6 Types of Activation Function in Neural Networks You Need to Know

Working in artificial intelligence, one quickly learns the importance of understanding the types of activation function in neural networks. These functions are the heartbeats of neural networks, determining the output of a neural node. They’re not merely mathematical tools; they act as decision-makers, enabling networks to capture complex patterns and undertake tasks ranging from straightforward classification to comprehending human languages.

In this article, I’ll explore the significance of activation functions, setting the stage for deeper insights into Artificial Neural Networks in soft computing, their core characteristics, components, and crucially, the process of selecting the appropriate activation function. My journey has underscored that grasping these functions is essential for developing effective neural models. Whether you’re starting out or seeking to deepen your AI expertise, mastering these functions is key to advancing in this field.

Read more about types of artificial neural networks in machine learning.

What is an Artificial Neural Network in Soft Computing?

Artificial Neural Network is a Deep Learning model that draws inspiration from the neural structure of the human brain. ANNs have been designed to mimic the functions of the human brain that learn from experiences and adapt accordingly to the situation. Like the human brain has a multi-tiered structure containing billions of neurons arranged in a hierarchy, ANN also has a network of neurons that are interconnected to each other via axons.

These interconnected neurons pass electrical signals (called synapses) from one layer to another. This imitation of brain modeling allows the ANN to learn from experience without requiring human intervention. 

Read: Artificial Neural Network in Data Mining

Thus, ANNs are complex structures containing interconnected adaptive elements known as artificial neurons that can perform large computations for knowledge representation. They possess all the fundamental qualities of the biological neuron system, including learning capability, robustness, non-linearity, high parallelism, fault and failure tolerance, ability to handle imprecise and fuzzy information, and generalizing ability. 

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Why do we use Activation functions with Neural Networks?

Let’s understand the reasons why we use activation functions with Neural Networks: 

• Introduction of Non-Linearity: Activation functions introduce non-linearities, enabling neural networks to capture complex patterns and relationships in data that linear functions cannot represent effectively. 
• Facilitating Complex Representations: Neural networks need to learn hierarchical and abstract representations, which activation functions allow. This ability is crucial for understanding intricate features in the data. 
• Mitigating Vanishing or Exploding Gradients: Activation functions control the scale of outputs, preventing issues like vanishing or exploding gradients during backpropagation. This ensures stable and effective training. 
• Enabling Decision Boundaries: Activation functions define decision boundaries, determining when neurons should activate or remain inactive based on input. This is fundamental for accurate classifications. 
• Handling Non-Linear Mappings: Activation functions empower networks to approximate non-linear mappings between inputs and outputs, crucial for modeling real-world problems with non-linear relationships. 

Core Characteristics of Artificial Neural Networks

• Non-linearity imparts a better fit to the data. 
• High parallelism promotes fast processing and hardware failure-tolerance. 
• Generalization allows for the application of the model to unlearned data.
• Noise insensitivity that allows accurate prediction even for uncertain data and measurement errors.
• Learning and adaptivity allow the model to update its internal architecture according to the changing environment. 

ANN-based computing primarily aims to design advanced mathematical algorithms that allow Artificial Neural Networks to learn by imitating the information processing and knowledge acquisition functions of the human brain.

Components of Artificial Neural Networks 

ANNs are comprised of three core layers or phases – an input layer, hidden layer/s, and an output layer.  

• Input Layer: The first layer is fed with the input, that is, raw data. It conveys the information from the outside world to the network. In this layer, no computation is performed – the nodes merely pass on the information to the hidden layer.
• Hidden Layer: In this layer, the nodes lie hidden behind the input layer – they comprise the abstraction part in every neural network. All the computations on the features entered through the input layer occur in the hidden layer/s, and then, it transfers the result to the output layer.
• Output Layer: This layer depicts the results of the computations performed by the network to the outer world.

Source 

Neural networks can be categorized into different types based on the activity of the hidden layer/s. For instance, in a simple neural network, the hidden units can construct their unique representation of the input. Here, the weights between the hidden and input units decide when each hidden unit is active.

Thus, by adjusting these weights, the hidden layer can choose what it should represent. Other architectures include the single layer and multilayer models. In a single layer, there’s usually only an input and output layer – it lacks a hidden layer. Whereas, in a multilayer model, there is one or more than one hidden layer.

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What are Activation Functions in a Neural Network?

As we mentioned earlier, ANNs are a crucial component of many structures that are helping revolutionize the world around us. But have you ever wondered, how do ANNs deliver state-of-the-art performance to find solutions to real-world problems?

The answer is – Activation Functions.

ANNs use the Activation Function in soft computing (AFs) to perform complex computations in the hidden layers and then transfer the result to the output layer. The primary purpose of AFs or Activation Function in soft computing is to introduce non-linear properties in the neural network.

They convert the linear input signals of a node into non-linear output signals to facilitate the learning of high order polynomials that go beyond one degree for deep networks. A unique aspect of AFs is that they are differentiable – this helps them function during the backpropagation of the neural networks.

In order to determine whether a neuron should be activated or not, the activation function in neural network calculate a weighted total and then adds bias to it. The activation functions’ goal is to make a neuron’s output less linear.

Explanation :-

We know that neurons in neural networks behave according to weight, bias, and their respective activation roles. We would adjust the weights and biases of the neurons in a neural network based on the output inaccuracy. Back-propagation is the term for this method. Activation functions make back-propagation possible since they provide the gradients and errors required to modify the weights and biases.

Why do we require Non-linear activation functions: An unactivated neural network is essentially a linear regression model. The activation function transforms the input in a non-linear way, enabling it to learn and carry out more difficult tasks. Here is the activation function in neural network example for you.

Mathematical proof:

Think we have a neutral net something like this:

Elements of the diagram :-

Hidden layer i.e. layer 1 :-

z(1) = W(1)X + b(1)

a(1) = z(1)

Here,

z(1) is the vectorized output of layer 1

W(1) be the vectorized weights assigned to neurons of hidden layer i.e. w1, w2, w3 and w4

X be the vectorized input features i.e. i1 and i2

b is the vectorized bias assigned to neurons in hidden layer i.e. b1 and b2

a(1) is the vectorized form of any linear function.

(Note: We won’t be considering activation function here)

Layer 2 i.e. output layer:

 //  Note : Input for layer

//   2 is output from layer 1

z(2) = W(2)a(1) + b(2) 

a(2) = z(2)

Calculation at Output layer: 

// Putting value of z(1) here

z(2) = (W(2) * [W(1)X + b(1)]) + b(2)

z(2) = [W(2) * W(1)] * X + [W(2)*b(1) + b(2)]

Let,

[W(2) * W(1)] = W

    [W(2)*b(1) + b(2)] = b

Final output : z(2) = W*X + b

Which is again a linear function.

This activation function in neural network example yields a linear function once more even after the addition of a hidden layer, leading us to the conclusion that no matter how many hidden layers we add to a neural network, all of them will behave consistently because of the union of two linear functions yields a linear function as well. With only a linear function attached to it, a neuron cannot learn. It can learn according to the difference in mistake rate given a non-linear activation function.

So, an activation function is required.

What is the need for non-linearity?

If activation functions are not applied, the output signal would be a linear function, which is a polynomial of one degree. While it is easy to solve linear equations, they have a limited complexity quotient and hence, have less power to learn complex functional mappings from data. Thus, without AFs, a neural network would be a linear regression model with limited abilities.

This is certainly not what we want from a neural network. The task of neural networks is to compute highly complicated calculations. Furthermore, without AFs, neural networks cannot learn and model other complicated data, including images, speech, videos, audio, etc.

 AFs help neural networks to make sense of complicated, high dimensional, and non-linear Big Data sets that have an intricate architecture – they contain multiple hidden layers in between the input and output layer.

Read: Deep Learning Vs Neural Network

Now, without further ado, let’s dive into the different types of activation functions used in ANNs.

Types of Activation Functions in Neural Networks

1. Sigmoid Function

The first type of activation function in neural network is the sigmoid function. The sigmoid function is a non-linear AF used primarily in feedforward neural networks. It is a differentiable real function, defined for real input values, and containing positive derivatives everywhere with a specific degree of smoothness. The sigmoid function appears in the output layer of the deep learning models and is used for predicting probability-based outputs. The sigmoid function is represented as:

Source 

Generally, the derivatives of the sigmoid function are applied to learning algorithms. The graph of the sigmoid function is ‘S’ shaped. 

Some of the major drawbacks of the sigmoid function include gradient saturation, slow convergence, sharp damp gradients during backpropagation from within deeper hidden layers to the input layers, and non-zero centered output that causes the gradient updates to propagate in varying directions.

2. Hyperbolic Tangent Function (Tanh)

The hyperbolic tangent function, a.k.a., the tanh function, is another type of AF. It is a smoother, zero-centered function having a range between -1 to 1. As a result, the output of the tanh function is represented by:

Source 

The tanh function is much more extensively used than the sigmoid function since it delivers better training performance for multilayer neural networks. The biggest advantage of the tanh function is that it produces a zero-centered output, thereby supporting the backpropagation process. The tanh function has been mostly used in recurrent neural networks for natural language processing and speech recognition tasks.

However, the tanh function, too, has a limitation – just like the sigmoid function, it cannot solve the vanishing gradient problem. Also, the tanh function can only attain a gradient of 1 when the input value is 0 (x is zero). As a result, the function can produce some dead neurons during the computation process.

3. Softmax Function 

The softmax function is another type of AF used in neural networks to compute probability distribution from a vector of real numbers. This function generates an output that ranges between values 0 and 1 and with the sum of the probabilities being equal to 1. The softmax function is represented as follows:

Source

This function is mainly used in multi-class models where it returns probabilities of each class, with the target class having the highest probability. It appears in almost all the output layers of the DL architecture where they are used. The primary difference between the sigmoid and softmax AF is that while the former is used in binary classification, the latter is used for multivariate classification. 

4. Softsign Function

The softsign function is another AF that is used in neural network computing. Although it is primarily in regression computation problems, nowadays it is also used in DL based text-to-speech applications. It is a quadratic polynomial, represented by:

Source

This function is mainly used in multi-class models where it returns probabilities of each class, with the target class having the highest probability. It appears in almost all the output layers of the DL architecture where they are used. The primary difference between the sigmoid and softmax AF is that while the former is used in binary classification, the latter is used for multivariate classification. 

4. Softsign Function

The softsign function is another AF that is used in neural network computing. Although it is primarily in regression computation problems, nowadays it is also used in DL based text-to-speech applications. It is a quadratic polynomial, represented by:

 Source

Here “x” equals the absolute value of the input. 

 The main difference between the softsign function and the tanh function is that unlike the tanh function that converges exponentially, the softsign function converges in a polynomial form. 

5. Rectified Linear Unit (ReLU) Function 

One of the most popular AFs in DL models, the rectified linear unit (ReLU) function, is a fast-learning AF that promises to deliver state-of-the-art performance with stellar results. Compared to other AFs like the sigmoid and tanh functions, the ReLU function offers much better performance and generalization in deep learning. The function is a nearly linear function that retains the properties of linear models, which makes them easy to optimize with gradient-descent methods. 

The ReLU function performs a threshold operation on each input element where all values less than zero are set to zero. Thus, the ReLU is represented as:

Source

By rectifying the values of the inputs less than zero and setting them to zero, this function eliminates the vanishing gradient problem observed in the earlier types of activation function in soft computing (sigmoid and tanh).

The most significant advantage of using the ReLU function in computation is that it guarantees faster computation – it does not compute exponentials and divisions, thereby boosting the overall computation speed. Another critical aspect of the ReLU function is that it introduces sparsity in the hidden units by squishing the values between zero to maximum.

6. Exponential Linear Units (ELUs) Function

The exponential linear units (ELUs) function is an AF that is also used to speed up the training of neural networks (just like ReLU function). The biggest advantage of the ELU function is that it can eliminate the vanishing gradient problem by using identity for positive values and by improving the learning characteristics of the model.

ELUs have negative values that push the mean unit activation closer to zero, thereby reducing computational complexity and improving the learning speed. The ELU is an excellent alternative to the ReLU – it decreases bias shifts by pushing mean activation towards zero during the training process. 

The exponential linear unit function is represented as:

The derivative or gradient of the ELU equation is presented as:

Source

Here “α” equals the ELU hyperparameter that controls the saturation point for negative net inputs, which is usually set to 1.0. However, the ELU function has a limitation – it is not zero-centered.

How to Choose the Right Activation Function?

I have mentioned the top points you should be using to choose an activation function:  

1. Problem Type Consideration:

• Different problems require different activation functions based on their characteristics. 
• For binary classification tasks, where the output is binary (0 or 1), the sigmoid function is commonly used. 
• For multi-class classification tasks, where the output is one of several classes, the softmax function is preferred. 
• For regression tasks, where the output is continuous, linear activation functions like the identity function are suitable. 

1. Address Gradient Issues:

• Some activation functions, like sigmoid and tanh, can cause vanishing or exploding gradients during training, hindering convergence. 
• Rectified Linear Unit (ReLU) and its variants (Leaky ReLU, Parametric ReLU) are effective in addressing this issue, as they do not saturate for positive input values. 

1. Handling Non-Linearity:

• Activation functions introduce non-linearity to the network, allowing it to learn complex patterns in the data. 
• Functions like ReLU, tanh, and sigmoid introduce non-linear transformations to capture intricate relationships between input and output. 

1. Computational Efficiency:

• Some activation functions are computationally expensive, which can affect training time and resource utilization. 
• ReLU is a computationally efficient choice, as it involves simple mathematical operations and is widely used in practice. 

1. Output Range Constraint:

• The choice of activation function should match the desired output range of the network. 
• The sigmoid function is suitable for tasks where the output needs to be bounded between 0 and 1, such as binary classification. 

1. Experimental Validation:

• Ultimately, the selection of the activation function should be validated empirically. 
• Experiment with different activation functions and assess their performance on a validation dataset to determine the most suitable option for the specific task and dataset. 

Conclusion

Understanding the types of activation function in neural networks is crucial for anyone venturing into the realm of artificial intelligence and machine learning. These functions are not just mathematical conveniences but the very essence that allows neural networks to make complex decisions and learn from data. From the sigmoid to ReLU, each activation function has its unique characteristics and applications, making the choice of the right one pivotal to the success of a neural network model. This article has traversed the landscape of artificial neural networks, highlighting their core characteristics, components, and, most importantly, the pivotal role of activation functions. Choosing the appropriate activation function is a nuanced decision that depends on the specific requirements of the application, including the nature of the data and the desired complexity of the model. Armed with this knowledge, practitioners and enthusiasts alike are better positioned to harness the power of neural networks, pushing the boundaries of what’s possible in soft computing and beyond.

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