Network Risk in Artificial Network-Flow Neural Networks with Capacities

Abstract:
Introducing of risk in the artificial neural networks, based on generalized network-flow is proposed in the present work. The risk is considered as a product of the corresponding signal’s level and the probability of an adverse event, related to the signal’s distortion. A case is considered when the probability of adverse events is one and the same for all neurons. It is proved that in this case a one-to-one mapping exists between the signals’ flow and the risk flow and a series of results are achieved for those two flows, as well as such related to the network coefficients for teaching. It is proved that their minimal cuts match each other. A numerical example is given, which demonstrates the validity of the results obtained and the possibility for their applications.