Lots of confusion about what a world model is. Here is my definition:

Given:

• an observation x(t)
  
• a previous estimate of the state of the world s(t)
  
• an action proposal a(t)
  
• a latent variable proposal z(t)
  
  A world model computes:
  
• representation: h(t) = Enc(x(t))
  
• prediction: s(t+1) = Pred( h(t), s(t), z(t), a(t) )
  Where
  
• Enc() is an encoder (a trainable deterministic function, e.g. a neural net)
  
• Pred() is a hidden state predictor (also a trainable deterministic function).
  
• the latent variable z(t) represents the unknown information that would allow us to predict exactly what happens. It must be sampled from a distribution or or varied over a set. It parameterizes the set (or distribution) of plausible predictions.
  
  The trick is to train the entire thing from observation triplets (x(t),a(t),x(t+1)) while preventing the Encoder from collapsing to a trivial solution on which it ignores the input.
  
  Auto-regressive generative models (such as LLMs) are a simplified special case in which
  
  1. the Encoder is the identity function: h(t) = x(t),
     
  2. the state is a window of past inputs
     
  3. there is no action variable a(t)
     
  4. x(t) is discrete
     
  5. the Predictor computes a distribution over outcomes for x(t+1) and uses the latent z(t) to select one value from that distribution.
     The equations reduce to:
     s(t) = [x(t),x(t-1),...x(t-k)]
     x(t+1) = Pred( s(t), z(t), a(t) )
     There is no collapse issue in that case.