Compositionality and Systematic Generalization › Summary

• Compositionality is the design commitment that a world model should represent the world as a combination of reusable parts (objects, relations, mechanisms, skills) rather than as a monolithic function from histories to predictions.
• Factorized mechanisms formalize this: the transition decomposes into independently varying modules, and worlds are points in the product of mechanism spaces. For $K$ families with $q$ values each, the representation stores $Kq$ value-specific components rather than a separate component for every one of the $q^K$ worlds. Balanced data let each trajectory update several reusable components, but the resulting sample-efficiency gain depends on the fixed data budget, coverage design, excitation, and dependence among trajectories.
• Recombination of objects, relations, and skills can give zero-shot coverage of novel pairings when the architecture enforces a valid composition rule and the components are identified on the relevant state-action support.
• Out-of-distribution composition comes in distinct kinds (novel recombination, novel instances, novel parameters, novel structure) with distinct remedies; conflating them hides both failures and cheap wins.
• Systematic generalization must be measured, with primitive-covered splits, held-out combinations, horizon-resolved rollout error, swap-consistency tests, and planning success rather than i.i.d. one-step loss alone.
• The factorization is a testable hypothesis. A wrong factorization can fail without warning, so pair structured models with uncertainty quantification and mechanism-level diagnostics.

One closing habit to carry forward from this chapter: whenever you evaluate or design a world model, ask what constrains its prediction for a novel combination. Learned parts and a valid composition rule provide one answer; other models may encode equivalent sharing or equivariance without explicit object modules. If no valid inductive bias or data support constrains the prediction, it is an unsupported off-data extension that planning may exploit—not necessarily interpolation, and not an inevitable property of every monolithic model.

The next part of the book turns from what world models should represent to how concrete architectures realize it. We begin with the recurrent state-space model, a recurrent latent-dynamics architecture that couples deterministic and stochastic state evolution. Keep this chapter's question in mind as we get there: nothing in the RSSM objective forces its latent transition to factorize, so whether these models compose is a property of their design and data, and a property you now know how to test.