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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:
Modern activation functions include the logistic function used in the 2012 speech recognition model developed by Hinton et al; [2] the ReLU used in the 2012 AlexNet computer vision model [3] [4] and in the 2015 ResNet model; and the smooth version of the ReLU, the GELU, which was used in the 2018 BERT model.
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]
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.
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.
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.
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.
CNN = convolutional layer (with ReLU activation) RN = local response normalization; MP = maxpooling; FC = fully connected layer (with ReLU activation) Linear = fully connected layer (without activation) DO = dropout; It used the non-saturating ReLU activation function, which trained better than tanh and sigmoid. [1]