Neural Network Activation Function

Activation functions are mathematical equations that specify how a neural network model outputs data. Activation functions also have a significant impact on the ability and speed of a neural network to converge. In certain situations, activation functions may even prevent neural networks from convergent in the first place. Additionally, the activation function aids in normalizing the output of any input in the range of 1 to -1 or 0 to 1. Finally, the activation function must be efficient and fast since neural networks are often trained on millions of data points.

Thus, activation is a critical component of an artificial neural network. They determine whether or not a neuron should be engaged. It is a non-linear modification that may be performed on the input before it is sent to the next layer of neurons or finalized.

Properties of Activation Functions

Linearity and Non-Linearity
Continuously Differentiable
Range of Input and Output
Monotonic
Approximation of identity near the origin

Softmax

The softmax function is sometimes referred to as the soft argmax function or logistic regression with multiple classes. This is because the softmax is an extension of logistic regression that may be used for multi-class classification. Its formula is highly similar to that of the logistic regression sigmoid function. Only if the classes are mutually distinct can the softmax function be employed in a classifier.

Gudermannian

The Gudermannian function connects circular and hyperbolic functions without utilizing complex numbers directly.

Rectified Linear Units or ReLU

Due to the vanishing gradient issue, the sigmoid and hyperbolic tangent activation functions cannot be employed in multilayer networks. The rectified linear activation function enables models to learn quicker and perform better by overcoming the vanishing gradient issue. When creating multilayer Perceptron and convolutional neural networks, the rectified linear activation is the default activation. The ReLU activation function is the most often used activation function in neural networks.

Leaky ReLU

When the learning rate is too high and a significant negative bias, the dying ReLU issue is likely to develop. The most frequent and successful approach to resolving a dying ReLU issue is through a leaky ReLU. However, it introduces a bit negative slope to avoid the ReLU problem from dying. Although parametric ReLU is the most often used and successful strategy for solving a dying ReLU issue, it does not address the exploding gradient issue.

Exponential Linear Unit (ELU)

ELU accelerates neural network learning, improves classification accuracy, and resolves the vanishing gradient issue. ELUs have superior learning properties as compared to other activation functions. ELUs contain negative values, which enable them to drive mean unit activations closer to zero in the same way as batch normalization does, but with less processing cost. ELU is intended to combine the best features of ReLU and leaky ReLU while avoiding the dying ReLU issue. It saturates for significant negative values, thereby rendering them inactive.

Swish function

Google created the Swish function, which outperforms the ReLU function while maintaining the same degree of processing efficiency. Even now, ReLU remains a critical component of deep learning research. However, investigations demonstrate that this novel activation function outperforms ReLU when applied to deeper networks.

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