EasyDeepLearn

Write the VAE ELBO and explain each term.

hard

Answer

  • ELBO(x)  =  Eq(z∣x)\mathrm{ELBO}(x)\; = \;E_{q}(z \mid x)[log⁡  p(x∣z)]  −  KL⁡(q(z∣x)  ∣∣  p(z))[\operatorname{log}\;p(x \mid z)]\; - \;\operatorname{KL}(q(z \mid x)\; \mid \mid \;p(z)).
  • Reconstruction term: how well the decoder reproduces x from a latent sampled by the encoder.
  • KL term: pushes the encoder's posterior q(z∣x)q(z \mid x) toward the prior p(z) (usually N(0, I)).
  • Maximizing ELBO ≤ log p(x).
  • The KL acts as regularizer — without it, VAE collapses to an autoencoder. β-VAE weights the KL term for disentanglement.
Check yourself — multiple choice
  • Only reconstruction loss
  • ELBO  =  E[log⁡  p(x∣z)]  −  KL⁡(q(z∣x)  ∣∣  p(z))\mathrm{ELBO}\; = \;E[\operatorname{log}\;p(x \mid z)]\; - \;\operatorname{KL}(q(z \mid x)\; \mid \mid \;p(z)) — reconstruction + regularizer toward prior
  • Only KL divergence
  • Same as GAN loss

VAE ELBO: reconstruction likelihood − KL⁡(posterior  ∣∣  prior)\operatorname{KL}(\mathrm{posterior}\; \mid \mid \;\mathrm{prior}).

#vae#generative#losses

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