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Plot of the ReLU (blue) and GELU (green) functions near x = 0. In the context of artificial neural networks, the rectifier or ReLU (rectified linear unit) activation function [1] [2] is an activation function defined as the non-negative part of its argument, i.e., the ramp function:
The activation function of a node in an artificial neural network is a function that calculates the output of ... Non-saturating activation functions, such as ReLU, ...
ReLU is the abbreviation of rectified linear unit. It was proposed by Alston Householder in 1941, [82] and used in CNN by Kunihiko Fukushima in 1969. [38] ReLU applies the non-saturating activation function = (,). [68] It effectively removes negative values from an activation map by setting them to zero. [83]
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]
In mathematics, the ramp function is also known as the positive part. In machine learning, it is commonly known as a ReLU activation function [1] [2] or a rectifier in analogy to half-wave rectification in electrical engineering. In statistics (when used as a likelihood function) it is known as a tobit model.
The model, in modern language, is an artificial neural network with ReLU activation function. [9] In a series of papers, Householder calculated the stable states of very simple networks: a chain, a circle, and a bouquet. Walter Pitts' first two papers formulated a mathematical theory of learning and conditioning.
The convex conjugate (specifically, the Legendre transform) of the softplus function is the negative binary entropy (with base e).This is because (following the definition of the Legendre transform: the derivatives are inverse functions) the derivative of softplus is the logistic function, whose inverse function is the logit, which is the derivative of negative binary entropy.
The swish paper was then updated to propose the activation with the learnable parameter β. In 2017, after performing analysis on ImageNet data, researchers from Google indicated that using this function as an activation function in artificial neural networks improves the performance, compared to ReLU and sigmoid functions. [1]