1.
Introduction
2.
Backpropagation
3.
Types of Backpropagation
3.1.
Static Backpropagation
3.2.
Recurrent Backpropagation
4.
5.
Applications of Backpropagation
6.
Essential derivatives
6.1.
Sigmoid
6.2.
Relu
6.3.
Softmax
7.
8.
Kay takeaways
Last Updated: Mar 27, 2024

# Backpropagation

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Ashwin Goyal
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## Introduction

Backpropagation is a general topic that people typically find difficult to understand. When studying neural networks, we generally get confused about solving errors and gradients, sigmoid functions, or the mathematics involved in the calculation.

But donâ€™t worry, today weâ€™ll learn everything about backpropagation in-depth.

## Backpropagation

Backpropagation is the short form of backward propagation of errors. It is an algorithm used for supervised learning of artificial neural networks using gradient descentGiven a neural network and an error function, the method calculates the gradient of the error function concerning the neural network's weights. Just like we used to optimize parameters with the help of gradient descent in linear regression, similarly in backpropagation, the gradient is used.

Backpropagation is a function of neural networks, a set of methods used to train artificial neural networks efficiently. The prime features of backpropagation are the iterative, recursive, and efficient methods. It calculates the updated weight to improve the network until it cannot perform the task it was being trained for. At the time of network design, derivatives of the activation function are required.

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## Types of Backpropagation

There are two types of backpropagation:

### Static Backpropagation

This type of backpropagation aims to produce a static output for a fixed input. This kind of neural network is used to solve a problem like optical character recognition.

### Recurrent Backpropagation

This type of backpropagation is a type of network employed in fixed-point leaning. The activations are fed forward till it stains a fixed value, followed by which an error is calculated and propagated backward.

• It is sensitive to irregular data
• It requires plenty of time to train
• The performance is highly reliant on the input

## Applications of Backpropagation

• It is used in speech recognition
• Used for face and character recognition
• The neural network is trained to pronounce each letter of a word

## Essential derivatives

### Sigmoid

The sigmoid derivation is a critical formula. The primary reason we use the sigmoid function is that it exists between 0 to 1. Thatswhy it is used for models where we have to predict the probability as an output. Since probability exists only between the range of 0 and 1, sigmoid is the right choice. The formula is:

### Relu

ReLU is the short form for Rectified Linear Activation Function. It is a piecewise linear function that will return the output as the input directly if it is positive, else it will output as zero. The ReLU is default activation when developing multilayer perceptron and convolutional neural networks. Mathematically it is represented as:

### Softmax

The softmax is used as the activation function in the output layer of neural network models that predict a multinomial probability distribution. While, If you use the softmax layer as a hidden layer, you will keep all your nodes linearly dependent, which could result in many problems and poor generalization. In other words, the softmax function is used as the activation function for multi-class classification problems. The mathematical representation is:

Here's the backpropagation's pseudocode:

1. What is the learning rate in backpropagation?
The learning rate is the speed by which a neural network can learn new data features and override old data.

2. What is the activation function in backpropagation?
In backpropagation, the activation function decides whether the neuron should be activated or triggered on the total sum.

3. What is bias in backpropagation?
Bias is an additional parameter in neural networks. It can be understood as the intercept of an equation. Bias value is added at each node, apart from the input node, in backpropagation.

## Kay takeaways

This article gave a brief explanation about backpropagation. We have discussed the types, applications, and functions of backpropagation, such as sigmoid, relu, and softmax functions. Apart from that, the mathematical representation of the derivative function used in backpropagation is presented. If you are interested to know more, check out our industry-oriented deep learning course curated by our faculty from Stanford University and Industry experts.