# Criticality as It Could Be: organizational invariance as self-organized criticality in embodied agents

## TL;DR

This paper presents a method for designing adaptive embodied agents that self-organize near critical points by maintaining organizational invariance, leveraging universality principles to achieve criticality without specific mechanistic requirements.

## Contribution

It introduces a novel synthetic approach that exploits organizational invariance and universality to induce criticality in embodied agents controlled by neural networks.

## Key findings

- Agents reach criticality at behavioral transition points
- Criticality maximizes mutual information between neurons and sensorimotor patterns
- Approach applicable to understanding criticality in biological systems

## Abstract

This paper outlines a methodological approach for designing adaptive agents driving themselves near points of criticality. Using a synthetic approach we construct a conceptual model that, instead of specifying mechanistic requirements to generate criticality, exploits the maintenance of an organizational structure capable of reproducing critical behavior. Our approach exploits the well-known principle of universality, which classifies critical phenomena inside a few universality classes of systems independently of their specific mechanisms or topologies. In particular, we implement an artificial embodied agent controlled by a neural network maintaining a correlation structure randomly sampled from a lattice Ising model at a critical point. We evaluate the agent in two classical reinforcement learning scenarios: the Mountain Car benchmark and the Acrobot double pendulum, finding that in both cases the neural controller reaches a point of criticality, which coincides with a transition point between two regimes of the agent's behaviour, maximizing the mutual information between neurons and sensorimotor patterns. Finally, we discuss the possible applications of this synthetic approach to the comprehension of deeper principles connected to the pervasive presence of criticality in biological and cognitive systems.