Emergent Criticality Through Adaptive Information Processing in Boolean Networks

Details Emergent Criticality Through Adaptive Information Processing in Boolean Networks Emergent Criticality Through Adaptive Information Processing in Boolean Networks

2011-04-20

arxiv.org/abs/1104.4141v2

Physical Review Letters, 108(12):128702 (2012)

Physics

Condensed Matter

Disordered Systems and Neural Networks

5 pages, 4 figures

Scientific paper

10.1103/PhysRevLett.108.128702

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.

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