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Day 31

Recall block

Diagnostic

Today's recall block is the neural-network prerequisite check: 8 short items on matrix shapes, dot products, derivatives and the chain rule, logistic regression as a one-layer network, and overfitting and regularization. Work them by hand or in your head, without a framework, and rate your confidence honestly for each.

This is not a grade. It shows which prerequisites to revisit before Days 31-33: if shapes and derivatives are solid, go straight to the primers; if not, work the worked examples in the Day 31 deep dive and the Day 32 primer first. A confident wrong answer is more useful to the plan than a skipped item.

Your progress

0 / 8

0 of 8 answered. Results feed your evidence profile; they are a starting point, revised at the Week 2 review.

Deep learning and neural networksClassical ML and model selectionStatistics and probability

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Question 1 · easy

A batch `X` has shape (64, 10): 64 flights, 10 features each. A dense layer with 32 units computes `H = X @ W + b`. What are the shapes of `W`, `b` and `H`?

OptionsA. W (10, 32), b (64, 32), H (64, 32)B. W (32, 10), b (32,), H (32, 64)C. W (64, 32), b (32,), H (64, 32)D. W (10, 32), b (32,), H (64, 32)

How confident are you? (optional, used for calibration)

Question 2 · easy

A single neuron has weights $w = (0.5, -1, 2)$ and bias $b = 0.4$. For input $x = (2, 3, 1)$, what is its pre-activation $z = w \cdot x + b$?

Your answer

How confident are you? (optional, used for calibration)

Question 3 · medium

A fully connected network has 10 inputs, one hidden layer of 32 units and 1 output unit, with a bias in every unit. It is trained with batches of 64. How many trainable parameters does it have?

Your answerparameters

How confident are you? (optional, used for calibration)

Question 4 · hard

A one-weight model predicts $\hat y = w x$ with squared-error loss $L = (w x - y)^2$. With $x = 2$, $y = 3$ and current $w = 1$, take one gradient-descent step with learning rate 0.1. What is the new value of $w$?

Your answer

How confident are you? (optional, used for calibration)

Question 5 · medium

Which neural network, trained how, is the same model as a logistic regression for "will this passenger be a no-show"?

OptionsA. A linear layer whose raw output $z = w \cdot x + b$ is read directly as the no-show probability.B. One linear layer with a single output unit, a sigmoid on that output, trained by minimizing binary cross-entropy.C. A network with a hidden layer of sigmoid units, because the sigmoid makes logistic regression non-linear in its inputs.

How confident are you? (optional, used for calibration)

Question 6 · medium

Why is binary cross-entropy (log loss) the standard training loss for a sigmoid output?

OptionsA. Minimizing it is maximum likelihood for a Bernoulli outcome: it is the negative log of the probability the model gave to the observed label.B. It directly maximizes accuracy, so a lower log loss always means more correct predictions.C. It makes training convex for any network, so a model with hidden layers always reaches the global minimum.

How confident are you? (optional, used for calibration)

Question 7 · medium

Training loss falls steadily for 40 epochs. Validation loss falls until epoch 12, then rises steadily. What is happening, and what is a sound first intervention?

OptionsA. Training is diverging; lower the learning rate.B. The model is underfitting; add layers and train for more epochs.C. Overfitting from about epoch 12. Keep the checkpoint at the validation-loss minimum (early stopping), or add weight decay or dropout, and confirm on data not used for these choices.

How confident are you? (optional, used for calibration)

Question 8 · hard

An L2-regularized logistic regression predicts no-shows from two unscaled features: `distance_km` (200 to 10,000) and `is_holiday` (0 or 1). Across their observed ranges both shift the no-show odds by a similar amount. What happens as you increase the penalty strength?

OptionsA. The `is_holiday` coefficient is shrunk much harder. The per-km coefficient is tiny because of the units, so it costs almost nothing in the penalty. Standardize inside the pipeline first.B. Both coefficients shrink by the same proportion, because the penalty treats all coefficients alike.C. Validation performance keeps improving, because a stronger penalty always reduces overfitting.

How confident are you? (optional, used for calibration)