Data Science Deep Learning Syllabus

Write the probability density function of the normal (Gaussian) distribution.

$f(x) = \dfrac{1}{\sigma\sqrt{2\pi}} \, e^{-\frac{(x-\mu)^{2}}{2\sigma^{2}}}$.

What is cross-entropy loss for binary classification?

$L = -\big[y \log(\hat{y}) + (1 - y)\log(1 - \hat{y})\big]$, where $y$ is the true label and $\hat{y}$ the predicted probability.

Write the mean squared error (MSE) loss for $n$ samples.

$\text{MSE} = \dfrac{1}{n}\sum_{i=1}^{n} (y_i - \hat{y}_i)^{2}$.

State the gradient descent parameter update rule.

$\theta \leftarrow \theta - \eta\, \nabla_{\theta} J(\theta)$, where $\eta$ is the learning rate and $J$ the cost function.

What is the difference between batch, mini-batch, and stochastic gradient descent?

Batch GD uses the entire dataset per update; SGD uses one sample per update; mini-batch GD uses a small subset (batch) per update, balancing stability and speed.

What does the Adam optimizer combine, and why is it popular?

Adam (Adaptive Moment Estimation) combines momentum (first moment of gradients) with RMSProp-style adaptive per-parameter learning rates (second moment), giving fast, robust convergence with little tuning.

What is the role of the learning rate $\eta$, and what happens if it is too large or too small?

It scales each gradient step. Too large causes divergence or oscillation; too small causes very slow convergence and possible trapping in poor minima.

What is momentum in optimization?

A technique that accumulates an exponentially decaying moving average of past gradients to accelerate descent and dampen oscillations: $v_t = \gamma v_{t-1} + \eta \nabla J$, then $\theta \leftarrow \theta - v_t$.

What is TensorFlow, and who developed it?

TensorFlow is an open-source deep learning framework developed by Google Brain that represents computations as dataflow graphs of tensors and supports CPU/GPU/TPU execution and production deployment.

What is a tensor in the context of deep learning frameworks?

A multi-dimensional array (generalization of scalars, vectors, and matrices) that is the fundamental data structure passed through neural networks.

What is PyTorch, and what is its defining computational feature?

PyTorch is an open-source deep learning framework developed by Meta (Facebook) AI that uses dynamic computation graphs (define-by-run), making debugging and variable-length models more flexible.

What is autograd in PyTorch?

PyTorch's automatic differentiation engine that records operations on tensors with requires_grad=True and computes gradients automatically via .backward().

What is Keras, and how does it relate to TensorFlow?

Keras is a high-level neural-network API focused on ease of use; it is the official high-level API of TensorFlow (tf.keras), providing simple model-building abstractions like Sequential and Functional APIs.

Compare the default computation-graph style of TensorFlow 1.x versus PyTorch.

TensorFlow 1.x used static graphs (define-then-run, compiled before execution); PyTorch uses dynamic graphs (define-by-run, built on the fly). TensorFlow 2.x adopted eager execution by default to match this.

What is a Convolutional Neural Network (CNN) primarily used for?

A CNN is a neural network using convolutional layers to extract spatial/local features; it is primarily used for image and grid-structured data tasks such as classification, detection, and segmentation.

In a CNN, what do the convolution operation and filters/kernels do?

A filter (kernel) slides over the input computing dot products to produce a feature map, detecting local patterns like edges or textures; weight sharing reduces parameters.

What is the purpose of a pooling layer in a CNN, and name a common type.

Pooling downsamples feature maps to reduce spatial dimensions and computation while adding translation invariance; max pooling (taking the maximum in each window) is most common.

Given input size $W$, filter size $F$, padding $P$, and stride $S$, what is the output spatial size of a convolution?

$O = \dfrac{W - F + 2P}{S} + 1$.

What is a Recurrent Neural Network (RNN), and what data is it suited for?

An RNN processes sequences by maintaining a hidden state passed across time steps, $h_t = f(W_h h_{t-1} + W_x x_t + b)$, making it suited for sequential/temporal data like text, speech, and time series.

What problem do LSTMs and GRUs solve compared to vanilla RNNs?

They mitigate the vanishing/exploding gradient problem over long sequences by using gating mechanisms (e.g., LSTM's input, forget, and output gates) to control information flow and retain long-term dependencies.

Name the three gates of an LSTM cell and their roles.

Forget gate (decides what to discard from cell state), input gate (decides what new information to store), and output gate (decides what to expose as the hidden state).

What is a Generative Adversarial Network (GAN), and what are its two components?

A GAN is a generative model with two networks trained adversarially: a Generator that creates fake samples from noise, and a Discriminator that tries to distinguish real from fake; they compete in a minimax game.

Write the GAN minimax objective.

$\min_{G}\max_{D}\; \mathbb{E}_{x \sim p_{\text{data}}}[\log D(x)] + \mathbb{E}_{z \sim p_{z}}[\log(1 - D(G(z)))]$.

What is an autoencoder, and what are its two main parts?

An unsupervised neural network that learns to reconstruct its input through a bottleneck; it has an encoder that compresses input to a latent representation and a decoder that reconstructs the input from it.

How does a Variational Autoencoder (VAE) differ from a standard autoencoder?

A VAE encodes inputs into a probability distribution (mean and variance) over latent space rather than a fixed vector, enabling generative sampling; it adds a KL-divergence regularization term to the reconstruction loss.

What is Transfer Learning?

A technique that reuses a model pre-trained on a large source task as the starting point for a related target task, leveraging learned features to reduce data and training requirements.

What is fine-tuning in transfer learning, and how does it differ from feature extraction?

Fine-tuning unfreezes some/all pre-trained layers and continues training them on the new task; feature extraction freezes the pre-trained backbone and trains only a new classifier head on top.

What is Deep Reinforcement Learning?

The combination of reinforcement learning with deep neural networks, where an agent learns a policy to maximize cumulative reward by interacting with an environment, using networks to approximate value functions or policies.

State the Bellman optimality equation for the action-value function $Q$.

$Q^{*}(s, a) = \mathbb{E}\big[r + \gamma \max_{a'} Q^{*}(s', a')\big]$, where $\gamma$ is the discount factor.

What is word embedding in NLP, and name one classic method?

A learned dense vector representation of words that captures semantic and syntactic relationships in a continuous space; Word2Vec (skip-gram / CBOW) and GloVe are classic methods.

What is the attention mechanism, and write the scaled dot-product attention formula used in Transformers?

Attention lets a model weigh the relevance of different input positions when producing each output. Scaled dot-product attention: $\text{Attention}(Q, K, V) = \text{softmax}\!\left(\dfrac{QK^{T}}{\sqrt{d_k}}\right)V$.

Why is data preprocessing (normalization/standardization) important before training, and write the standardization formula.

It puts features on comparable scales, speeding and stabilizing gradient descent and preventing features with large ranges from dominating. Standardization: $x' = \dfrac{x - \mu}{\sigma}$.