Energy-Based Models Quiz

Answers and explanations appear as you take the quiz.

1. In an energy-based model, how is energy related to the probability of a data point?
   • High energy means high probability
   • Low energy means high probability (p(x) is proportional to exp(-E(x)))
   • Energy and probability are unrelated
   • Probability equals the energy directly
2. What makes training energy-based models difficult?
   • The energy function cannot be a neural network
   • They require labeled data only
   • They cannot represent images
   • The partition function Z (normalizer over all inputs) is usually intractable to compute
3. Which sampling method is commonly used to draw samples from an EBM?
   • Langevin dynamics (gradient-based MCMC)
   • Beam search
   • Quicksort
   • A single forward pass
4. Why can methods like score matching avoid computing the partition function Z?
   • Because Z is always equal to 1
   • Because they ignore the energy function
   • Because the gradient of log p(x) is -gradient of E(x), and Z (a constant in x) drops out when differentiating
   • Because they only work on discrete data
5. Which of these is a classic energy-based model?
   • The Transformer
   • The decision tree
   • The k-means algorithm
   • The Hopfield network
6. For a differentiable EBM density with Z constant in x, how does its score relate to energy?
   • The score equals the partition function itself
   • The score equals the negative input gradient of energy
   • The score ignores the learned energy entirely
   • The score is always the positive energy gradient
7. An EBM adds the same constant c to every E(x). What happens to normalized probabilities?
   • Every probability increases by c
   • All inputs become equally probable
   • They remain unchanged after the partition function is adjusted
   • The normalizer must be set to zero
8. For two configurations with E(a) lower than E(b), what follows under the same normalized Gibbs model?
   • Configuration a has greater probability than b
   • Configuration b has greater probability because its energy is higher
   • Both probabilities must be exactly one
   • The comparison requires different partition functions for each point