Phase transitions in in vivo or in vitro populations of spiking neurons belong to different universality classes

TL;DR

This paper develops a renormalization group approach to analyze phase transitions in neural populations, revealing different universality classes for in vivo and in vitro circuits and providing insights into critical neural dynamics.

Contribution

The authors introduce a novel renormalization group method tailored for biologically constrained neural models, establishing a scaling theory for neural activity at criticality and distinguishing universality classes.

Findings

In vivo and in vitro neural circuits belong to different universality classes.

Both circuit types can exhibit anomalous scaling at critical excitation-inhibition balance.

Theoretical predictions are validated through neural activity simulations.

Abstract

The "critical brain hypothesis" posits that neural circuitry may be tuned close to a "critical point" or "phase transition" -- a boundary between different operating regimes of the circuit. The renormalization group and theory of critical phenomena explain how systems tuned to a critical point display scale invariance due to fluctuations in activity spanning a wide range of time or spatial scales. In the brain this scale invariance has been hypothesized to have several computational benefits, including increased collective sensitivity to changes in input and robust propagation of information across a circuit. However, our theoretical understanding of critical phenomena in neural circuitry is limited because standard renormalization group methods apply to systems with either highly organized or completely random connections. Connections between neurons lie between these extremes, and may be either excitatory (positive) or inhibitory (negative), but not both. In this work we develop a renormalization group method that applies to models of spiking neural populations with some realistic biological constraints on connectivity, and derive a scaling theory for the statistics of neural activity when the population is tuned to a critical point. We show that the scaling theories differ for models of in vitro versus in vivo circuits -- they belong to different "universality classes" -- and that both may exhibit "anomalous" scaling at a critical balance of inhibition and excitation. We verify our theoretical results on simulations of neural activity data, and discuss how our scaling theory can be further extended and applied to real neural data.