Neural Network

Q3: For the network below to demonstrate forward propagation the inputs are (1, 1) & the target is (0) & apply the activation function (sigmoid function)f(Cx)to the hidden layer sums for activation to get the final value. (10- Mark)

## Expert Answer

In **Forward Propagation,** we apply set of weights to the input data andcalculate an output.

Neutral Network repeats for both Forward and Backward Propagation until the desired output comes.

We use the X-OR ( Exclusive OR) Operation for solving the problem.

It would provide correct output given any input acceptable by XOR function. The table is as follows:

Inputs | Outputs |

0, 0 | 0 |

0, 1 | 1 |

1, 0 | 1 |

1, 1 | 0 |

Let’s use last row from the table ( 1 , 1) => 0 for forward propagation

We Sum the Product of inputs with their corresponding set opf weights arrive at the hidden layer as follows:

( 1 * 0.8 ) + ( 1 * 0.2 ) = 1

( 1 * 0.4 ) + ( 1 * 0.9 ) = 1.3

( 1 * 0.3 ) + ( 1 * 0.5 ) = 0.8

We put these sums in the circles of hidden layer as follows:-

Now to get the final value we apply the activation function i.e. sigmoid function to hidden layers sums. it’s purpose is to translate input signal to output soignals.

Sigmod Function : 1 / 1 + e^{-x}

The 2D graphical representation of such function is as follows:

Now applying Sigmod Function to the three hidden layers as follows:

Now we add these calculations to neutral network as hidden layer result:

Now we Calculate the SOP of hidden layers with second set of weights drom hidden to output layer as follows:

( 0.73 * 0.3 ) + ( 0.78 * 0.5) + ( 0.68 * 0.9 ) = 1.221

Now we finally calculate final output result by applying Sigmoid function as follows:

The full diagram is as follows:

We use the random set of initial weights so the output is off the mark in this case by +0.77. To get more accurate result you should use the Backward propagation. it doesn’t provide accurate result but sometimes near to the solution.