Repertoire of scaling exponents across brain areas captured by a simple latent variable model

The ability to record from thousands of neurons simultaneously raises new possibilities for examining the emergent behavior of neural populations, hinting at simpler descriptions of complicated datasets. Along these lines, the recently developed phenomenological renormalization group (pRG) analysis has revealed scale-free properties of large neural population recordings in multiple brain regions and different modalities. Observed scaling phenomena (variance, free energy, covariance spectra) of neural networks under coarse graining may be evidence of criticality. However, scaling can also arise in a model without phase transitions, in which the evolution of neurons is driven by a few latent variables. Previously, such a model reproduced scaling phenomena reported in mouse hippocampus, but some parameter tuning was required and its generalization to capture scaling observed in other brain regions was unclear. Here, we systematically vary model parameters to examine the conditions under which scaling under pRG analysis emerges and how scaling exponents depend on model parameters. We show that while the model requires some tuning to produce scaling, the same tuning is required to match the heavy-tailed distribution of the firing rates observed in neural data. Additionally, we find that signatures in most other brain regions can also be captured by the model by changing the number of latent variables and the strength of coupling to the latent variables. Our results suggest that low dimensional structure and skewed firing rate distributions are the key ingredients for signatures of neural criticality under pRG analysis.