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Table of contents
Data flow in an ANN
Forward Propagation
Frequently Asked Questions
Key Learnings
Last Updated: Mar 27, 2024

Understanding Forward Propagation

Author Arun Nawani
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Deep Learning has been one of the most revolutionised domains in Artificial Intelligence in the past decade. It wasn’t too long ago when Deep Learning was an area of research beyond the reach of an ordinary citizen. Now, almost every gadget we use today, smartphones, laptops, gaming consoles, etc make use of this technology in more ways than we can fathom. In fact, many of you probably start with your day by using the popular use case of Deep Learning, The face recognition feature on your smartphone. Today, we’ll dig into the finer details of how DL works in the backend. 

Also Read, Resnet 50 Architecture


The blog considers the reader to be versed with the basic architecture of artificial neural networks as well as the terminologies related to it like neurons and Activation function. You can check out our previous blogs on Artificial neural networks if you wish to refresh yourself up with the basics before proceeding further in this blog.

Data flow in an ANN

We are aware that an ANN architecture consists of 3 major components - The input layer, The hidden layers, and the output layers. 

The input layer, as the name gives out, receives and preprocesses the input, which is then sent out to the hidden layer. This is where most of the work is done. After making the computations, the results are then passed on to the output layer. This makes the first part of a single training iteration. This is called Forward Propagation. After the output layer receives the data, the generated results are then compared with the actual outputs, and the error is reduced based on the feedback that’s received. This is known as Backpropagation. This is a very high-level overview of how ANNs work. For this blog, we’ll stick to Forward Propagation and cover it in-depth. 

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Forward Propagation

So, what is Forward Propagation? As discussed earlier, it’s the first part of one training iteration. The movement of data from the input layer to the next subsequent layers computing the neurons is known as forward propagation. 


Source- link

Beginning with the notations, Here-


a1[0] denotes the first neuron of the input layer

a2[0] denotes the second neuron of the input layer and so on…


a1[1] denotes the first neuron of the hidden layer

a2[1] denotes the second neuron of the hidden layer and so on…

Lastly, a1[2] is the first and the only neuron in the output layer. There can be more than one neuron in the final layer as well. 

Source - link

Here each neuron in the input layer is connected with each neuron in the next subsequent layer. 

The weight between one neuron to another is denoted by w. 

For example,

the weight between the second neuron of the first layer (a2[0]) and the first neuron of the second layer(a2[0]) is denoted by w12[1]. Now since all the neurons in the first layer connect with each neuron in the second layer, hence a1[1] is given by 

a1[1] = f(w11[1]*a1[0] + w12[1]*a2[0] + w13[1]*a3[0] + B1)

Where B1 is the bias term and f is the activation function. 

We can compute other neurons in a similar fashion. This operation can be denoted as matrix multiplication. 

Source - link

Here, W is the matrix of weights associated with every neuron in a layer arranged row-wise, starting with the first layer. Multiplying it with the matrix of neurons from the previous layer, adding the bias term B(i), and passing it through the activation function, we get the matrix of all the neurons in the next subsequent layer. 

Here A1 denotes the matrix of neurons in the second layer, and W1 denotes the matrix of weights associated with the first layer. 

This way, we can find all the subsequent layers in the neural network. 

This subsequent computation of layers is called Forward propagation. Now, the question arises, how should we select the weights. This is done with the feedback received after comparing the output generated with the actual output, which is then sent back. The weights are then adjusted to minimise the error in the feedback. This is known as Backpropagation. You can check out our blog on Backpropagation to get a better understanding. 

Also see, Artificial Intelligence in Education

Frequently Asked Questions

  1. What is meant by forward propagation?
    Ans. Computation of each layer in the neural network, starting from the input layer all the way to the output layer, is known as Forward Propagation. 
  2. How are weights associated with each layer selected? 
    Ans. The first iteration starts with a random selection of weights. However, the weights are gradually adjusted as the neural network receives feedback about the output generated. Adjusting weights and minimising the cost function is the purpose of Backpropagation.
  3. What is the difference between Forward Propagation and backward propagation? 
    Ans. Forward propagation is tasked to make the computations, while backward propagation is tasked to get the feedback based on which the computations are corrected. 

Key Learnings

Artificial Neural Networks make the basis for Deep learning. Hence it’s important to know exactly how ANNs work. This blog thoroughly covers the principle behind Forward Propagation and what purpose it serves. It also covers how it is different from Backpropagation in its objective. It is advisable to visit our other blogs on ANN to understand them in their entirety. If you wish to build upon your skills in deep learning, then you may check out our industry-oriented courses on deep learning curated by industry experts. 

Happy Learning!

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