Criticality or Supersymmetry Breaking ?

TL;DR

This paper links the noise-induced chaos phase in stochastic dynamical systems, characterized by supersymmetry breaking, to neurodynamics, suggesting the conscious brain operates within this phase, supported by theoretical and hardware-based evidence.

Contribution

It applies the supersymmetric theory of stochastic differential equations to neurodynamics, identifying the noise-induced chaos phase as essential for brain activity and consciousness.

Findings

The N-phase exhibits positive stochastic Lyapunov exponents.

Neurodynamics in the N-phase is dominated by instantonic processes.

The phase diagram on neuromorphic hardware shows the N-phase vanishes in the deterministic limit.

Abstract

In many stochastic dynamical systems, ordinary chaotic behavior is preceded by a full-dimensional phase that exhibits 1/f-type power-spectra and/or scale-free statistics of (anti)instantons such as neuroavalanches, earthquakes, etc. In contrast with the phenomenological concept of self-organized criticality, the recently developed approximation-free supersymmetric theory of stochastic differential equations, or stochastics, (STS) identifies this phase as the noise-induced chaos (N-phase), i.e., the phase where the topological supersymmetry pertaining to all stochastic dynamical systems is broken spontaneously by the condensation of the noise-induced (anti-)instantons. Here, we support this picture in the context of neurodynamics. We study a 1D chain of neuron-like elements and find that the dynamics in the N-phase is indeed featured by positive stochastic Lyapunov exponents and dominated by (anti)instantonic processes of (creation)annihilation of kinks and antikinks, which can be viewed as predecessors of boundaries of neuroavalanches. We also construct the phase diagram of emulated stochastic neurodynamics on Spikey neuromorphic hardware and demonstrate that the width of the N-phase vanishes in the deterministic limit in accordance with STS. As a first result of the application of STS to neurodynamics comes the conclusion that a conscious brain can reside only in the N-phase.