Modeling higher-order network adaptation by multilevel network reification

In network models for real-world domains, often some form of network adaptation has to be incorporated, based on certain network adaptation principles. In some cases, also higher-order adaptation occurs: the adaptation principles themselves also change over time. To model such multilevel adaptation processes, it is useful to have some generic architecture. Such an architecture should describe and distinguish the dynamics within the network (base level), but also the dynamics of the network itself by certain adaptation principles (first-order adaptation), and also the adaptation of these adaptation principles (second-order adaptation), and maybe still more levels of higher-order adaptation. This chapter introduces a multilevel network architecture for this, based on the notion of network reification. Reification of a network occurs when a base network is extended by adding explicit reification states representing the characteristics of the structure of the base network (Connectivity, Aggregation, and Timing). In Chap. 3, it was shown how this construction can be used to explicitly represent network adaptation principles within a network. In the current chapter, it is discussed how, when the reified network is itself also reified, also second-order adaptation principles can be explicitly represented. For the multilevel network reification construction introduced here, it is shown how it can be used to model plasticity and metaplasticity as known from Cognitive Neuroscience. Here, plasticity describes how connections between neurons change over time, for example, based on a first-order adaptation principle for Hebbian learning, and metaplasticity describes second-order adaptation principles determining how the extent of plasticity is affected by certain circumstances; for example, under which circumstances plasticity will be accelerated or decelerated.