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May 2026 term · Mathematical Foundations of Generative AI

Mathematical Foundations of Generative AI Quiz 2: 16 August 2026 (May 2026 term)

The IIT Madras BS Mathematical Foundations of Generative AI (Mathematical Foundations of Generative AI) Quiz 2 paper sat on 16 Aug 2026, in the May 2026 term: 17 questions for 48 marks in 120 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.

Questions
17
Marks
48
Duration
120 min
MCQ
5
MSQ
6
Numerical
6
Take as mock testPractise with answers

Updated

Official paper: Mathematical Foundations Of Generative Ai 16 Aug 26 · No negative marking.

Question 1

+1 markOne correct option
  1. A

    Deterministic neural network

  2. B

    Probabilistic neural network

Show answer

Correct answer

  • B

    Probabilistic neural network

Question 1 on its own page

Question 2

+3 marksOne correct option

A Variational Autoencoder (VAE) has been trained on a dataset. Which of the following procedures correctly generates a new data sample from the trained model?

  1. A
  2. B
  3. C
  4. D

    Optimize the KL divergence term during inference until it becomes zero, and then decode the resulting latent representation.

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Correct answer

  • B
Question 2 on its own page

Question 3

+3 marksOne correct option
  1. A
  2. B
  3. C
  4. D

    To make the critic network deeper.

Show answer

Correct answer

  • B
Question 3 on its own page

Question 4

+2 marksOne correct option
  1. A
  2. B
  3. C
  4. D

    None of these

Show answer

Correct answer

  • B
Question 4 on its own page

Question 5

+4 marksOne correct option
  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • B
Question 5 on its own page

Question 6

+4 marksOne or more correct options

Select all that apply.

  1. A
  2. B
  3. C
  4. D
  5. E
  6. F
Show answer

Correct answers

  • C
  • F
Question 6 on its own page

Question 7

+3 marksOne or more correct options

Select all that apply.

  1. A
  2. B

    Choosing a very small value of β increases the influence of the KL divergence term, forcing the approximate posterior to collapse towards the prior.

  3. C

    Choosing a very large value of β places greater emphasis on matching the approximate posterior to the prior, which may degrade reconstruction quality.

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Correct answers

  • A
  • C

    Choosing a very large value of β places greater emphasis on matching the approximate posterior to the prior, which may degrade reconstruction quality.

Question 7 on its own page

Question 8

+3 marksOne or more correct options

A latent variable model defines

Select all that apply.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answers

  • B
  • C
Question 8 on its own page

Question 9

+3 marksOne or more correct options

Which of the following statements correctly contrast DDPM sampling with a standard GAN/VAE?

Select all that apply.

  1. A
  2. B

    A trained DDPM directly generate a data sample in a single network evaluation.

  3. C
  4. D

    During sampling, a DDPM starts from a real training sample and removes the added noise in a single denoising step.

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Correct answers

  • A
  • C
Question 9 on its own page

Question 10

+3 marksOne or more correct options

Which of the following statements about the generator and discriminator in a standard GAN are correct?

Select all that apply.

  1. A

    The generator never sees real data directly; it learns only through the gradient signal that flows back from the discriminator.

  2. B

    The discriminator is a binary classifier trained on a mix of real samples (label 1) and generated samples (label 0).

  3. C

    The discriminator's role is to distinguish real samples from generated ones.

  4. D

    The discriminator generates new data samples from the latent space.

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Correct answers

  • A

    The generator never sees real data directly; it learns only through the gradient signal that flows back from the discriminator.

  • B

    The discriminator is a binary classifier trained on a mix of real samples (label 1) and generated samples (label 0).

  • C

    The discriminator's role is to distinguish real samples from generated ones.

Question 10 on its own page

Question 11

+2 marksOne or more correct options

Which among the following is true for a denoising diffusion probabilistic model (DDPM)?

Select all that apply.

  1. A

    The forward process in DDPM gradually adds noise to the input.

  2. B

    The forward process in DDPM learns to generate data by denoising.

  3. C

    In the reverse process of DDPM, we stack the VAE decoders.

  4. D

    In the reverse process of DDPM, we stack the VAE encoders.

Show answer

Correct answers

  • A

    The forward process in DDPM gradually adds noise to the input.

  • C

    In the reverse process of DDPM, we stack the VAE decoders.

Question 11 on its own page

Question 12

+2 marksNumerical answer
Show answer

Correct answer: 0

Question 12 on its own page

Question 13

+3 marksNumerical answer
Show answer

Correct answer: 2

Question 13 on its own page

Question 14

+3 marksNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 0.12 (accepted within ±0.02)

Question 14 on its own page

Question 15

+3 marksNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 0.79 (accepted within ±0.02)

Question 15 on its own page

Question 16

+3 marksNumerical answer
Show answer

Correct answer: 0.9 (accepted within ±0.02)

Question 16 on its own page

Question 17

+3 marksNumerical answer
Show answer

Correct answer: 0.6 (accepted within ±0.02)

Question 17 on its own page