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A sigmoid function is any mathematical function whose 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: [ 1 ]
Neurons also cannot fire faster than a certain rate, motivating sigmoid activation functions whose range is a finite interval. The function looks like () = (+ ′), where is the Heaviside step function.
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.
Kumar suggested that the distribution of initial weights should vary according to activation function used and proposed to initialize the weights in networks with the logistic activation function using a Gaussian distribution with a zero mean and a standard deviation of 3.6/sqrt(N), where N is the number of neurons in a layer.
A sigmoid curve of an autocatalytic reaction. When t = 0 to 50, the rate of reaction is low. ... Wilkinson's catalyst requires activation before it can participate in ...
The Hill equation can be applied in modelling the rate at which a gene product is produced when its parent gene is being regulated by transcription factors (e.g., activators and/or repressors). [11] Doing so is appropriate when a gene is regulated by multiple binding sites for transcription factors, in which case the transcription factors may ...
A widely used type of composition is the nonlinear weighted sum, where () = (()), where (commonly referred to as the activation function [3]) is some predefined function, such as the hyperbolic tangent, sigmoid function, softmax function, or rectifier function. The important characteristic of the activation function is that it provides a smooth ...
The first examples were the arbitrary width case.George Cybenko in 1989 proved it for sigmoid activation functions. [3] Kurt Hornik [], Maxwell Stinchcombe, and Halbert White showed in 1989 that multilayer feed-forward networks with as few as one hidden layer are universal approximators. [1]