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Backpropagation Algorithm


The backpropagation Algorithm is broadly used in machine learning. This algorithm is greatly used for training feed-forward neural networks. It permits the information from the cost to then flow backward through the network, acceptable to compute the gradient.

Backpropagation is the core of neural network training. It is the way of adjusting the weights of a neural network. Those are based on the error rate found in the preceding epoch. Accurate tuning of the weights permits us to decrease error rates. It makes the model dependable by growing its generalization.

In this article, we will go through the backpropagation algorithm and know that how it works?


Backpropagation is a normal method of training artificial neural networks. It supports the calculation of the gradient of a loss function regarding all the weights in the network.

We use a feedforward neural network to accept an input x and produce an output y, and the information moves onward over the network. The inputs x find the early information that then spreads to the unseen units at each layer and lastly produces yˆ. This is called forward propagation. The forward propagation may remain onward till it produces a scalar cost J (θ) during training.

The backpropagation algorithm was first presented in the 1970s. Its significance is solely valued in a well-known 1986 paper. That paper terms numerous neural networks where backpropagation works extremely faster than previous methods to learning. That makes it likely to use neural nets to solve problems that had before been difficult. Nowadays, the backpropagation algorithm is the rock of learning in neural networks.

How does Backpropagation Algorithm Work?

  • The Backpropagation algorithm in a neural network computes the gradient of the loss function for a single weight.
  • That is done with the help of the chain rule.
  • It competently computes one layer at a time, different from a native direct computation.
  • It calculates the gradient. Though, it does not define how the gradient is used.
  • It simplifies the calculation in the delta rule.

Look at the below Backpropagation neural network example diagram to understand:

Backpropagation Algorithm

  • Inputs X, reach over the pre-connected route.
  • Input is demonstrated using actual weights W.
  • The weights are typically randomly designated.
  • Calculate the output for every neuron from
  • the input layer
  • to the hidden layers
  • to the output layer
  • Compute the error in the outputs

ErrorB= Actual Output – Desired Output

  • Go back from the output layer to the hidden layer to correct the weights such that the error is reduced.
  • Keep iterating the process up to the wanted output is attained.

Importance of Backpropagation algorithm

The word back-propagation is frequently misinterpreted. By way of meaning the complete learning algorithm for multi-layer neural networks. Essentially, back-propagation mentions only the way for computing the gradient. However, another algorithm, for example, stochastic gradient descent, is used to do learning using this gradient.

Moreover, back-propagation is frequently misunderstood as being precise to multilayer neural networks. Then, in standard it may calculate derivatives of any function, the accurate reply is to report that the derivative of the function is undefined. In detail, we will define;

  • How to calculate the gradient ∇of(x, y) for an arbitrary function f.
  • Where x is a set of variables. Its derivatives are wanted.
  • The y is an extra set of variables that are input into the function.
  • Though, its derivatives are not needed.
  • The gradient we most regularly need is the gradient of the cost function with respect to the parameters, ∇θ J(θ) in learning algorithms.
  • A lot of machine learning tasks include computing other derivatives, whichever is part of the learning process.
  • The backpropagation algorithm may be used for these tasks as well.
  • This is not limited to computing the gradient of the cost function regarding the parameters.
  • The impression of computing derivatives by propagating information from side to side of a network is very general.
  • This can be used to calculate values for example the Jacobian of a function f with various outputs.
  • We limit our description here to the most normally used case where f has a single output.

Types of Backpropagation

There are two types of Backpropagation Networks:

  • Static Back-propagation
  • Recurrent Backpropagation

Static back-propagation:

In this kind of backpropagation network, we produce a mapping of a static input for static output. This is valuable to solve static classification matters like optical character recognition. The mapping is fast in static back-propagation.

Recurrent Backpropagation:

In data mining, Recurrent Backpropagation is fed forward until a fixed value is attained. Then, the error is calculated and propagated backward. The mapping is nonstatic in recurrent backpropagation.


  • Backpropagation is an abbreviation for backward propagation.
  • This is a normal method of training artificial neural networks
  • The backpropagation algorithm in machine learning is rapid and easy to program.
  • Two Types of Backpropagation are Static Back-propagation and Recurrent Backpropagation
  • Backpropagation in data mining makes simpler network building by removing weighted links.
  • It is particularly valuable for deep neural networks working on error-prone projects, for example, image or speech recognition.