Document Type





Sigmoids, Simple sigmoids, Hyperbolic sigmoids






Sigmoid functions, whose graphs are “S-shaped” curves, appear in a great variety of contexts, such as the transfer functions in many neural networks. Their ubiquity is no accident; these curves are among the simplest non-linear curves, striking a graceful balance between linear and non-linear behavior. .. This paper undertakes a study of two classes of sigmoids: the simple sigmoids, defined to be odd, asymptotically bounded, completely monotone functions in one variable, and the Hyperbolic sigmoids, a proper subset of simple sigmoids and a natural generalization of the hyperbolic tangent. The class of hyperbolic sigmoids includes a surprising number of well know sigmoids. The regular structure of the simple sigmoids often makes a theory tractable, paving the way for more general analysis.

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Creative Commons Attribution 3.0 License
This work is licensed under a Creative Commons Attribution 3.0 License.

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Mathematics Commons



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