da5002_2026T1_Q1_NA.pdf

The [[IMAGE:c3240b78982312ff_3_2]] -divergence is written as [[IMAGE:c3240b78982312ff_3_3]] with [[IMAGE:c3240b78982312ff_3_4]] convex and [[IMAGE:c3240b78982312ff_3_5]] . Which choice of [[IMAGE:c3240b78982312ff_3_6]] gives the reverse KL divergence [[IMAGE:c3240b78982312ff_3_7]] ?

Total variation distance [[IMAGE:c3240b78982312ff_4_12]] corresponds to which [[IMAGE:c3240b78982312ff_4_13]] in the same [[IMAGE:c3240b78982312ff_4_14]] -divergence form?

Consider [[IMAGE:c3240b78982312ff_4_19]] (forward KL). Its convex conjugate is [[IMAGE:c3240b78982312ff_4_20]] Which is the correct closed form for [[IMAGE:c3240b78982312ff_4_21]] ?

Let the discriminator be parameterized via a logit [[IMAGE:c3240b78982312ff_4_26]] : [[IMAGE:c3240b78982312ff_4_27]] , [[IMAGE:c3240b78982312ff_4_28]] . If [[IMAGE:c3240b78982312ff_5_29]] , then the optimal logit satisfies:

[[IMAGE:c3240b78982312ff_5_34]]

Let [[IMAGE:c3240b78982312ff_6_39]] . Compare generator gradients w.r.t. the discriminator logit [[IMAGE:c3240b78982312ff_6_40]] for: [[IMAGE:c3240b78982312ff_6_41]] If [[IMAGE:c3240b78982312ff_6_42]] , which magnitude is correct?

WGAN-GP adds the penalty [[IMAGE:c3240b78982312ff_6_49]] If for a sampled [[IMAGE:c3240b78982312ff_6_50]] you measure [[IMAGE:c3240b78982312ff_6_51]] and [[IMAGE:c3240b78982312ff_6_52]] , what is the penalty contribution for that sample?

If the true data is conditional [[IMAGE:c3240b78982312ff_6_53]] and the generator matches it perfectly, then the marginal of generated samples satisfies:

In PyTorch, you run: [[IMAGE:c3240b78982312ff_7_59]] without calling **zero_grad()**. What happens to [[IMAGE:c3240b78982312ff_7_60]] ?

For fixed [[IMAGE:c3240b78982312ff_7_61]] , the pointwise optimal discriminator [[IMAGE:c3240b78982312ff_7_62]] for the minimax GAN is:

Assume [[IMAGE:c3240b78982312ff_8_67]] and [[IMAGE:c3240b78982312ff_8_68]] are disjoint and the discriminator reaches [[IMAGE:c3240b78982312ff_8_69]] . Consider the minimax generator loss [[IMAGE:c3240b78982312ff_8_70]] Which statement about [[IMAGE:c3240b78982312ff_8_71]] is correct?

(Classifier-guided sampler) Suppose you want an acceptance probability of the form [[IMAGE:c3240b78982312ff_8_76]] and you approximate [[IMAGE:c3240b78982312ff_8_77]] If [[IMAGE:c3240b78982312ff_8_78]] and [[IMAGE:c3240b78982312ff_8_79]] , what is [[IMAGE:c3240b78982312ff_8_80]] ?

Which objective correctly represents a conditional GAN with condition [[IMAGE:c3240b78982312ff_9_81]] ?

In Wasserstein GAN, the discriminator is replaced by a critic [[IMAGE:c3240b78982312ff_9_86]] . Which statement is correct?

(Kantorovich–Rubinstein dual) The Wasserstein-1 distance can be written as:

“Latent regression” inversion trains an encoder / regressor [[IMAGE:c3240b78982312ff_10_96]] so that:

In BiGAN, what does the discriminator receive as “real” vs “fake” inputs?

In WGAN, why are multiple critic updates typically performed per generator update? The most accurate reason is:

For 1D Gaussian features, let real features be [[IMAGE:c3240b78982312ff_11_114]] and generated features be [[IMAGE:c3240b78982312ff_11_115]] . The FID simplifies to [[IMAGE:c3240b78982312ff_11_116]] If [[IMAGE:c3240b78982312ff_11_117]] , [[IMAGE:c3240b78982312ff_11_118]] , [[IMAGE:c3240b78982312ff_11_119]] , [[IMAGE:c3240b78982312ff_11_120]] , what is the FID?

At an ideal BiGAN equilibrium (infinite capacity, optimal discriminator), the matched joint distributions imply most directly that:

The original minimax GAN objective is:

Given a trained generator [[IMAGE:c3240b78982312ff_12_132]] and a target image [[IMAGE:c3240b78982312ff_12_133]] , “GAN inversion via optimization” computes: