Learning, Generalization, and Functional Entropy in Random Automata Networks

TL;DR

This paper investigates how random Boolean networks can learn and generalize simple tasks through evolution, revealing how network connectivity influences their performance and introducing a new measure to describe their behavior.

Contribution

It extends previous work by experimentally demonstrating evolution-driven learning and generalization in random Boolean networks, and introduces a new measure for network behavior analysis.

Findings

Higher connectivity networks achieve better memorization.

Networks near critical connectivity show higher perfect generalization.

Maximum entropy network connectivity scales as a power-law with system size.

Abstract

It has been shown \citep{broeck90:physicalreview,patarnello87:europhys} that feedforward Boolean networks can learn to perform specific simple tasks and generalize well if only a subset of the learning examples is provided for learning. Here, we extend this body of work and show experimentally that random Boolean networks (RBNs), where both the interconnections and the Boolean transfer functions are chosen at random initially, can be evolved by using a state-topology evolution to solve simple tasks. We measure the learning and generalization performance, investigate the influence of the average node connectivity $K$, the system size $N$, and introduce a new measure that allows to better describe the network's learning and generalization behavior. We show that the connectivity of the maximum entropy networks scales as a power-law of the system size $N$. Our results show that networks with higher average connectivity $K$ (supercritical) achieve higher memorization and partial generalization. However, near critical connectivity, the networks show a higher perfect generalization on the even-odd task.