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

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.

Further streamlined version of the manuscript

References in corpus (18)

• Exact evolution equation for the effective potential
• The nonperturbative functional renormalization group and its applications
• Criticality in the brain: A synthesis of neurobiology, models and cognition
• Poisson point process models solve the "pseudo-absence problem" for presence-only data in ecology
• Griffiths phases on complex networks
• Non-perturbative fixed point in a non-equilibrium phase transition
• From local to critical fluctuations in lattice models: a non-perturbative renormalization-group approach
• Laplacian Renormalization Group for heterogeneous networks
• Non-perturbative Approach to Critical Dynamics
• Testing the critical brain hypothesis using a phenomelogical renormalization group
• Fully developed isotropic turbulence: symmetries and exact identities
• Complex networks with tuneable dimensions as a universality playground
• The dynamic critical exponent $z$ for 2d and 3d Ising models from five-loop $\epsilon$ expansion
• Gell-Mann-Low criticality in neural networks
• Fluctuating landscapes and heavy tails in animal behavior
• Critical dynamical behavior of the Ising model
• Long-Range and Many-Body Effects in Coagulation Processes
• Universal scaling in real dimension