sigmoidto

Sigmoidto is a term used in mathematics and data science to denote a family of sigmoid-like transfer functions. Unlike the standard logistic sigmoid, sigmoidto functions incorporate additional shape parameters that allow greater flexibility in the curvature and asymptotes, enabling closer fits to data with uneven growth on the two sides of the inflection point.

Definition and properties: A sigmoidto function is monotone increasing, smooth, and bounded between 0 and 1. It typically preserves the key sigmoidal S-shape but permits variable left- and right-tail behavior and a tunable inflection location. Common implementations introduce one or more shape parameters that control steepness, asymmetry, and crossover point. In practice, sigmoidto is used as an activation function in neural networks or as a link function in probabilistic models.

Variations and examples: The explicit formula varies by implementation; a typical form generalizes the logistic function by adding a second tuning parameter that adjusts the tail widths. Other variants substitute a different base function or use piecewise definitions to achieve similar flexibility. In software libraries, sigmoidto is sometimes included as an option alongside the standard sigmoid, hyperbolic tangent, and softplus activations.

History and usage: The term sigmoidto appears in recent literature and software projects as a descriptive name for parameterized sigmoid activations and link functions. It is not a standardized mathematical object with a single canonical definition, and its exact form depends on the context.

See also: Sigmoid function, Logistic function, Activation function, Softplus, Monotone function.