Spatial Organization of Neural Networks: A Probabilistic Modeling Approach

ABSTRACT The aim of this paper is to explore the spatial organization of neural networks under Markovian assumptions, in what concerns the behaviour ofindividual cells and the interconnection mechanism. Spaceorganizational propertiesof neural nets are very relevant in image modeling and pattern analysis, where spatial computations on stochastic two-dimensionalimage fields are involved. As a first approach we develop a random neural network model, based upon simple probabilistic assumptions,whose organization is studied by means of discrete-event simulation.We then investigate the possibility of approXimating therandom network's behaviour by using an analytical approach originating from the theory of general product-form queueing networks. The neural network is described by an open network of nodes, inwhich customers moving from node to node represent stimulations andconnections between nodes are expressed in terms of suitably selectedrouting probabilities. We obtain the solution of the model under different disciplines affecting the time spent by a stimulation ateach node visited.