World model

Something that answers one question: if the world looks like this and I do that, what happens next?

Like you're twelve

You know what happens if you push a glass off a table. You have never done a physics calculation about it, and you do not need to watch to find out — you already know the glass ends up on the floor. Somewhere in your head is a rehearsal of the world that runs faster than the world does.

That rehearsal is a world model, and you use it constantly. It is how you catch a ball, how you decide a gap in traffic is too small, and how you notice that someone has moved the furniture.

Precisely

A world model is a function from a state and an action to the next state. In an associative memory that function is a stored binding: the state is a vector, each available action is a role, and the transition for a state is a bundle of bindings, one per action —

M_s = Σ_a bind(a, s'_a)

Prediction is unbinding the action you are considering and then cleaning up the result. Nothing is added to the store to make this work; a memory of transitions is a simulator, and the same read path that recalls a pattern predicts a consequence.

Two bounds follow. Prediction is approximate, so accuracy falls as a rollout lengthens. And because binding commutes, two actions applied in either order produce the same vector — order needs a non-commutative operator such as permutation, or a sequence is unrecoverable in principle rather than merely noisy.

Related

Rollout · Plan · Bind · Cleanup memory · Curiosity