Neural networks, CNNs and model selection (HL) – IB Computer Science exam questions with mark scheme

1StandardHL only4 marks

A single artificial neuron has weights w₁ = 0.5, w₂ = −0.4, w₃ = 0.3 and bias b = −0.6. It uses a step activation: output 1 if the total is > 0, otherwise 0.

(a) Calculate the output for inputs (1, 0, 1). [3]

(b) State the output for inputs (0, 1, 1). [1]

(a) Weighted sum = 1(0.5) + 0(−0.4) + 1(0.3) = 0.8 (allow 0.5 + 0.3 − 0.6 = 0.2 written in one line for this mark and the next)(1)
(a) Adds the bias: 0.8 − 0.6 = 0.2(1)
(a) 0.2 > 0, so the output is 1 (follow-through from their total)(1)
(b) 0 (working not required; total = −0.4 + 0.3 − 0.6 = −0.7)(1)
Answer: (a) 1 (b) 0
Examiner tip: Do not forget to add the bias before applying the activation function.

2CoreHL only4 marks

A perceptron is the basic building block of an artificial neural network (ANN).

(a) Outline the function of the weights in a perceptron. [1]

(b) Outline the function of the bias in a perceptron. [1]

(a) Each weight multiplies its input to set how much influence/importance that input has on the output (accept: weights are adjusted during training to change the strength of each connection)(1)
(b) The bias is added to the weighted sum so the threshold/decision boundary can be shifted, allowing the neuron to fire (or not) even when all inputs are 0 (accept: an offset that is learned like a weight)(1)
(c) Any two from: decides whether / how strongly the neuron fires (produces the output) based on the weighted sum plus bias; maps the total into a fixed range (e.g. 0 or 1 for step, 0 to 1 for sigmoid);(1)
introduces non-linearity so that networks of neurons can learn non-linear (complex) relationships (ignore naming a specific function without a function described)(1)
Answer: (a) scale each input's influence (b) shifts the threshold / offset (c) e.g. decides output/firing; adds non-linearity
Examiner tip: Naming an activation function (e.g. “sigmoid”) is not outlining what it does; state its effect on the output.

3StandardHL only4 marks

The diagram shows a small multi-layer perceptron. Each hidden neuron uses the ReLU activation, $\text{ReLU}(z)=\max(0,z)$. The output neuron uses the sigmoid activation, $\sigma(z)=\dfrac{1}{1+e^{-z}}$. The bias of each neuron is shown next to it. The weights are: $x_1 \to h_1 = 0.4$, $x_2 \to h_1 = -0.2$, $x_1 \to h_2 = -0.6$, $x_2 \to h_2 = 0.8$, $h_1 \to y = 1.5$, $h_2 \to y = 0.9$.

The inputs are $x_1 = 1.0$ and $x_2 = 0.5$.

Calculate the output $y$ of the network. Show your working and give your answer to 3 decimal places. [4]

$h_1$: $0.4(1.0) + (-0.2)(0.5) + 0.1 = 0.4$, so $h_1 = 0.4$(1)
$h_2$: $-0.6(1.0) + 0.8(0.5) - 0.3 = -0.5$, ReLU gives $h_2 = 0$ (must show ReLU applied to a negative total)(1)
Output weighted sum: $1.5(0.4) + 0.9(0) - 0.2 = 0.4$ (follow through from their $h_1$, $h_2$)(1)
$y = \sigma(0.4) = 0.599$ (accept 0.5987; follow through from their weighted sum)(1)
Answer: $h_1=0.4$, $h_2=0$, $z=0.4$, $y\approx0.599$
Examiner tip: Students often forget that ReLU turns the negative total for $h_2$ into 0 and carry −0.5 forward.

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4HardHL only5 marks

A single perceptron has two binary inputs $x_1$ and $x_2$, weights $w_1 = w_2 = 1$, bias $b = -1.5$ and a step activation that outputs 1 if the total is greater than 0 and outputs 0 otherwise.

(a) Show that this perceptron implements the logical AND function. [2]

(b) The XOR function outputs 1 only when exactly one input is 1. Explain why no single perceptron can implement XOR, and how a multi-layer perceptron overcomes this. [3]

(a) Correct totals for all four input pairs: (0,0) → −1.5, (0,1) and (1,0) → −0.5, (1,1) → 0.5(1)
(a) Hence outputs 0, 0, 0, 1, which matches the AND truth table (must state the comparison)(1)
(b) A single perceptron computes a linear function of its inputs, so it can only separate classes with a single straight line / hyperplane (decision boundary)(1)
(b) The XOR outputs cannot be split by one straight line / XOR is not linearly separable ((0,1),(1,0) lie on opposite corners to (0,0),(1,1))(1)
(b) An MLP has a hidden layer (with non-linear activation) whose neurons each create a boundary (e.g. one for OR, one for NAND) which the output neuron combines (e.g. ANDs) to produce XOR (accept: hidden layer transforms inputs into a representation that is linearly separable)(1)
Answer: (a) totals −1.5, −0.5, −0.5, 0.5 give 0,0,0,1 = AND. (b) XOR is not linearly separable; a hidden layer combines two linear boundaries.
Examiner tip: For (b), “XOR is too complex” earns nothing; the key phrase is that XOR is not linearly separable.

5StandardHL only4 marks

A convolutional neural network (CNN) applies the 3×3 kernel shown to the 4×4 greyscale image shown. The kernel moves with a stride of 1 and no padding is used.

(a) State the dimensions of the resulting feature map. [1]

(b) Calculate the value in the top-left position of the feature map. Show your working. [2]

(a) 2 × 2(1)
(b) Multiplies the top-left 3×3 region element-by-element by the kernel: $(1+0+2) - (2+3+0)$ (accept the nine products written out)(1)
(b) $= -2$(1)
(c) Vertical edges (accept: change in brightness from left to right / horizontal intensity change; do not accept “edges” alone)(1)
Answer: (a) 2×2 (b) −2 (c) vertical edges
Examiner tip: In (b) the kernel is laid over the top-left 3×3 region only; candidates who use the whole image lose both marks.

6HardHL only6 marks

A CNN is trained to identify species of bird from photographs. Its architecture contains several convolutional layers, each followed by a pooling layer, and then fully connected layers.

Describe how this CNN adaptively learns a spatial hierarchy of features from the photographs. [6]

Convolutional layers slide small kernels/filters across the image, producing feature maps showing where a pattern occurs(1)
The kernel values are weights that are not hand-designed but learned during training (by backpropagation / gradient descent minimising the loss), so the network adapts its filters to the bird data(1)
Early layers learn low-level features such as edges, lines, colours or simple textures(1)
Deeper layers combine the earlier feature maps to detect more complex features / parts, e.g. feathers, eyes, beaks, wings(1)
Pooling (e.g. max pooling) downsamples the feature maps, so each deeper layer has a larger receptive field / sees a wider region of the image (accept: gives some translation invariance and reduces computation)(1)
Fully connected layers use the high-level features to classify the image / output a probability for each species(1)
Answer: Learned kernels → edges → parts → whole-object features, with pooling enlarging the receptive field and fully connected layers classifying.
Examiner tip: The word “adaptively” is a cue: say that the filter values are learned in training, not programmed.

7CoreHL only4 marks

The table shows a 4×4 feature map produced by a convolutional layer.

3	1	0	2
5	2	4	1
0	6	2	2
1	3	7	0

(a) Max pooling with a 2×2 window and a stride of 2 is applied. Determine the output. [2]

(b) Outline two reasons why pooling layers are used in a CNN. [2]

(a) A 2×2 output(1)
(a) with values 5, 4 (top row) and 6, 7 (bottom row) (all four correct)(1)
(b) Any two from: reduces the size of the feature maps, so fewer computations / parameters in later layers (faster training);(1)
makes detection less sensitive to the exact position of a feature (translation invariance); helps reduce overfitting; keeps the strongest response / most important feature in each region(1)
Answer: (a) [[5, 4], [6, 7]] (b) e.g. reduces size/computation; gives translation invariance
Examiner tip: Max pooling takes the largest value in each non-overlapping 2×2 block; do not average.

8HardHL only6 marks

A developer is building a plant-identification app that must work offline on a mid-range smartphone. Three models were trained on the same training set and tested on the same validation set.

Model	Type	Training accuracy (%)	Validation accuracy (%)	Size (MB)	Time per image (ms)
A	Small CNN	91	89	12	30
B	Large CNN	99.8	90	480	900
C	Multi-layer perceptron on flattened pixels	78	76	40	25

(a) Identify the model that shows the most overfitting. Justify your answer using the data. [2]

(b) Recommend which model the developer should choose. Justify your recommendation with reference to the data. [3]

(a) Model B(1)
(a) Large gap between training accuracy (99.8%) and validation accuracy (90%) / about 10 percentage points, showing it has memorised the training data and does not generalise(1)
(b) Model A(1)
(b) Validation accuracy (89%) is almost the same as B (90%) / only 1 percentage point lower, and far higher than C (76%)(1)
(b) It is 40 times smaller (12 MB vs 480 MB) and 30 times faster (30 ms vs 900 ms) than B, so it fits in phone storage/memory and runs in real time without a server (accept either size or speed with figures)(1)
(c) Flattening the image loses the spatial relationships between neighbouring pixels, so C cannot learn local features such as edges/shapes as convolution does (accept: an MLP has no shared kernels so needs far more parameters to learn the same patterns)(1)
Answer: (a) B (99.8% vs 90%) (b) A: near-equal validation accuracy, 40× smaller, 30× faster (c) flattening loses spatial structure
Examiner tip: In model-selection questions, quote figures from the table and compare against the scenario’s constraints (offline, phone) rather than just choosing the highest accuracy.

9StandardHL only4 marks

The graph shows the training loss and validation loss of a neural network recorded every 2 epochs during training.

(a) State the epoch at which training should be stopped. [1]

(b) Explain what is happening to the model after this epoch. [2]

(c) The developer also keeps a separate test set that is never used while training or choosing the stopping epoch. Outline why. [1]

(a) Epoch 12 (where validation loss is lowest, 0.34)(1)
(b) Training loss continues to fall but validation loss rises (from 0.34 to about 0.51 by epoch 20)(1)
(b) so the model is overfitting: learning noise/specific details of the training data and generalising worse to unseen data(1)
(c) The validation set has influenced choices about the model, so performance on it is optimistic / biased; the untouched test set gives an unbiased estimate of performance on new data(1)
Answer: (a) 12 (b) validation loss rises while training loss falls: overfitting (c) unbiased final estimate
Examiner tip: Stop where the validation loss is minimum, not where the training loss is lowest.

10StretchHL only6 marks

A team compares two classifiers, P and Q, using 5-fold cross-validation. The accuracy on each validation fold is shown.

Fold	1	2	3	4	5
Model P	0.84	0.86	0.83	0.85	0.87
Model Q	0.92	0.74	0.88	0.79	0.90

(a) Calculate the mean accuracy of each model. [2]

(b) Recommend which model the team should deploy. Justify your answer. [2]

(c) Explain why k-fold cross-validation gives a more reliable comparison of models than a single train/validation split. [2]

(a) P: 0.85(1)
(a) Q: 0.846 (accept 0.85 to 2 d.p. only if 0.846 seen or implied)(1)
(b) Model P: it has a (slightly) higher mean accuracy(1)
(b) and its fold accuracies are far more consistent (range 0.04 vs 0.18 for Q / Q varies from 0.74 to 0.92), so it is more likely to perform reliably on new data (do not award recommendation of Q unless justified by variability being acceptable — no marks for Q on highest single fold)(1)
(c) Every data item is used for validation exactly once (and for training in the other folds), so the estimate does not depend on one lucky/unlucky split(1)
(c) Averaging over k folds reduces the variance of the estimate and also shows the spread/stability of performance, making the comparison between models fairer(1)
Answer: (a) P = 0.85, Q = 0.846 (b) P: higher mean and much more consistent (c) each item validated once; average over folds reduces dependence on one split
Examiner tip: A model that scores highest on one fold (Q, 0.92) is not necessarily the best; compare the mean and the spread.

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