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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 the node based on its individual inputs and their weights. Nontrivial problems can be solved using only a few nodes if the activation function is nonlinear .
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]
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.
This is an existence result. It says that activation functions providing universal approximation property for bounded depth bounded width networks exist. Using certain algorithmic and computer programming techniques, Guliyev and Ismailov efficiently constructed such activation functions depending on a numerical parameter.
Alternative activation functions have been proposed, including the rectifier and softplus functions. More specialized activation functions include radial basis functions (used in radial basis networks, another class of supervised neural network models). In recent developments of deep learning the rectified linear unit (ReLU) is more frequently ...
where is the matrix of node representations , is the matrix of node features , () is an activation function (e.g., ReLU), ~ is the graph adjacency matrix with the addition of self-loops, ~ is the graph degree matrix with the addition of self-loops, and is a matrix of trainable parameters.
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 ...