Efficient coding under constraint drives neural systems towards criticality and sloppiness

TL;DR

This paper presents a theoretical framework linking efficient coding to neural criticality, explaining how resource constraints lead to critical states and neural sloppiness, supported by numerical simulations.

Contribution

It introduces a Gaussian population coding model that connects efficient coding principles to neural criticality and sloppiness, unifying different perspectives.

Findings

Maximizing Fisher information under constraints leads to criticality features.

Spatial structure unifies statistical and dynamical criticality.

Optimization results in power-law neural responses.

Abstract

It is widely accepted that the brain operates near a critical state, characterized by neural avalanches that follow power-law distributions. However, the functional rationale for why neural systems attain criticality remains unclear. Here, we present a theoretical framework that links efficient coding to criticality in neural populations. Using a Gaussian population coding model, we demonstrate that maximizing Fisher information under resource constraints naturally leads to the emergence of soft modes and diverging correlation lengths, which are hallmarks of criticality. By introducing spatial structure, we unify two distinct perspectives of criticality: statistical criticality with diverging correlation lengths and dynamical criticality with critical slowing down as well as bifurcation. Furthermore, this framework provides a natural explanation for the sloppiness observed in neural systems. Numerical simulations confirm that optimization results in power-law response, providing a mechanistic link between efficient coding, sloppiness and the critical brain hypothesis.