Emergent Criticality Through Adaptive Information Processing in Boolean Networks

TL;DR

This paper demonstrates that Boolean networks with evolving connectivity naturally evolve towards a critical state at K=2, optimizing learning, robustness, and diversity, especially near criticality, with implications for designing adaptive computational systems.

Contribution

It solves a long-standing open question by showing that adaptive Boolean networks tend toward critical connectivity, optimizing information processing and robustness.

Findings

Networks approach critical connectivity as system size increases.

Learning and generalization are maximized near criticality.

Topological diversity peaks at critical connectivity.

Abstract

We study information processing in populations of Boolean networks with evolving connectivity and systematically explore the interplay between the learning capability, robustness, the network topology, and the task complexity. We solve a long-standing open question and find computationally that, for large system sizes $N$, adaptive information processing drives the networks to a critical connectivity $K_{c}=2$. For finite size networks, the connectivity approaches the critical value with a power-law of the system size $N$. We show that network learning and generalization are optimized near criticality, given task complexity and the amount of information provided threshold values. Both random and evolved networks exhibit maximal topological diversity near $K_{c}$. We hypothesize that this supports efficient exploration and robustness of solutions. Also reflected in our observation is that the variance of the values is maximal in critical network populations. Finally, we discuss implications of our results for determining the optimal topology of adaptive dynamical networks that solve computational tasks.