final - Department of Mechanical Engineering Massachusetts...

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Department of Mechanical Engineering Massachusetts Institute of Technology 2.160 Identification, Estimation, and Learning End-of-Term Examination May 17, 2006 1:00 – 3:00 pm (12:30 – 2:30 pm) Close book. Two sheets of notes are allowed. Show how you arrived at your answer. Problem 1 (40 points) Consider the neural network shown below. All the units are numbered 1 through 6, where units 1 and 2 are input units relaying the two inputs, and , to units 3 and 4. The output function of each unit is a sigmoid function; 1 x 2 x 1 () 1 i ii i z yg z e == + , where variable is the weighted sum of all the inputs connected to that unit: i z . = j j ij i x w z There are three hidden units, units 3, 4 and 5, connected to the output unit, unit 6. The output of the network, , is connected to a known, but nonlinear process: 6 y 3 6 ˆ yy = A distal teacher provides a training signal y, which is compared to the above estimate . The weights of the network are corrected based on the error back propagation algorithm with learning rate y ˆ η
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final - Department of Mechanical Engineering Massachusetts...

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