Classification Checkpoint

Trace stable probabilities, batch gradients, threshold decisions, and calibration. Select one answer per multiple-choice question.

Get every question correct to pass this checkpoint. You can review feedback, revise your answers, and submit again.

1. A direct sigmoid implementation overflows at z=-1000. Which equivalent negative-logit branch avoids this overflow?

Select one answer.

1/(1+exp(z)) exp(z)/(1+exp(z)) exp(-z)/(1+exp(-z)) 1/(1+z)

2. What does softmax([1007,1007,1007]) return, up to rounding?

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[1007,1007,1007] [1,1,1] [0,0,0] [1/3,1/3,1/3]

3. A batch has x values [0,4], targets [0,1], and current w=b=0. What is the mean weight gradient (1/n)*sum(x*(p-y))? Enter a number.

4. X has shape (7,2), with 4 classes. Which shapes match the multiclass exercise?

Select one answer.

W:(2,4), logits:(7,4) W:(4,2), logits:(4,7) W:(7,4), logits:(2,4) W:(2,7), logits:(4,7)

5. A learner sets E=(P-Y)/n, then computes dW=X.T@E/n. What happens to the gradient?

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It is multiplied by n It becomes a per-row update It is divided by n twice It is unaffected because softmax rows sum to one

6. Probabilities are [0.8,0.5,0.3] and targets [1,0,1]. Under the exercise rule p>=threshold, lowering the threshold from 0.5 to 0.3 does what?

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Adds a false positive and leaves recall unchanged Adds a true positive and leaves the false-positive count unchanged Changes all three estimated probabilities Removes the false positive at probability 0.5

7. On 200 held-out cases assigned probabilities near 0.8, only 100 are positive. Which conclusion is justified?

Select one answer.

Logistic regression cannot produce these predictions The default threshold must be above 0.8 The model is calibrated because every output is between zero and one This bin suggests overconfidence; calibration must be checked beyond this bin too

8. An evaluation set has 98 negatives and 2 positives. An always-negative classifier gets 98% accuracy. What is its positive-class recall? Enter 0 or 1.

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