# 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 sota.ai.community@gmail.com.* **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! --- ## 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.