Coursera Learner working on a presentation with Coursera logo and
Coursera Learner working on a presentation with Coursera logo and

Activate function is an essential element for designing a neural network. Choosing the activation function will give you complete control over the network model’s training process. After adding these functions in the hidden layers, the model will learn efficiently. The type of predictions depends on the choice of the activation function. Therefore, you should carefully choose the activation function for each deep learning network.

Activation Functions

An activation function signifies the transformation of the input with the help of a weighted sum to the output. It utilizes a single node or more for the network to generate the prediction. You can also refer to the activation function as a transfer function. Or, you can call this a squashing function when the output range has limitations. Activation functions can also be nonlinear and referred to as the nonlinearity of the network design. No matter what activation function you choose, it will boast a significant impact on the performance and capability of different parts in the machine learning model.

It is better to use the activation function within and after using the internal processing for every node in the network. However, the design of the model encourages the use of identical activation functions in a layer. Here are the three layers a network includes:

  • Input Layers

Input layers collect the raw input and use it in the computing process.

  • Hidden Layers

Hidden layers gather the input from the other layer and generate output for the other layer.

  • Output Layers

Output layers will predict the result.

Every hidden layer relies on the same activation function. The output layer includes various activation functions. It collects information from hidden layers. This layer is dependent on generating different types of predictions the model requires.

The neural networks learn from the backpropagation of the error algorithm. To update the weights of the hidden layer, the model requires derivatives of the predictive error. You can easily differentiate between activation functions to calculate the first-order derivative for a given input value. Neural networks include numerous types of activation functions. But to improve the performance of the hidden and output layers, you should only use a few functions.

Advantages of the Rectified Linear Activation Function

While developing different neural network types, rectified linear activation function is becoming a default choice of data scientists. Major benefits of Relu Activation function are:

  1. Simplicity in Computation

It is unimportant to implement the rectifier function when you require a max() function. This is different than the sigmoid and tanh activation function, for which you require the exponential calculation.

  1. Representational Sparsity

Another benefit of the rectifier function is the capability to generate output with a true zero value. It indicates that the negative inputs will produce true zero output. This way, neural networks can enable hidden layers and include one or additional true zero values. You can refer to this as sparse representation as it simplifies the model and accelerates the learning process. This makes the function desirable for representational learning.

  1. Linear Behavior

The rectifier function is similar to the linear activation function. It has the same performance and actions. Generally, you can easily optimize the behavior of the neural networks when the behavior is close to linear.

How to Code the ReluActivation Function

We will be using Python for the implementation of rectified linear with the easy and straightforward method. The simplest application of using this function would be the max() function. Here is the example for using the function properly:

# rectified linear function

def rectified(x):

                return max(0.0,x)

According to the expectation, the positive value will return unchanged. However, the negative value or the input value of 0.0 will return back to 0.0. Here you can find some inputs and outputs examples of the Relu activation function:

# demonstrate the rectified linear function


# rectified linear function

def rectified(x):



# demonstrate with a positive input


print(‘rectified(%.1f) is %.1f’%(x,rectified(x)))


print(‘rectified(%.1f) is %.1f’%(x,rectified(x)))

# demonstrate with a zero input


print(‘rectified(%.1f) is %.1f’%(x,rectified(x)))

# demonstrate with a negative input


print(‘rectified(%.1f) is %.1f’%(x,rectified(x)))


print(‘rectified(%.1f) is %.1f’%(x,rectified(x)))

While running the above examples, we can identify the return of positive values irrespective of their size. Though, the negative values will snap to the value 0.0.






rectified(1.0) is 1.0

rectified(1000.0) is 1000.0

rectified(0.0) is 0.0

rectified(-1.0) is 0.0

rectified(-1000.0) is 0.0

After plotting the input series and the calculated outputs, we will understand the relationship between the inputs and outputs. Here are some examples of generating a series of integers starting from -10 to 10. It helps with the calculation of the Reluactivation for individual input. Next, the model will plot the results.

# plot inputs and outputs

from matplotlib import pyplot

# rectified linear function

def rectified(x):



# define a series of inputs


# calculate outputs for our inputs


# line plot of raw inputs to rectified outputs



The Reluactivation function helps neural networks form deep learning models. Due to the vanishing gradient issues in different layers, you cannot use the hyperbolic tangent and sigmoid activation. You can overcome the gradient problems through the Relu activation function. This allows the model to perform better and learn faster. When you develop the convolutional and Multilayer Perceptron, neural networks rectified linear activation function will be the default option.



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