Subspace Extracting Adaptive Cellular Network for Layered Architectures with Circular Boundaries

An abstract interpretation of an adaptive neural network is where each cell is considered as an agent that has internal states and interaction rules along with a set of strategies that modulates its internal states and its interaction with neighboring agents. While the internal states are governed by the processing equation, the selection of strategies is governed by the learning equations. Adaptivity of agents as a collective behavior that perform subspace extraction is observed in many different areas like cell differentiation in multi-cellular organisms, smart fluids, synaptic plasticity in neuronal ensemble and being applied in other areas like economic strategies, social networks, vlsi designing etc and thus studies of such models for more complex architectures (other than traditionally layered) become very relevant for modeling real world applications. Since, no such widely accepted matrix notation for arbitrary graph exists, the study of such network structures is hindered. In this paper, we study such a recursive cellular network for layered networks and its behavior when applied over a special class of layered architecture where the boundaries of the network are merged.