On the Effect of Criticality and Topology on Learning in Random Boolean Networks

Random Boolean networks (RBN) are discrete dynamical systems composed of N automata with a binary state, each of which interacts with other automata in the network. RBNs were originally introduced as simplified models of gene regulation. In this presentation, I will present recent work done conjointly with Natali Gulbahce (UCSF), Thimo Rohlf (MPI, CNRS), and Christof Teuscher (PSU). We extend the study of learning in feedforward Boolean networks to random Boolean networks (RBNs) and systematically explore the relationship between the learning capability, the network topology, the system size N, the training sample T, and the complexity of the computational task. We find experimentally that for large system sizes N, there exists a critical connectivity Kc=2 that improves the learning in networks. We show that in finite size networks, the critical Kc scales as a power law of the system size N and the training sample T. During the learning process, the in-degree distribution evolves from a Poissonian to an exponential distribution. The improved learning capability is explained by a maximal topological diversity near Kc. Our findings have important implications for determining the optimal topology of complex dynamical networks that solve specific computational tasks.https://pdxscholar.library.pdx.edu/systems_science_seminar_series/1058/thumbnail.jp