On the Effect of Topology on Learning and Generalization in Random Automata Networks

We extend the study of learning and generalization in feedforward Boolean networks [70, 93] to random Boolean networks (RBNs). We explore the relationship between the learning capability and the network topology, the system size, the training sample size, and the complexity of the computational tasks. We show experimentally that there exists a critical connectivity Kc that improves the generalization and adaptation in networks. In addition, we show that in finite size networks, the critical K is a power-law function of the system size N and the fraction of inputs used during the training. We explain why adaptation improves at this critical connectivity by showing that the network ensemble manifests maximal topological diversity near Kc. Our work is partly motivated by self-assembled molecular and nanoscale electronics. Our findings allow to determine an automata network topology class for efficient and robust information processing.