CS 7643 – Quiz 7 | Questions and Answers | spring 2026 | 100% Correct – GT.

CS 7643 – Quiz 7 | Questions and Answers | spring 2026 | 100% Correct – GT.



🔵 SECTION 1: Generative vs Discriminative
Models

Q1. What is the difference between a discriminative and generative model?

Answer:

Discriminative Model

 Learns:

P(y∣x)P(y|x)P(y∣x)

 Labels compete for probability mass.
 No modeling of input distribution.
 Cannot reject unreasonable inputs.
 Examples: Neural Networks, SVM.

Generative Model

 Learns:

P(x)P(x)P(x)

 All possible inputs compete for probability mass.
 Can assign low probability to outliers.
 Can generate new samples.
 Often unsupervised.



Q2. What is a conditional generative model?

Answer:

Learns:

P(x∣y)P(x|y)P(x∣y)

,Unlike discriminative models, it models input distribution conditioned on label and can:

 Reject outliers
 Generate new data for specific labels




🔵 SECTION 2: Taxonomy of Generative
Models

Q3. What is explicit density modeling?

Answer:

Define and maximize likelihood:

θ∗=arg⁡max⁡θ∑ilog⁡pθ(xi)\theta^* = \arg\max_\theta \sum_i \log p_\theta(x_i)θ∗=argθmax
i∑logpθ(xi)

Requires tractable likelihood.

Examples:

 PixelRNN
 PixelCNN
 VAE



Q4. What is implicit density modeling?

Answer:

Does NOT explicitly compute p(x)p(x)p(x).

Instead:

 Learns to sample from distribution.
 No likelihood available.

Example:

,  GANs




🔵 SECTION 3: PixelRNN / PixelCNN

Q5. How does PixelRNN factorize image likelihood?

Using chain rule:

p(x)=∏i=1n2p(xi∣x1,...,xi−1)p(x) = \prod_{i=1}^{n^2} p(x_i | x_1, ..., x_{i-1})p(x)=i=1∏n2p(xi
∣x1,...,xi−1)

Like language modeling:

 Predict next pixel given previous pixels.



Q6. How is PixelCNN different from PixelRNN?

PixelRNN

 Sequential RNN recurrence.
 Slow training.

PixelCNN

 Masked convolutions.
 Parallel training.
 Still sequential generation.



Q7. What are advantages of PixelCNN?

 Explicit likelihood
 Good evaluation metric
 Maximum likelihood training

, Q8. What are disadvantages of PixelCNN?

 Sequential generation (slow)
 Limited long-range context
 Assumes fixed pixel ordering




🔵 SECTION 4: GANs

Q9. Write the full GAN objective.

min⁡Gmax⁡DV(D,G)\min_G \max_D V(D,G)GminDmaxV(D,G)
=Ex∼pdata[log⁡D(x)]+Ez∼p(z)[log⁡(1−D(G(z)))]= \mathbb{E}_{x\sim p_{data}}[\log D(x)]
+ \mathbb{E}_{z\sim p(z)}[\log(1 - D(G(z)))]=Ex∼pdata[logD(x)]+Ez∼p(z)[log(1−D(G(z)))]


Q10. What is the generator trying to do?

Push:

D(G(z))→1D(G(z)) \to 1D(G(z))→1

Fool discriminator into believing fake is real.



Q11. What is the discriminator trying to do?

Push:

 D(x)→1D(x) \to 1D(x)→1
 D(G(z))→0D(G(z)) \to 0D(G(z))→0

Classify correctly.



Q12. Why does the original GAN objective give poor gradients for the
generator?

Because when: