Learning, Generalization, and Functional Entropy in Random Automata Networks
This work incrementally extends prior research on feedforward Boolean networks by applying state-topology evolution to random Boolean networks, with potential implications for understanding learning in complex systems.
The authors tackled the problem of evolving random Boolean networks to perform simple tasks, showing that networks with higher connectivity achieve better memorization and partial generalization, while near-critical connectivity yields higher perfect generalization on the even-odd task.
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.