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Multilayer neural networks use a most common technique from a variety of learning technique, called the back propagation algorithm.

**Back Propagation neural network**

Multilayer neural networks use a most common technique from a variety of
learning technique, called the back propagation algorithm. In back propagation
neural network, the output values are compared with the correct answer to
compute the value of some predefined error function. By various techniques the
error is then fed back through the network. Using this information, the
algorithms adjust the weights of each connection in order to reduce the value of
the error function by some small amount. After repeating this process for a
sufficiently large number of training cycles the network will usually converge
to some state where the error of the calculation is small.

The goal of back propagation, as with most training algorithms, is to
iteratively adjust the weights in the network to produce the desired output by
minimizing the output error. The algorithm’s goal is to solve credit assignment
problem. Back propagation is a gradient-descent approach in that it uses the
minimization of first-order derivatives to find an optimal solution. The
standard back propagation algorithm is given below.

**Step1:**

Build a network with the choosen number of input, hidden and output
units.

**Step2:**

Initialize all the weights to low random values.

**Step3:**

Randomly, choose a single training pair.

**Step4:**

Copy the input pattern to the input layer.

**Step5:**

Cycle the network so that the activation from the inputs generates the
activations in the hidden and output layers.

**Step6:**

Calculate the error derivative between the output activation and the
final output.

**Step7:**

Apply the method of back propagation to the summed products of the
weights and errors in the output layer in order to calculate the error in the
hidden units.

**Step8:**

Update the weights attached the each unit according to the error in that
unit, the output from the unit below it and the learning parameters, until the
error is sufficiently low.

To derive the back propagation algorithm, let us consider the three layer
network shown in figure .

To propagate error signals, we start at the output layer and work
backward to the hidden layer. The error signal at the output of neuron k at
iteration x is defined as

Generally, computational learning theory is concerned with training
classifiers on a limited amount of data. In the context of neural networks a
simple heuristic, called early stopping often ensures that the network will
generalize well to examples not in the training set. There are some problems
with the back propagation algorithm like speed of convergence and the
possibility of ending up in a local minimum of the error function. Today there
are a variety of practical solutions that make back propagation in multilayer
perceptrons the solution of choice for many machine learning tasks.

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