorial complexity of possible cell-cell interactions. A remedy is to note that many systems may be macroscopically described with models simpler than the system's microscopic behavior. This has been probed via a coarse-graining procedure on experimental neural recordings, which shows over two decades of scaling in free energy, variance, eigenvalue spectra, and correlation time [1], hinting that a mouse hippocampus operates in a critical regime. We investigated whether this scaling behavior could be explained as a result of coupling the neural population to latent dynamic stimuli. We conducted simulations of conditionally independent binary neurons coupled to a small number of long-timescale stochastic fields with and without periodic spatial stimuli (depicting neural place cells) and replicated the coarse-graining shown in [1]. In a biologically relevant regime, we find that much of the observed scaling [1] may be recreated by this model. This suggests that aspects of the scaling may be explained by coupling to hidden dynamic processes, a ubiquitous trait of neural systems.
[1] L. Meshulam et al. arXiv:1812.11904 [physics.bio-ph], 2019