Theory test: Classification

6 questions. Pass with 5 correct.

1. 01 What is $\sigma (0)$, the sigmoid of zero?

   00.51$e$
2. 02 A model predicts $p=0.9$ for an example whose true label is 0. What is its binary cross-entropy loss?

   $-\log 0.9\approx 0.105$$-\log 0.1\approx 2.30$$0.9^2=0.81$0
3. 03 For logistic regression with cross-entropy, $\partial \text{loss}/\partial z$ for one example equals:

   $\sigma (z)(1-\sigma (z))$$p-y$$(p-y{)}^2$$-\log p$
4. 04 What is $\text{softmax}(1,1,1)$?

   $(1,1,1)$$(1/3,1/3,1/3)$$(0,0,0)$$(e,e,e)$
5. 05 In two dimensions, the decision boundary of logistic regression is:

   A circleA straight lineAny curve the data needsA single point
6. 06 Why do implementations subtract $\max (\mathbf{z})$ from the logits before computing softmax?

   It changes the probabilities to be more confidentIt avoids overflow in $e^z$, and doesn't change the resultIt makes the gradient largerIt's required for the probabilities to sum to 1