Sufficient State and State Abstraction › Summary

• Sufficiency is relative to a consumer. A state is predictively sufficient if it determines action-conditioned future observation distributions, and control-sufficient if it preserves the action values needed to choose optimally. Control can need far less than prediction, while finite-capacity prediction losses can underweight control-critical information.
• Bisimulation gives an exact behavioral quotient. Two states are bisimilar when they match in reward and in transition probabilities over equivalence classes for every action. Its quotient preserves action values and policies and is the coarsest exact bisimulation partition, though a fixed-task control abstraction can sometimes be coarser. Bisimulation metrics grade the equivalence with a bound on value differences.
• Minimality is separate from sufficiency. Reconstruction loss rewards retained observation detail but does not by itself target a minimal control abstraction. Nuisance invariance is a task-relative choice of what the fixed representation will ignore.
• Task-aware representation learning makes the trade-off explicit, adding control-relevant objectives and invariances at the cost of transfer across task families and coupling to the current policy. Under the universal task-family conditions defined above, preserving every task and forced action sequence recovers predictive sufficiency.

We now know what a world model's latent state must contain and what it may discard. The next question is how to represent what remains, especially when the state should carry uncertainty rather than a point estimate. The next chapter, Latent-Variable Representations, develops exactly that machinery: latent states as random variables with learned posteriors, and the variational machinery that trains them.