The stability analysis for a novel feedback neural network with partial connection

This paper develops a new Partially Feedback Neural Network with partial connection, which is so-called “Partially Connected Feedback Neural Network” (PCFNN). The information capacity improves and there is more hidden information for partially connected systems because the connections between neurons are random and there can be more than one layer. The proving of the convergence of PCFNN is provided. Owing to the complexities in partially connected systems, two theorems of its stability are proved theoretically by constructing a novel energy function expectation. Three examples are provided to simulate various conditions of stability by constructing different activation functions and weight matrixes. The simulation results show that this novel neural network is stable under different conditions. The expressive space of the network architecture is also much larger than the original Hopfield neural network architecture in the partially connected neural network architecture.