artificial intelligence Artificial intelligence (AI) is the capability of computer, computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making. It is a field of re ...

, especially

computer vision Computer vision tasks include methods for image sensor, acquiring, Image processing, processing, Image analysis, analyzing, and understanding digital images, and extraction of high-dimensional data from the real world in order to produce numerical ...

and

artificial neural network In machine learning, a neural network (also artificial neural network or neural net, abbreviated ANN or NN) is a computational model inspired by the structure and functions of biological neural networks. A neural network consists of connected ...

s, a hard sigmoid is non- smooth function used in place of a

sigmoid function A sigmoid function is any mathematical function whose graph of a function, graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the logistic function, which is defined by the formula :\sigma(x ...

. These retain the basic shape of a sigmoid, rising from 0 to 1, but using simpler functions, especially

piecewise linear function In mathematics, a piecewise linear or segmented function is a real-valued function of a real variable, whose graph is composed of straight-line segments. Definition A piecewise linear function is a function defined on a (possibly unbounded) ...

s or

piecewise constant function In mathematics, a function on the real numbers is called a step function if it can be written as a finite linear combination of indicator functions of intervals. Informally speaking, a step function is a piecewise constant function having only ...

s. These are preferred where speed of computation is more important than precision.

Examples

The most extreme examples are the

sign function In mathematics, the sign function or signum function (from '' signum'', Latin for "sign") is a function that has the value , or according to whether the sign of a given real number is positive or negative, or the given number is itself zer ...

Heaviside step function The Heaviside step function, or the unit step function, usually denoted by or (but sometimes , or ), is a step function named after Oliver Heaviside, the value of which is zero for negative arguments and one for positive arguments. Differen ...

, which go from −1 to 1 or 0 to 1 (which to use depends on normalization) at 0. Other examples include the

Theano In Greek mythology, Theano (; Ancient Greek: Θεανώ) may refer to the following personages: * Theano, wife of Metapontus, king of Icaria. Metapontus demanded that she bear him children, or leave the kingdom. She presented the children of M ...

library, which provides two approximations: ultra_fast_sigmoid, which is a multi-part piecewise approximation and hard_sigmoid, which is a 3-part piecewise linear approximation (output 0, line with slope 0.2, output 1).Theano/sigm.py at 38a6331ae23250338290e886a72daadb33441bc4 · Theano/Theano · GitHub
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References

Artificial neural networks Computer vision {{artificial-neural-network-stub