# Statistical models of neural activity, criticality, and Zipf's law

## TL;DR

This paper explores the relationship between criticality in neural dynamics, statistical models like maximum entropy, and Zipf's law, highlighting differences between statistical and dynamical criticality and their implications for neural activity analysis.

## Contribution

It clarifies the distinction between statistical and dynamical criticality in neural systems and examines the emergence of Zipf's law and Fisher information as indicators of criticality.

## Key findings

- Zipf's law observed in retinal activity under various conditions
- Divergence of specific heat as a signature of statistical criticality
- Examples of systems critical in one sense but not the other

## Abstract

In this overview, we discuss the connections between the observations of critical dynamics in neuronal networks and the maximum entropy models that are often used as statistical models of neural activity, focusing in particular on the relation between "statistical" and "dynamical" criticality. We present examples of systems that are critical in one way, but not in the other, exemplifying thus the difference of the two concepts. We then discuss the emergence of Zipf laws in neural activity, verifying their presence in retinal activity under a number of different conditions. In the second part of the chapter we review connections between statistical criticality and the structure of the parameter space, as described by Fisher information. We note that the model-based signature of criticality, namely the divergence of specific heat, emerges independently of the dataset studied; we suggest this is compatible with previous theoretical findings.