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Implementation feasibility of convex recursive deletion regions using multi-layer perceptrons

A constructive algorithm to implement convex recursive deletion regions via two-layer perceptrons has been presented in a recent study. In the algorithm, the absolute values of the weights become larger and larger when the number of nested layers of a convex recursive deletion region increases. In addition, the absolute values of the weights are determined according to the complexity of the structure of the convex recursive deletion region. More complicated convex recursive deletion regions result in larger values of weights. Besides, the constructive procedure is needed to get the parameters (weights and thresholds) for the neural networks. In this paper, we propose a simple three-layer network structure to implement the convex recursive deletion regions in which all weights of the second and third layers are all 1's and the thresholds for the nodes in the second layer are pre-determined according to the structures of the convex recursive deletion regions. This paper also provides the activation function for the output node. In brief, all of parameters (weights and activation functions) in the proposed structure are pre-determined and no constructive algorithm is needed for solving the convex recursive deletion region problems. We prove the feasibility of the proposed structure and give an illustrative example to demonstrate how the proposed structure implements the convex recursive deletion regions. Finally, we provide the conceptual diagram of the hardware implementation of the proposed network structure.