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In particular see "Chapter 4: Artificial Neural Networks" (in particular pp. 96–97) where Mitchell uses the word "logistic function" and the "sigmoid function" synonymously – this function he also calls the "squashing function" – and the sigmoid (aka logistic) function is used to compress the outputs of the "neurons" in multi-layer neural ...
The activation function of a node in an artificial neural network is a function that calculates the output of the node ... Exponential Linear Sigmoid SquasHing ...
The standard logistic function is the logistic function with parameters =, =, =, which yields = + = + = / / + /.In practice, due to the nature of the exponential function, it is often sufficient to compute the standard logistic function for over a small range of real numbers, such as a range contained in [−6, +6], as it quickly converges very close to its saturation values of 0 and 1.
Also, certain non-continuous activation functions can be used to approximate a sigmoid function, which then allows the above theorem to apply to those functions. For example, the step function works. In particular, this shows that a perceptron network with a single infinitely wide hidden layer can approximate arbitrary functions.
The swish family was designed to smoothly interpolate between a linear function and the ReLU function. When considering positive values, Swish is a particular case of doubly parameterized sigmoid shrinkage function defined in [2]: Eq 3 . Variants of the swish function include Mish. [3]
The generalized logistic function or curve is an extension of the logistic or sigmoid functions. Originally developed for growth modelling, it allows for more flexible S-shaped curves. The function is sometimes named Richards's curve after F. J. Richards, who proposed the general form for the family of models in 1959.
The logistic function is a sigmoid function, which takes any real input , and outputs a value between zero and one. [2] For the logit, this is interpreted as taking input log-odds and having output probability. The standard logistic function : (,) is defined as follows:
Because it it maps a very large input domain to a small range of outputs, it is often referred to as the squashing function of the unit [cf Figure 4.6 The sigmoid threshold unit; in this drawing, σ(y) = 1/(1+e-net), where net = Σ 0 i (w i *x i) and w i is the i th weight for the i th input x i and x 0 is a constant -- x 0 is important ...