engineering

neural network ; deep learning .

Question # 3 (55 pts) Given the following neural network with initialized wejghes as in the picture below, we are trying to distinguish between apples and bananas. An example of training set is as follows: Apple: Input (0.2, 0.3) and desired output (1, 0) Banana: Input (0.1, 0.4) and desired output (0, 1) Assume that all the neurons have a sigmoid activation function. Let the learning rate n be 0.2 and the weights are as indicated in the figure below. a. Apply the forward propagation of the signals in the network using (0.2, 0.3) as input, then perform the back propagation of the error. Show the changes of the weights. (25 pts) b. Apply the forward propagation of the signals in the network using (0.1, 0.4) as input, then perform the back propagation of the error. Show the changes of the weights. (25 pts) c. Calculate the average error energy E- (5 pts) P.S: You can use the equations below as output neurons 0.1 hidden neurons 06 02 2 05 0.1 0.5 brput nerons b. PS. The inputs are denoted a and b, the neurons are numbered from 1 to 4 and the biases are represented at the right side of each neuron. ) Un) =n) ((uYa);a{uya = (uye ald,(n)-0,(n)(n)[1-0,(n)]. neuron j is an output node 8(m) = 4(v,(n)) 6,(n)w,(n) - ay,(m){1 - y,(m)| &,(n)w,{n), neuron j is hidden Question # 3 (55 pts) Given the following neural network with initialized wejghes as in the picture below, we are trying to distinguish between apples and bananas. An example of training set is as follows: Apple: Input (0.2, 0.3) and desired output (1, 0) Banana: Input (0.1, 0.4) and desired output (0, 1) Assume that all the neurons have a sigmoid activation function. Let the learning rate n be 0.2 and the weights are as indicated in the figure below. a. Apply the forward propagation of the signals in the network using (0.2, 0.3) as input, then perform the back propagation of the error. Show the changes of the weights. (25 pts) b. Apply the forward propagation of the signals in the network using (0.1, 0.4) as input, then perform the back propagation of the error. Show the changes of the weights. (25 pts) c. Calculate the average error energy E- (5 pts) P.S: You can use the equations below as output neurons 0.1 hidden neurons 06 02 2 05 0.1 0.5 brput nerons b. PS. The inputs are denoted a and b, the neurons are numbered from 1 to 4 and the biases are represented at the right side of each neuron. ) Un) =n) ((uYa);a{uya = (uye ald,(n)-0,(n)(n)[1-0,(n)]. neuron j is an output node 8(m) = 4(v,(n)) 6,(n)w,(n) - ay,(m){1 - y,(m)| &,(n)w,{n), neuron j is hidden