Notes

Every link on the map, explained in one sentence.

• Law of Large NumbersderivesTypical Set & AEP

  Applying the law of large numbers to −log p(X) gives the AEP.

• Shannon EntropyrequiresTypical Set & AEP

  Entropy sets the size of the typical set, about 2^{nH}.

• Shannon Entropyextends toKL Divergence & Cross Entropy

  KL divergence is relative entropy: entropy extended from one distribution to a pair.

• KL Divergence & Cross Entropyapplied inVAE & ELBO

  The regularizer in the ELBO is a KL divergence.

• MDPs & Value FunctionsrequiresPolicy Gradient

  The objective J(θ) is defined over the MDP's trajectory distribution.

• Stochastic Gradient Methodsapplied inPolicy Gradient

  The update is stochastic gradient ascent on J(θ); its convergence analysis is that of stochastic nonconvex optimization.

• VAE & ELBOextends toScore Matching

  From a likelihood bound for latent-variable models to objectives that learn the score directly.

• Score Matchingextends toConditional Technique

  Conditioning makes the score matching objective tractable.

• Conditional Techniqueextends toProbability Flow ODE

  Once the score is learned, the SDE can be replaced by an equivalent deterministic ODE.

• VAE & ELBOcontrastLeWorldModel / SIGReg

  Both learn latent representations: the VAE reconstructs observations, LeWorldModel predicts only in latent space and relies on SIGReg against collapse.