Normalizing Flows Quiz

Answers and explanations appear as you take the quiz.

1. What mathematical property must every transformation in a normalizing flow have?
   • It must be a random, non-invertible mapping
   • It must be invertible (bijective) and differentiable
   • It must reduce the dimensionality at each step
   • It must be a discrete lookup table
2. Which formula lets normalizing flows compute exact likelihoods?
   • The softmax function
   • The Bellman equation
   • Bayes' rule applied to logits
   • The change-of-variables formula using the Jacobian determinant
3. Why do flow architectures like RealNVP and Glow use coupling layers?
   • To make the Jacobian triangular so its determinant is cheap to compute
   • To make the model non-invertible
   • To remove the need for a base distribution
   • To convert the model into a GAN
4. What does a tractable normalizing flow provide that an ordinary GAN generator generally does not?
   • A guarantee of perfect anomaly detection
   • A guarantee of faster sampling than every GAN
   • An explicitly evaluable model density through change of variables
   • A non-invertible mapping with no base distribution
5. How should a team use normalizing-flow likelihoods for anomaly detection?
   • Assume every high-likelihood input is familiar
   • Treat density as the probability mass of a single point
   • Skip checking real anomaly labels
   • Validate them as a signal against relevant in-distribution and anomalous examples
6. Which modern technique, used in systems like Stable Diffusion 3, grew out of continuous flow ideas?
   • Backpropagation through time
   • Flow matching (learning a velocity field that transports noise to data)
   • Tokenization
   • Beam search
7. A one-dimensional flow inverse is z = x / 2. What log-Jacobian term appears in log p(x)?
   • log(2)
   • The parameter count of the network
   • log(1/2)
   • No term because the inverse is linear
8. Why must a normalizing flow account for stretching or shrinking volume?
   • A transformed region’s density must reflect the changed volume
   • The transformation must lose half its dimensions
   • Every output point must have probability mass one
   • The base distribution must be discarded after training