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**A smoothing interval neural network.**
*(English)*
Zbl 1257.68130

Summary: 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.

### MSC:

68T05 | Learning and adaptive systems in artificial intelligence |

92B20 | Neural networks for/in biological studies, artificial life and related topics |

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\textit{D. Yang} and \textit{W. Wu}, Discrete Dyn. Nat. Soc. 2012, Article ID 456919, 25 p. (2012; Zbl 1257.68130)

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