Biological plausibility: One-sided, compared to the antisymmetry of tanh.
Sparse activation: For example, in a randomly initialized network, only about 50% of hidden units are activated.
Better gradient propagation: Fewer vanishing gradient problems compared to sigmoidal activation functions that saturate in both directions.
Efficient computation: Only comparison, addition and multiplication.
Scale-invariant:.
Rectifying activation functions were used to separate specific excitation and unspecific inhibition in the neural abstraction pyramid, which was trained in a supervised way to learn several computer vision tasks. In 2011, the use of the rectifier as a non-linearity has been shown to enable training deep supervised neural networks without requiring unsupervised pre-training. Rectified linear units, compared to sigmoid function or similar activation functions, allow faster and effective training of deep neural architectures on large and complex datasets.
Potential problems
Non-differentiable at zero; however, it is differentiable anywhere else, and the value of the derivative at zero can be arbitrarily chosen to be 0 or 1.
Not zero-centered.
Unbounded.
Dying ReLU problem: ReLU neurons can sometimes be pushed into states in which they become inactive for essentially all inputs. In this state, no gradients flow backward through the neuron, and so the neuron becomes stuck in a perpetually inactive state and "dies". This is a form of the vanishing gradient problem. In some cases, large numbers of neurons in a network can become stuck in dead states, effectively decreasing the model capacity. This problem typically arises when the learning rate is set too high. It may be mitigated by using leaky ReLUs instead, which assign a small positive slope for x < 0 however the performance is reduced.
Variants
Softplus
A smooth approximation to the rectifier is the analytic function which is called the softplus or SmoothReLU function. A sharpness parameter may be included: The derivative of softplus is the logistic function. Starting from the parametric version, The logistic sigmoid function is a smooth approximation of the derivative of the rectifier, the Heaviside step function. The multivariable generalization of single-variable softplus is the LogSumExp with the first argument set to zero: The LogSumExp function is and its gradient is the softmax; the softmax with the first argument set to zero is the multivariable generalization of the logistic function. Both LogSumExp and softmax are used in machine learning.
Swish
Swish is a smooth approximation to the rectifier. It has a non-monotonic “bump” when x < 0.
Rectified linear units can be extended to include Gaussian noise, making them noisy ReLUs, giving Noisy ReLUs have been used with some success in restricted Boltzmann machines for computer-vision tasks.
Leaky ReLU
Leaky ReLUs allow a small, positive gradient when the unit is not active.
Parametric ReLU
Parametric ReLUs take this idea further by making the coefficient of leakage into a parameter that is learned along with the other neural-network parameters. Note that for a ≤ 1, this is equivalent to and thus has a relation to "maxout" networks.
ELU
Exponential linear units try to make the mean activations closer to zero, which speeds up learning. It has been shown that ELUs can obtain higher classification accuracy than ReLUs. where is a hyper-parameter to be tuned, and is a constraint.
