# Detecting Signatures of Criticality Using Divergence Rate

## TL;DR

This paper introduces a new method to detect criticality in complex systems, linking it to optimal information processing in biology and other domains.

## Contribution

A novel measure based on rate-distortion theory is proposed to detect criticality and support the hypothesis of optimal processing.

## Key findings

- The measure accurately identifies critical trade-off parameters in rate-distortion problems.
- It supports the hypothesis that critical behavior is linked to optimal processing in various systems.
- Applications include sensory coding, machine learning, and natural language processing.

## Abstract

Oftentimes in a complex system it is observed that as a control parameter is varied, there are certain intervals during which the system undergoes dramatic change. In biology especially, these signatures of criticality are thought to be connected with efficient computation and information processing. Guided by the classical theory of rate–distortion (RD) from information theory, we propose a measure for detecting and characterizing such phenomena from data. When applied to RD problems, the measure correctly identifies exact critical trade-off parameters emerging from the theory and allows for the discovery of new conjectures in the field. Other application domains include efficient sensory coding, machine learning generalization, and natural language. Our findings give support to the hypothesis that critical behavior is a signature of optimal processing.