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Lab 5: Artificial Neural Networks II Solution




Problem Description




Implement (in C++) a fully connected feed-forward neural network that con-sists of 3 input neurons, 2 hidden layer neurons and 1 output neuron. The hidden layer neurons and output neuron use the Sigmoid (chapter 4 [Mitchell, 1997]) activation function.




The ANN input nodes 1, 2 and 3, respectively, have the following inputs:




x = [ 1:30, 2:70, 0:80 ]




The ANNs expected output is:




y = 0:36




Table 1 speci es the weights connecting the inputs to the hidden layer neu-rons. Note that each column denotes a given node connected to a given hidden layer. For example, the top value in column 1 is the value of the weight con-necting input node 1 to hidden layer node 1, and the bottom value in column 1 is the value of weight connecting input node 1 to hidden layer node 2.




The bias values for the hidden layer neurons 1 and 2, respectively, are:




b = [ 0:1, 0:3 ]



Table 1: Values of weights connecting input to hidden layer nodes.




Input 1
Input 2
Input 3






0:1
0:2
0:5






0:4
1:0
0:6






Question 1:




Given the ANN input x, what are the output values of hidden layer neurons 1 and 2 ?




Question 2:




Given that the weights from hidden layer nodes 1 and 2, respectively, are:




w = [ 0:8, 1:0 ]




And the bias value for the output node is: b = 0:3, and the ANN input x, what is the output value of the output neuron ?




Question 3:




Given this output, what is the Mean Squared Error for ANN input x.










In a ZIP le, place the source code, executable, and a text le containing your list of training examples, as well as answers to questions 1, 2 and 3. Upload the ZIP le to Vula before 10.00 AM, 7 September, 2018.







References




[Mitchell, 1997] Mitchell, T. (1997). Machine Learning. McGraw Hill, New York, USA.










































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