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-standin
g 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.
Independent of the technology, it is generally expected that future nanoscale devices will be built from vast numbers of densely arranged devices that exhibit high failure rates. Other than that, there is little consensus on what type of technology a
nd computing architecture holds most promises to go far beyond todays top-down engineered silicon devices. Cellular automata (CA) have been proposed in the past as a possible class of architectures to the von Neumann computing architecture, which is not generally well suited for future parallel and fine-grained nanoscale electronics. While the top-down engineered semi-conducting technology favors regular and locally interconnected structures, future bottom-up self-assembled devices tend to have irregular structures because of the current lack precise control over these processes. In this paper, we will assess random dynamical networks, namely Random Boolean Networks (RBNs) and Random Threshold Networks (RTNs), as alternative computing architectures and models for future information processing devices. We will illustrate that--from a theoretical perspective--they offer superior properties over classical CA-based architectures, such as inherent robustness as the system scales up, more efficient information processing capabilities, and manufacturing benefits for bottom-up designed devices, which motivates this investigation. We will present recent results on the dynamic behavior and robustness of such random dynamical networks while also including manufacturing issues in the assessment.
