The nlogistic-sigmoid function
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The variants of the logistic-sigmoid functions used in artificial neural networks are inherently, by definition, limited by vanishing gradients. Defining the logistic-sigmoid function to become n-times repeated over a finite input-output mapping can significantly reduce the presence of this limitation. Here we propose the nlogistic-sigmoid function as a generalization for the definition of logistic-sigmoid functions. Our results demonstrate that by its definition, the nlogistic-sigmoid function can reduce this vanishing of gradients, as it outperforms both the classic logistic-sigmoid function and the rectified linear-unit function in terms of learning and generalization on two representative case studies. We anticipate that this function will be the choice sigmoid activation function for deep learning.
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