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In recent years, commercial banks and rural financial institutions in and below the county area have developed rapidly, and the number of outlets has increased rapidly. But for the vast rural areas of the country, the number of outlets is still limited. At present, there are still a large number of areas with zero financial coverage in rural the country. The development of the financial industry in a region not only affects the level of local economic growth but also has a good effect on improving the income level of local residents and changing the way of local economic development. To better develop rural finance and county economy, this paper constructs an artificial neural network model and FA model to predict the rural finance industry, and four indicators are selected to test the performance measurement of the model. The hit rates of the five models are 54.65%, 53.75%, 59.78%, 65.1%, and 73.08%, respectively. The model proposed in this paper has the highest hit rate and can predict rural finance more accurately as well, allowing for clearer changes in county economic and industrial growth. [ABSTRACT FROM AUTHOR]

How the human brain does recognition is still an open question. No physical or biological experiment can fully reveal this process. Psychological evidence is more about describing phenomena and laws than explaining the physiological processes behind them. The need for interpretability is well recognized. This paper proposes a new method for supervised pattern recognition based on the working pattern of implicit memory. The artificial neural network (ANN) is trained to simulate implicit memory. When an input vector is not in the training set, the ANN can treat the input as a "do not care" term. The ANN may output any value when the input is a "do not care" term since the training process needs to use as few neurons as possible. The trained ANN can be expressed as a function to design a pattern recognition algorithm. Using the Mixed National Institute of Standards and Technology database, the experiments show the efficiency of the pattern recognition method. [ABSTRACT FROM AUTHOR]

In many applications, it is natural to use interval data to describe various kinds of uncertainties. This paper is concerned with an interval neural network with a hidden layer. For the original interval neural network, it might cause oscillation in the learning procedure as indicated in our numerical experiments. In this paper, a smoothing interval neural network is proposed to prevent the weights oscillation during the learning procedure. Here, by smoothing we mean that, in a neighborhood of the origin, we replace the absolute values of the weights by a smooth function of the weights in the hidden layer and output layer. The convergence of a gradient algorithm for training the smoothing interval neural network is proved. Supporting numerical experiments are provided. [ABSTRACT FROM AUTHOR]

The online gradient method has been widely used in training neural networks. We consider in this paper an online split-complex gradient algorithm for complex-valued neural networks. We choose an adaptive learning rate during the training procedure. Under certain conditions, by firstly showing the monotonicity of the error function, it is proved that the gradient of the error function tends to zero and the weight sequence tends to a fixed point. A numerical example is given to support the theoretical findings. [ABSTRACT FROM AUTHOR]

The problem of stochastic stability is investigated for a class of neural networks with both Markovian jump parameters and continuously distributed delays. The jumping parameters are modeled as a continuous-time, finite-state Markov chain. By constructing appropriate Lyapunov-Krasovskii functionals, some novel stability conditions are obtained in terms of linear matrix inequalities (LMIs). The proposed LMI-based criteria are computationally efficient as they can be easily checked by using recently developed algorithms in solving LMIs. A numerical example is provided to show the effectiveness of the theoretical results and demonstrate the LMI criteria existed in the earlier literature fail. The results obtained in this paper improve and generalize those given in the previous literature. [ABSTRACT FROM AUTHOR]