Backpropagation is the foundation of neural network training. It is the practice of fine-tuning a neural net's weights based on the error rate (i.e. loss) achieved in the preceding epoch (i.e. iteration). Proper weight tuning ensures decreased error rates, boosting the model's reliability by increasing its generalization.

When training a neural network, backpropagation is a step that must be taken. Backpropagation uses the neural network's error rate during forward propagation as a loss to adjust the weights of the network's inner layers. 

Backpropagation networks can be split into two categories.

• Static backpropagation is a network that converts inputs into outputs that remain unchanged. These networks, such as OCR (Optical Character Recognition), can solve static classification issues.
• Another network used for fixed-point learning is recurrent backpropagation. Feed-forward activation is used in recurrent backpropagation until a threshold is met. While recurrent backpropagation does not offer instant mapping, static backpropagation does.

Features

It uses the same gradient descent method as a simple perceptron network with a differentiable unit. How the weights are calculated during the learning time of the network is different from how other networks do it.

There are three steps to training: 

1. The input training pattern that goes back to the source
2. How the mistake was calculated and spread backwards
3. Change in the weight

Benefits of Backpropagation in Neural Networks

• It's simple to construct because you don't need prior experience with neural networks. 
• It's easy to code because you only need to worry about the inputs.
• It can perform a task without first learning its specifics, saving time. 
• The model's generalizability and ease of implementation make it highly versatile. 

To train a network to its full potential, Backpropagation uses an iterative, recursive, and efficient method to calculate the updated weight until the network can no longer do the task at hand. It is necessary to know the derivatives of the activation function during network design.

Backpropagation Algorithm:

• Step 1: Inputs X arrive via the pre-established path.
• Step 2 involves modelling the input using true weights W. Typically, weights are determined randomly.
• Step 3: Calculate the output of each neuron from the input layer to the hidden layer and the layered output.
• Step 4: Calculate the output error. Error in Backpropagation = Actual Output - Desired Output
• Step 5: Return to the hidden layer from the output layer to modify the weights to minimize the error.
• Step 6: Repeat the procedure until the desired result is reached.

Time complexity

Each algorithmic iteration has a different temporal complexity based on the nature of the underlying network. Matrix multiplications are the main time-consuming operation in multilayer perceptrons.

Limitations

• Training data can affect how well the model works, so it's essential to use high-quality data. 
• Noisy data can also affect backpropagation, making its results less accurate.  
• Backpropagation models can take a while to train and get up to speed.  
• Backpropagation needs a method based on matrices, which can cause other problems.

Backpropagation has some challenges, but it is still an excellent way to test and improve the performance of neural networks.

Image source: Unsplash

Algorithm source: Geeksforgeeks