implement a network that learns the multiplication table . Using MATLAB, design/implement a three-layer feedforward neural netwok. Use the backpropagation learning algorithm.

In this problem, you are going to implement a network that learns (or memorizes) the multiplication table (\carpm tablosu" in Turkish). Using MATLAB, design/implement a three-layer feedforward neural network that multiplies two integers in the range {1; 2; : : : ; 10}. Use the backpropagation learning algorithm. You are free to design the network as you like, as long as it is capable of multiplying two integers between 1 and 10. Alternatively, you can refer to my suggestions below.

• Use the hyperbolic tangent function as the activation function.
• Use 20 neurons in the input layer. Neurons 1:10 will represent the rst integer, and neurons 11:20will represent the second integer. Use a binary input scheme (i.e., -1's and 1's). For example, ifyou are multiplying 3 and 8, 3rd neuron in the rst set and 8th neuron in the second set will be1, others will be -1. In other words, neurons 3 and 18 will be 1 and others will be -1. If you aremultiplying 9 and 5, neurons 9 and 15 will be 1 and others will be -1.
• Use 100 neurons in the output layer and use a binary desired output scheme. For example, ifyou are multiplying 3 and 8, the desired output vector will have 1 in the 24th entry and -1 inother entries. If you are multiplying 9 and 5, the desired output will have 1 in the 45th entryand -1 in the other entries.

Choose an appropriate number of hidden neurons, an appropriate learning rate, an appropriate error threshold, and/or an appropriate number for maximum number of epochs to stop the iterations. Train the network using all 100 possible multiplications and report how the error decreases with the number of epochs. Does your network converge? In how many epochs? Then test the network using all 100 possible multiplications and demonstrate that it works. How many of the 100 possible multiplications does your network calculate correctly?