Homework-8
Question 1
Consider a deep neural net applied to decide between the following four categories:
cat, tiger, human face, lion
The neural net uses a softmax unit at the output layer. Consider the case where the values fed into the
output layer are:
cat 0.5
tiger 0.8
human face -3
lion 0.6
The softmax converts these values into a probability vector.
1. Compute the probabiity vector.
Answer:
2. Which outcome is the most likely?
Answer:
3. Which outcome is the least likely?
Answer:
4. What is the result of cross-entropy cost function if the target output is lion?
Answer:
Question 2
In the table below cases 3,4 are distributions, and cases 1, 2 can be converted into distributions.
case A B C D
1 1 -2 3 -4
2 1 2 -3 0
3 1 0 0 0
4 1/4 1/4 1/4 1/4
1. Use cross entropy to determine which distribution among 1,2,3 is most similar to 4. Show your computations.
Answer: 1 / 2 / 3
2. Use cross entropy to determine which distribution among 1,2,4 is most similar to 3. Show your computations.
Answer: 1 / 2 / 4
