Reference no: EM132782201

58072 Neural Networks - Sharif University of Technology

Assignment 1

Use MATLAB NEURAL NETWORKS TOOLBOX or the Neunet (Desire) system to develop and study Learning process in Back-Propagation networks.

1. Train the 2-2-1 network to learn the XOR patterns.
2. Modify the 2-2-1 network so that only one hidden unit is used.
3. Train the 2-2-1 network to learn the XOR patterns when the Bias term is fixed at zero. (Note that you must modify a few statements in the program to accomplish this.)
4. Do not randomize the weights before training the 2-2-1 network. (Remove the initialization to random values statements; by default, the weights will be initialized to zero.)
5. Modify the program to include a Temperature parameter. Then, train the 2-2-1 network with several different Temperature parameter values.

Question 1. How many epochs are required to learn the patterns correctly?

Question 2. Does the system converge to the same set of weights after each learning session?

Question 3. What is the effect of the learning rate (Lrate) on the speed of learning?

Question 4. What is the effect of setting the initial weights to zero?

Question 5. Can the Network learn the patterns without a Bias term?

Question 6. What is the effect of the Temperature parameter on the speed of learning?

Question 7. Did you encounter any local minima for which there were global minima of zero?

Assignment 2

Use MATLAB NEURAL NETWORKS TOOLBOX or the Neunet (Desire) system to develop and study Learning process in Back-Propagation networks. The patterns to be learned are the mapping from θ to cos(θ). The patterns are generated using a loop in the program which varies θ from 0 to 2Π in steps of 2Π/Npat. The output values are selected to be in the range [0,1] instead of [-1,1].

1. Train a 1-x-1 network to learn the patterns.
2. Modify the program so that a different activation function is used. For example try one of: Bipolar hidden and output units (tanh function); linear output units;
3. Test the ability of the network to generalize by presenting a set of Test patterns that the network was not trained with.

Question 1. How many epochs are required to learn the patterns reasonably well ( tss ≤ 0.01)?

Question 2. How many hidden units are required? (There will be a range of hidden units that provide similar results.)

Question 3. What is the effect of changing the activation function?

Question 4. How well is the network able to generalize?

Question 5. Are there any other changes that could be made to reduce tss (not the speed of learning)?