Theory Round

Theory Round

English translation by SOTA – AI Community of the Hungarian original. Licensed CC BY-NC-SA 4.0, like the original. Organisers who would like this translation removed can email [email protected].

Magyar MI Diákolimpia (Hungarian AI Olympiad)
National Selection
Round 1

May 30, 2026

Name: ______________________________

Contestant ID: ____________________

You have exactly 60 minutes to complete the paper. The round consists of 30 questions, and the whole paper is worth a maximum of 150 points.

This paper is the first round of the Magyar Mesterséges Intelligencia Diákolimpia (Hungarian Artificial Intelligence Olympiad), which must be completed on paper, without the use of any aids.

The questions test your knowledge in the main topic areas: machine learning (ML), deep learning (DL), computer vision (CV) and natural language processing (NLP).

Scoring per question (5 points):

• 5 points: you select every true statement, and only those (perfect answer).
• 3 points: you select only true statements, but not all of them (i.e. you mark no false statement, but you leave out at least one true statement).
• 1 point: you mark exactly one false statement, but you also mark at least one true statement. The number of true statements left out does not matter.
• 0 points: in every other case (blank answer; you mark no true statement at all; or you mark two or more false statements). There are no negative points.

A total of 450 points can be earned during the olympiad. The result of the first round counts towards the final score.

We wish you the best of luck!

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Multiple-choice questions (5 points per question)

1. Select exactly those statements that are true:

• ○ Regression is a supervised learning task.
• ○ The goal of the dimensionality reduction task is to create several groups from the data points in such a way that the most similar data points end up in the same group.
• ○ The goal of regression is to sort the data points into several categories.
• ○ Clustering is an unsupervised learning task.
• ○ None of the other statements is true.
• ○ The goal of clustering is to create several groups from the data points in such a way that the most similar data points end up in the same group.
• ○ The goal of classification is to sort the data points into several categories.

2. Select exactly those statements that are true:

• ○ The role of the hypothesis function is to characterise, with a single number, the error of the predicted labels relative to the true labels.
• ○ When we work with a neural network, the input of the neural network is the same as the input of the hypothesis function.
• ○ When training a neural network, we want to minimise the value of the hypothesis function.
• ○ When training a neural network, our goal is to find true labels in the dataset that are as close as possible to the predicted labels.
• ○ None of the other statements is true.

3. Select exactly those statements that are true:

• ○ The value (output) of the loss function can be a scalar.
• ○ The value (output) of the loss function can be a vector.
• ○ The value (output) of the hypothesis function can be a scalar.
• ○ The value (output) of the hypothesis function can be a vector.
• ○ None of the other statements is true.

4. The statements below are about the two data scaling methods that we have studied. The range of a variable is defined as the difference between its maximum and its minimum. Select exactly those statements that are true:

• ○ In standardisation, we first subtract the standard deviation from the values of the variable, and then divide them by the mean.
• ○ In standardisation, we first subtract the mean from the values of the variable, and then divide them by the standard deviation.
• ○ In min-max scaling to the interval $[0, 1]$, we first divide the values of the variable by the minimum, and then subtract the range of the variable from them.
• ○ In min-max scaling to the interval $[0, 1]$, we first subtract the minimum from the values of the variable, and then divide them by the range of the variable.
• ○ None of the other statements is true.

5. We are given a dataset of 150 flats, in which 5 different attributes and the price are available for each flat. We want to train a machine learning model that uses these 5 attributes as input variables to predict the price of the flat. We want to apply data scaling to the input variables beforehand. Select exactly those statements that are true:

• ○ To perform min-max scaling on this dataset, we need to compute 1 minimum and 1 maximum value in total.
• ○ To perform min-max scaling on this dataset, we need to compute 5 minimum and 5 maximum values in total.
• ○ To perform standardisation on this dataset, we need to compute 150 mean and 150 standard deviation values in total.
• ○ If we add a single outlier data point to the dataset, the outlier is expected to affect the result of min-max scaling more strongly than the result of standardisation.
• ○ None of the other statements is true.

6. Consider the hypothesis function of a fully connected neural network layer: $h(\mathbf{x}) = g(\mathbf{W}\mathbf{x} + \mathbf{b})$, where $g$ is the ReLU activation function. Let $\mathbf{x} \in \mathbb{R}^q$ be the input of the layer. Let $r$ be the number of neurons in the layer. Select exactly those statements that are true:

• ○ $\mathbf{W}$ is a matrix of size $r \times q$.
• ○ $\mathbf{W}$ is a matrix of size $q \times r$.
• ○ $\mathbf{b}$ is a vector of size $q$.
• ○ $\mathbf{b}$ is a vector of size $r$.
• ○ None of the other statements is true.

7. Consider a fully connected neural network layer with the following hypothesis function: $h(\mathbf{x}) = g(\mathbf{W}\mathbf{x} + \mathbf{b})$, where $g$ is the activation function. Let $\mathbf{x} \in \mathbb{R}^n$ be the input of the layer. The value (output) of $h(\mathbf{x})$ is now a vector. Select exactly those statements that are true:

• ○ If we use a sigmoid activation function (logistic curve) in the layer, the output of the layer will contain only values between 0 and 1.
• ○ If we use a softmax activation function in the layer, the output of the layer will contain only values between 0 and 1.
• ○ If we use a ReLU activation function in the layer, the output of the layer will contain only values between 0 and 1.
• ○ If we use a sigmoid activation function (logistic curve) in the layer, the sum of the layer's output vector will be 1.
• ○ If we use a softmax activation function in the layer, the sum of the layer's output vector will be 1.
• ○ If we use a ReLU activation function in the layer, the sum of the layer's output vector will be 1.
• ○ None of the other statements is true.

8. We want to predict the price of flats in Budapest with a machine learning model, based on the following three pieces of information: floor area, distance from the city centre, floor number. We want to train our model on a dataset of 300 flats. Select exactly those statements that are true:

• ○ Linear regression is a more suitable approach for solving this task than logistic regression.
• ○ Logistic regression is a more suitable approach for solving this task than linear regression.
• ○ This is a regression task.
• ○ This is a classification task.
• ○ None of the other statements is true.

9. We want to predict the price of flats in Budapest with a simple linear regression model, based on the following two pieces of information: the floor area and the distance from the city centre. We want to train our model on a dataset of 300 flats. Select exactly those statements that are true:

• ○ Our hypothesis function is a straight line.
• ○ Our hypothesis function is a sigmoid curve.
• ○ Our model will have 300 parameters.
• ○ Our model will have 301 parameters.
• ○ None of the other statements is true.

10. We want to solve a binary classification task with a two-layer MLP neural network. We have 10 input variables, and the first layer of the network contains 5 neurons. To train the network, we use the BCE (Binary Cross-Entropy) loss. Select exactly those statements that are true:

• ○ The network has 61 parameters in total. ($5 \times 10 + 5 + 1 \times 5 + 1 = 61$)
• ○ The network has 67 parameters in total. ($5 \times 10 + 5 + 2 \times 5 + 2 = 67$)
• ○ The network has 70 parameters in total. ($5 \times 10 + 10 + 1 \times 5 + 5 = 70$)
• ○ The network has 75 parameters in total. ($5 \times 10 + 10 + 2 \times 5 + 5 = 75$)
• ○ The second layer will contain a single neuron.
• ○ None of the other statements is true.

11. Select exactly those statements that are true:

• ○ The early stopping technique stops the training of the model when the validation loss is visibly no longer improving.
• ○ Adding the sum of the parameters to the loss function (with a suitable scaling factor) is expected to reduce the overfitting of the model.
• ○ Adding the sum of the squares of the parameters to the loss function (with a suitable scaling factor) is expected to reduce the overfitting of the model.
• ○ Increasing the number of parameters of the model generally reduces overfitting.
• ○ Increasing the size of the training set generally reduces the overfitting of the model.
• ○ None of the other statements is true.

12. Select exactly those statements that are true:

• ○ An artificial neuron without an activation function is equivalent to a multivariable linear regression.
• ○ The decision boundary is the set of data points that the model classifies correctly.
• ○ The decision boundary of an artificial neuron with a sigmoid activation function has the shape of a sigmoid curve.
• ○ None of the other statements is true.

13. Select exactly those statements that are true:

• ○ An artificial neuron without an activation function is equivalent to a multivariable logistic regression.
• ○ An artificial neuron with a sigmoid activation function is not a linear function.
• ○ An artificial neuron with a sigmoid activation function cannot form a non-linear decision boundary.
• ○ None of the other statements is true.

14. Select exactly those statements that are true:

• ○ An artificial neuron without an activation function is equivalent to a multivariable linear regression.
• ○ An artificial neuron without an activation function is equivalent to a multivariable logistic regression.
• ○ The decision boundary is the set of data points that the model classifies correctly.
• ○ The decision boundary of an artificial neuron with a sigmoid activation function has the shape of a sigmoid curve.
• ○ An artificial neuron with a sigmoid activation function is not a linear function.
• ○ An artificial neuron with a sigmoid activation function cannot form a non-linear decision boundary.
• ○ None of the other statements is true.

15. We want to predict the price of flats in Budapest with a linear regression model, based on the following three pieces of information for each flat: floor area, distance from the city centre, floor number. The hypothesis function of our model is $h(\mathbf{X}) = \mathbf{X}\boldsymbol{\theta}$, which predicts the prices of all the flats in our dataset at once, in vectorised form, and the parameters of the model are in the vector $\boldsymbol{\theta}$. We formulate the hypothesis function for a dataset of 200 flats. Select exactly those statements that are true:

• ○ $\mathbf{X}$ is a matrix of size $201 \times 3$.
• ○ $\mathbf{X}$ is a matrix of size $200 \times 4$.
• ○ The model has 603 parameters ($3 \times 201$).
• ○ The model has 800 parameters ($4 \times 200$).
• ○ None of the other statements is true.

16. We want to apply data augmentation to a cat/dog binary classification task with photographs. Select exactly those statements that are true:

• ○ Horizontal flipping is generally an acceptable transformation (the label of the flipped image is unchanged).
• ○ Horizontal flipping cannot be used, because it changes the content of the image.
• ○ Slight rotation (e.g. $\pm 15^\circ$) is generally an acceptable transformation.
• ○ Random cropping is generally an acceptable transformation.
• ○ Swapping the red and blue colour channels is a recommended transformation for improving performance.
• ○ None of the other statements is true.

17. We want to apply data augmentation to the MNIST dataset of handwritten digits. Select exactly those statements that are true:

• ○ Horizontal flipping is generally an acceptable transformation (e.g. the mirrored form of a 6 can also be correctly classified as a 6).
• ○ Slight rotation (e.g. $\pm 10^\circ$) is generally an acceptable transformation.
• ○ Rotation by $180^\circ$ is an acceptable transformation (the label remains unchanged).
• ○ A small random shift is generally an acceptable transformation.
• ○ Data augmentation is performed only on the training set, not on the test set.
• ○ None of the other statements is true.

18. About the train() and eval() methods of the PyTorch torch.nn.Module class. Select exactly those statements that are true:

• ○ train() puts the network into training mode, in which dropout and batch normalisation exhibit their training behaviour.
• ○ eval() puts the network into evaluation mode, in which dropout is switched off and batch normalisation uses the running mean/standard deviation.
• ○ train() starts the training process (it computes the gradients and updates the parameters).
• ○ eval() switches off gradient computation (autograd).
• ○ None of the other statements is true.

19. We are given a convolutional layer whose input is a 3-channel (RGB) image, and the layer uses 16 filters of size $5 \times 5$ (with a stride of 1, with bias). Select exactly those statements that are true:

• ○ The layer has 1216 parameters in total. ($16 \times (5 \times 5 \times 3) + 16 = 1216$)
• ○ The layer has 400 parameters in total. ($16 \times 5 \times 5 = 400$)
• ○ The layer has 1200 parameters in total. ($16 \times 5 \times 5 \times 3 = 1200$)
• ○ The output of the layer contains 16 channels (heatmaps).
• ○ The output of the layer contains 3 channels (heatmaps).
• ○ None of the other statements is true.

20. We are given a convolutional layer whose input is a 1-channel (greyscale) image, and the layer uses 32 filters of size $3 \times 3$ (with a stride of 1, with bias). Select exactly those statements that are true:

• ○ The layer has 320 parameters in total. ($32 \times (3 \times 3 \times 1) + 32 = 320$)
• ○ The layer has 9 parameters in total. ($3 \times 3 = 9$)
• ○ The layer has 288 parameters in total. ($32 \times 3 \times 3 = 288$)
• ○ The output of the layer contains 32 channels (heatmaps).
• ○ The output of the layer contains 1 channel (heatmap).
• ○ None of the other statements is true.

21. We are given an input tensor of spatial size $4 \times 4$ and a max-pooling layer that operates with a block size of $2 \times 2$ and stride $= 2$. Select exactly those statements that are true:

• ○ The spatial size of the output is $2 \times 2$.
• ○ The spatial size of the output is $3 \times 3$.
• ○ The pooling layer has learnable parameters.
• ○ The pooling layer reduces the spatial resolution and makes the network more tolerant of small shifts.
• ○ By using max pooling instead of average pooling, we extract the strongest (maximum) feature from each block.
• ○ None of the other statements is true.

22. About the properties of translation equivariance and translation invariance. Select exactly those statements that are true:

• ○ A convolutional layer is translation-equivariant: if the input is shifted, the output is shifted in the same way.
• ○ A convolutional layer is translation-invariant: if the input is shifted, the output remains completely unchanged.
• ○ Pooling layers (and especially global pooling) contribute to achieving translation invariance.
• ○ Translation invariance and translation equivariance are equivalent properties.
• ○ None of the other statements is true.

23. About batch normalisation. Select exactly those statements that are true:

• ○ Batch normalisation standardises the activations of the layer using the mean and standard deviation within the mini-batch, and then refines them with a learnable scaling ($\gamma$) and shifting ($\beta$) transformation.
• ○ Batch normalisation has exactly 2 learnable parameters per layer (one scalar $\gamma$ and one scalar $\beta$).
• ○ At inference (test) time, batch normalisation uses the running mean and standard deviation collected during training, not the statistics of the current batch.
• ○ Batch normalisation mitigates the unstable gradient problem.
• ○ None of the other statements is true.

24. We are given a residual block: $\mathbf{y} = F(\mathbf{x}) + \mathbf{x}$, where $F$ is a non-linear transformation (e.g. a few convolutional or fully connected layers). Select exactly those statements that are true:

• ○ The residual connection makes it possible to train deeper networks by mitigating the unstable gradient problem.
• ○ For the addition to be well defined, a difference in dimension between $F(\mathbf{x})$ and $\mathbf{x}$ is bridged with a linear projection.
• ○ Residual networks work only with fully connected layers.
• ○ The skip connection is the $+\mathbf{x}$ term in the formula.
• ○ None of the other statements is true.

25. About the unstable gradient problem. Select exactly those statements that are true:

• ○ The combined phenomenon of the "vanishing gradient" and the "exploding gradient" is the "unstable gradient problem".
• ○ The sigmoid activation function contributes to the vanishing gradient, because its derivative is at most 0.25 and takes values close to 0 in its flat regions.
• ○ The ReLU activation function never has a vanishing gradient problem.
• ○ Batch normalisation and residual connections are frequently used tools for mitigating the unstable gradient.
• ○ None of the other statements is true.

26. About transfer learning. Select exactly those statements that are true:

• ○ Transfer learning uses a network pre-trained on a large dataset as the starting point for a new task defined on an often smaller dataset.
• ○ Transfer learning is expected to be most useful when the pre-training task and the target task are similar to each other.
• ○ The goal of transfer learning is to retrain the pre-trained network completely on the new task, starting from a random initialisation of the parameters.
• ○ Weight freezing keeps the parameters of certain layers of the pre-trained network unchanged during training.
• ○ None of the other statements is true.

27. RNN-based tasks can be sorted into categories (N→1, 1→N, N→N, M→N, where $M \neq N$) according to the relationship between the lengths of the input and output sequences. Select exactly those statements that are true:

• ○ A text-based emotion classifier (one sentence → one emotion label) is a task of type N→1.
• ○ Machine translation is a task of type M→N (input and output of different lengths).
• ○ Weather forecasting (data from the previous 24 hours → temperature in the next hour) is an M→N task.
• ○ Image captioning (image → sentence) is a 1→N task.
• ○ None of the other statements is true.

28. About the LSTM and GRU network architectures compared with the Vanilla RNN. Select exactly those statements that are true:

• ○ LSTM and GRU handle long-range dependencies better than the Vanilla RNN.
• ○ LSTM/GRU uses a mechanism of gates to selectively retain or forget past information.
• ○ The number of parameters of an LSTM and of a GRU is the same as that of a Vanilla RNN with the same hidden size.
• ○ LSTM/GRU mitigates the vanishing gradient problem, which makes it difficult to train a Vanilla RNN on long sequences.
• ○ None of the other statements is true.

29. In a single-layer (single-head) self-attention layer, the input is a sequence of length $N$, in which every element is a $d$-dimensional vector. Select exactly those statements that are true:

• ○ The number of attention scores is $N \times N$.
• ○ The scaling factor $\sqrt{d_k}$ appears before the softmax so that the value of the dot product does not grow too large and does not saturate the softmax function.
• ○ Like the Vanilla RNN, the self-attention layer must operate sequentially: the $i$-th output can be computed only after the $(i-1)$-th output has been computed.
• ○ The learnable parameters of the self-attention layer are the $Q$, $K$, $V$ projection matrices.
• ○ None of the other statements is true.

30. We want to train an autoencoder to compress $28 \times 28$ handwritten digits (MNIST). Both the input and the output of the network are 784-element vectors. Select exactly those statements that are true:

• ○ A frequently used loss function for the network is the mean squared error (MSE) between the input and the reconstructed output.
• ○ The labels (true labels) of the network are the classes of the digits (0–9).
• ○ The compressed representation appears at the low-dimensional bottleneck between the encoder and decoder parts of the network.
• ○ To avoid the trivial identity mapping, we choose the dimension of the hidden layer to be smaller than the input dimension.
• ○ If the value of the loss is 0 (measured with MSE), the network has reconstructed the original image exactly.
• ○ None of the other statements is true.