Neural Network Capstone Checkpoint

Check XOR expressiveness, forward shapes, gradient reduction, and training diagnostics.

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

1. On the four equally weighted XOR rows, the score x1+x2-0.5 predicts 1 when nonnegative. What accuracy does it achieve?

Select one answer.

50% 100% 0% 75%

2. X has shape (5,2), W1 is (2,3), and W2 is (3,1). Which expression and shape are correct for hidden preactivations?

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X @ W1 + b1 has shape (5,3) W1 @ X + b1 has shape (3,5) X @ W2 + b2 has shape (5,1) W2 @ W1 has shape (5,3)

3. For one example with target 1 and predicted probability 0.8, what is the unaveraged output-logit error p-y? Enter a decimal.

4. Every batch row and target is duplicated. Loss and all parameter gradients double. What convention was likely missed?

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Random initialization Dividing the summed loss and parameter gradients by the number of examples Transposing the output predictions Changing the target labels

5. A backward pass updates W2, then uses that updated W2 to propagate error to the hidden layer. Why is the hidden gradient wrong?

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Bias vectors cannot receive gradients The sigmoid derivative must be omitted It uses parameters different from those that produced the forward computation Only the output weights may be updated during training

6. There are two examples and two output columns; every individual binary loss is 0.5. Under this exercise's sum-over-outputs, mean-over-examples convention, what total loss is returned? Enter a number.

7. Training loss decreases, but finite differences disagree with hidden-layer gradients on non-saturated inputs. What should you do first?

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Train longer until the disagreement disappears Add more hidden units Treat any decreasing loss as proof of correct gradients Check chain-rule factors, transposes, and update order

8. A training run records one pre-update loss in each of 10 epochs and returns the final weights. Which statement is correct?

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The last recorded loss precedes the tenth update; recompute loss to evaluate returned weights The last recorded loss must equal loss on the returned weights Only nine updates were performed The final loss is guaranteed to be the smallest recorded loss

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