Relating a Reified Adaptive Network’s Emerging Behaviour Based on Hebbian Learning to Its Reified Network Structure

Abstract

In this chapter another challenge is analysed for how emerging behaviour of an adaptive network can be related to characteristics of the adaptive network’s structure. By applying network reification, the adaptation structure is modeled itself as a network too: as a subnetwork of the reified network extending the base network. In particular, this time the challenge is addressed for mental networks with adaptive connection weights based on Hebbian learning. To this end relevant properties of the network and the adaptation principle that have been identified are discussed. Using network reification for modeling of the adaptation principle, a central role is played by the combination function specifying the aggregation for the reification states of the connection weights, and in particular, identified mathematical properties of this combination function. As one of the results it has been found that under some conditions in an achieved equilibrium state the value of a connection weight has a functional relation to the values of the connected states that can be identified.