Deep Learning: Choosing an Activation Function

The selection of an activation function is one of the most important decisions a data scientist must make when constructing a neural network, as it has a direct effect on the network’s performance. Activation functions are used to decide whether or not to activate a node in a neural network, and as a result, data scientists must carefully consider which of the many available activation functions to utilise in order to optimise the network’s performance.

In this article, we will explore the different types of activation functions, their purpose and function, as well as their advantages and disadvantages. To begin, let us provide a brief overview of how neural networks operate. Neural networks are computing systems that are designed to model and imitate the way the human brain functions. They are composed of a series of layers, each composed of a set of interconnected nodes, which are responsible for processing and recognising patterns in data. Activation functions are a crucial component of these networks, as they are responsible for determining the output of each neuron, or node. Activation functions work by introducing a non-linearity to the network, allowing it to learn complex patterns and solve complex problems.

A neural network is defined as.

The human mind is a powerful tool capable of resolving complex issues such as deciphering unclear captchas and deciphering ancient texts. To build on this impressive capability, computer scientists have created artificial neural networks that are structured similarly to the human brain. Neural networks are composed of nodes, which function similarly to neurons in the human brain. Each node receives data as input, processes it, and then produces an output. While the human brain is capable of performing these tasks without any additional training, neural networks require training before they can be utilised.

Commonly, a neural network is trained in three stages, or layers:

“Input layer”: At this point, the neural network is provided with data, which can consist of any form of raw information, including images and audio recordings. This data is received in its original state, and is then forwarded to other nodes for further processing.

Unseen depth: This layer is responsible for the processing of all data that is inputted. It is possible to train a neural network with a maximum of up to n hidden layers. Upon the completion of processing, the generated information is transmitted to the output layer.

It’s the Layer that’s Responsible for Generating Output. The output comes from this level.

Each circle in this representation is a node that has a value in the range of zero to one. This value is known as “activation” and indicates that the neuron is activated. Every node in this layer is connected to all other nodes in the higher layer. The amount of nodes and layers in the hidden layer of a neural network, “n,” can be adjusted based on the specific requirements of the network. This information is transferred from one layer to another and from one node to another until it reaches the output layer. The output that is generated is optimal when the nodes have higher values.

Consider the following illustration:

If you supply the system with a fuzzy number, it will decompose it into individual pixels and send one activation signal to each node. Since each number is distinct, the computer must first learn to identify its boundaries. This is achieved by matching the input to its original number through a process of trial and error. Consequently, some, but not all, of the nodes will be activated during this process.

The enigma of the activation and deactivation of particular neurons remains unresolved. Consequently, the factors that dictate this phenomenon must be examined. In this context, the role of activation functions becomes especially noteworthy.

A definition of an activation function would be helpful.

A node’s activation status is determined by a mathematical expression known as an activation function. When a node is activated, it will send signals to the nodes within the layer that is located above it. To calculate the activation function, the input must be multiplied by the weight, followed by the application of a bias.

Its mathematical representation is as follows:

Z = (weights*input + bias) * activation function

Consequently, if the inputs are x1, x2, x3,…, xn, and the weights are w1, w2, w3,……, wn, then

activation = activation function + bias = (x1 w1 + x2 w2 + x3 w3 + xn wn)

Coefficients in an equation are referred to as weights, which are used to adjust the output of the equation. The addition of a fixed number to the sum of the input and weights is known as a ‘bias’, which can influence the output of the equation by skewing the result in either direction.

The use of an activation function is essential for introducing nonlinearity into neural networks. Training a neural network to reach a desired output often requires a number of iterations and, thus, the process of backpropagation is employed to adjust the weights and biases of the neural network. Activation functions enable backpropagation to take place by guiding gradients into the appropriate neurons and allowing them to adjust the weights and biases accordingly.

Characteristics of Activation Functions

There is a binary step function.

As a mathematical expression, f(z) = 0 when z 0 and z 1, and 1 otherwise.

The step function, also known as the threshold function, has a unique capability that enables it to trigger a node based on a set point. It is capable of producing a single output value if the input is greater than the set point, and nothing if it is not. This makes it an ideal solution for resolving complex patterns. Additionally, the step function has a key advantage over backpropagation in that the gradient is always 0, rendering the technique useless.


Formula: f(z) = 1/(1+ez)

Nonlinear functions, such as the sigmoid, are widely used in regression analysis. When visualised, the sigmoid appears as a ‘S’-shaped curve, whereby the input is transformed into a probability value between 0 and 1. Notably, large negative numbers are effectively rounded down to -1, while large positive numbers are inverted to +1.

Due to its computationally intensive nature, this operation is excluded from the hidden layers of a convolutional neural network. This is because the network cannot improve or learn effectively if it is receiving a weak gradient for values outside of the range [3; -3]. This phenomenon is referred to as a diminishing gradient.


For example, the formula f(x) = a = tanh(z) = (ez – ez)/(ez + ez) is a mathematical equation for finding the ratio between two numbers.

The hyperbolic tangent (tanh) function can be used to divide a data set into two distinct categories. This function is similar to the sigmoid function in that it is a non-linear graph with the shape of an ‘S’ and its values can be either -1 or 1. The tanh function has a zero-centred design, which allows for faster optimisation of the output. When the input is a large positive number, the output is closer to 1, and when the input is a large negative number, the output is closer to -1. The tanh function should not be utilised at the final output stage.


This is a mathematical expression: f(z) = maximum (0,z)

One of the most widely employed activation functions for convolutional neural networks and deep learning is the Rectified Linear Unit (ReLu). ReLu is a variation of both the sigmoid and tanh activation functions and does not face the problem of a vanishing gradient, which occurs when the gradient approaches zero. The range of ReLu is bounded between zero and positive infinity.

Given the lack of exponential terms, the ReLu function offers faster results; however, it is important to note that during the training phase, calculation difficulties could arise if its positive side reaches extreme levels.


Calculation: f(x) = exi / (j=0 exi)

Nonlinear multiclass handling can be achieved by using the softmax function. This function is often implemented at the output layer of a neural network and can be used for multi-class input classification. It works by adjusting the outputs for each class between 0 and 1, and then dividing the total by the total to calculate the chance of an input value falling into a certain class.

Optimal neural network activation function selection

When selecting an activation function, it is a highly subjective process that is dependent on the specifics of the task. For those unfamiliar with deep learning, the sigmoid function is an excellent starting point. As expertise increases, the range of activation functions that one can draw from can be expanded.

There are two distinct types of problems that can be encountered in data analysis: regression and classification. For regression tasks, the linear activation function has proven to be an effective solution, while for classification tasks, nonlinear functions are generally more suitable.

The sigmoid function is useful for binary classification, whereas the softmax activation is useful for multiclass classification.

While making your choice, consider the following extra advice:

  • In order to ensure that the neural network model is adequately equipped to handle more sophisticated scenarios, it is recommended to utilise a differential nonlinear function in the hidden layers of the model. This approach will enable the model to better cope with more complex situations.
  • When working with obfuscated layers, you should always use the ReLu algorithm.
  • In most cases, the softmax function is utilised for the last layer, the output.
  • At present, the Rectified Linear Unit (ReLu) activation function is the most popular, and is thus a great starting point for those who are uncertain about which activation function to use.

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