# A New Network Flow Platform for Building Artificial Neural Networks

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## Abstract

A number of results are exposed in the present work, related to the transition being proposed from the widely spread nowadays platform for building up multilayer ANNs to a new platform, based on generalized network flows with gains and losses on directed graphs. It is shown that the network flow ANNs are of more general network structure than the multilayer ANNs and consequently all results obtained through the multilayer ANN are a part of the new network flow platform. A number of advantages of this new platform are pointed out. Generalized network flow with gains and losses is used in it as a base and on this ground, a mathematical model of ANN is proposed. A number of results are obtained for the network flow ANNs that are corollaries of the Ford-Fulkerson’s *mincut*-*maxflow* theorem, namely: existence of upper bound \(v_{max}\) of the flow from sources to consumers and lower bound \(c_{min}\) of capacity on all possible cuts, as well as equality between the maximal flow and the minimal cut. A way for building in additional linear constraints between the different signals in the ANN is pointed out. Defining of the optimal coefficients is carried out through corresponding optimization procedures with polynomial computational complexity of the network flow programming. The possibility for effective training and recognition is proven through rigorous procedures for the network flow platform and without using of heuristic algorithms for approximate solutions, characteristic to the multilayer ANNs.

## Keywords

Artificial neural networks Multilayer neural networks Network flow neural networks Mincut-maxflow theorem Network optimization procedures## References

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