da5002_2025T3_Q1_NA.pdf

Mathematical Foundations of Generative AI · Quiz 1 · Sep 2025

Questions and published explanations below are available without starting a test. Some questions may not have a published solution yet.

Question 232 MCQ · 2.0 marks

Suppose you replace the log-loss in the original GAN with a general f-divergence minimization framework. Which of the following cannot be directly represented as an f-divergence?

KL divergence
Reverse KL divergence
Total Variation distance
Wasserstein distance

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Question 233 MCQ · 2.0 marks

[[IMAGE:7df4816df8150d15_3_1]]

−log 2
0
−log(0.3)
log 2

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Question 234 MCQ · 2.0 marks

[[IMAGE:7df4816df8150d15_3_2]]

[[IMAGE:7df4816df8150d15_3_3]]
[[IMAGE:7df4816df8150d15_3_4]]
[[IMAGE:7df4816df8150d15_3_5]]
[[IMAGE:7df4816df8150d15_3_6]]

A published solution is not available for this question yet.

Question 235 MCQ · 2.0 marks

[[IMAGE:7df4816df8150d15_4_7]]

−0.8008
−0.6432
−1.1412
−0.4794

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Question 236 MCQ · 2.0 marks

[[IMAGE:7df4816df8150d15_4_8]]

80,402
99,402
242,503
159,3

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Question 237 MCQ · 2.0 marks

[[IMAGE:7df4816df8150d15_5_9]]

0.22
0.28
0.34
0.41

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Question 238 MCQ · 2.0 marks

[[IMAGE:7df4816df8150d15_5_10]]

[[IMAGE:7df4816df8150d15_5_11]]
[[IMAGE:7df4816df8150d15_5_12]]
[[IMAGE:7df4816df8150d15_5_13]]
[[IMAGE:7df4816df8150d15_5_14]]

A published solution is not available for this question yet.

Question 239 MCQ · 2.0 marks

[[IMAGE:7df4816df8150d15_6_15]]

The first term measures bias shift; the second term measures covariance mismatch.
Both terms measure covariance only.
Both terms are dominated by the generator’s variance.
The first term measures variance difference; the second measures mean shift.

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Question 240 MCQ · 2.0 marks

FID compares real and generated image distributions by assuming they follow multivariate Gaussian distributions in a feature space extracted from a pretrained neural network. Which layer’s activations are typically used to compute this feature space in practice?

The output logits of the generator
Raw RGB pixel values
The first convolution layer of the discriminator
The penultimate layer of an Inception-v3 network

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Question 241 MCQ · 2.0 marks

[[IMAGE:7df4816df8150d15_6_16]]

[[IMAGE:7df4816df8150d15_6_17]]
[[IMAGE:7df4816df8150d15_6_18]]
[[IMAGE:7df4816df8150d15_6_19]]
[[IMAGE:7df4816df8150d15_7_20]]

A published solution is not available for this question yet.

Question 242 MCQ · 3.0 marks

[[IMAGE:7df4816df8150d15_7_21]]

[[IMAGE:7df4816df8150d15_7_22]]
[[IMAGE:7df4816df8150d15_7_23]]
[[IMAGE:7df4816df8150d15_7_24]]
[[IMAGE:7df4816df8150d15_7_25]]

A published solution is not available for this question yet.

Question 243 MCQ · 3.0 marks

[[IMAGE:7df4816df8150d15_7_26]]

0.20
0.35
0.55
0.75

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Question 244 MCQ · 3.0 marks

[[IMAGE:7df4816df8150d15_8_27]]

0.57
0.24
0.32
0.137

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Question 245 MCQ · 3.0 marks

[[IMAGE:7df4816df8150d15_8_28]]

[−2.1, 0.4]
[−2.2, −4.3]
[0.2, 0.1]
[0, 0]

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Question 246 MSQ · 3.0 marks

Which of the following are valid reasons why GAN training based on JSD minimization is unstable?

JSD saturates when the supports of pdata and pg do not overlap.
Gradients for the generator can vanish when the discriminator becomes too strong.
JSD is not continuous w.r.t. the parameters of the generator distribution.
JSD always provides unbiased gradients in high dimensions.

A published solution is not available for this question yet.