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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 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.
This property is desirable (ReLU is not continuously differentiable and has some issues with gradient-based optimization, but it is still possible) for enabling gradient-based optimization methods. The binary step activation function is not differentiable at 0, and it differentiates to 0 for all other values, so gradient-based methods can make ...
PyTorch defines a module called nn (torch.nn) to describe neural networks and to support training. This module offers a comprehensive collection of building blocks for neural networks, including various layers and activation functions, enabling the construction of complex models.
Torch is an open-source machine learning library, a scientific computing framework, and a scripting language based on Lua. [3] It provides LuaJIT interfaces to deep learning algorithms implemented in C. It was created by the Idiap Research Institute at EPFL. Torch development moved in 2017 to PyTorch, a port of the library to Python. [4] [5] [6]
In the field of mathematical modeling, a radial basis function network is an artificial neural network that uses radial basis functions as activation functions.The output of the network is a linear combination of radial basis functions of the inputs and neuron parameters.
The original proofs, such as the one by Cybenko, use methods from functional analysis, including the Hahn-Banach and Riesz–Markov–Kakutani representation theorems. Notice also that the neural network is only required to approximate within a compact set . The proof does not describe how the function would be extrapolated outside of the region.
The swish function is a family of mathematical function defined as follows: . The swish function = = +. [1]. where can be constant (usually set to 1) or trainable.. The swish family was designed to smoothly interpolate between a linear function and the ReLU function.