Compositionality and Systematic Generalization › Compositionality and Systematic Generalization

Imagine you have trained a world model for a household robot on a stipulated dataset containing thousands of hours of kitchen activity. The model predicts, with impressive accuracy, how a mug slides across a countertop when pushed, and how a drawer swings open when pulled. Now you place the mug on a different counter and ask the robot to slide it while a drawer stands open nearby. Nothing about the physics is new under the example's autonomy assumptions: the sliding mechanism is the same, the drawer mechanism is the same, and neither depends on the other. A human predicts the outcome by putting the two known pieces together. A monolithic model trained on the observed distribution of scenes can fail, because the exact combination "this mug, that counter, drawer open" never appeared in its training data and no compositional constraint ties it to the observed scenes.

The failure here is subtle and worth dwelling on before we fix it. The stipulated dataset is large in duration, but duration alone does not establish coverage of the combinations that matter. What this particular model lacked was the right inductive structure. Every ingredient of the novel prediction was demonstrated in training, but the model was never forced to represent the ingredients separately, so its output on their new combination is not determined by those demonstrations. It learned answers, not a grammar for producing answers. Without another useful inductive bias, it may fail outright or produce a confident guess with no grounding in the missing combination.

This chapter is about designing and evaluating world models so that this kind of prediction is possible. The core idea is compositionality: represent the world as a set of reusable parts (objects, relations, mechanisms, skills) whose behaviors are learned separately and combined by known rules. A model can predict unobserved combinations after seeing a vanishing fraction of the configuration space only when the reusable components are adequately identified on the state-action support the new combinations require and the composition rule remains valid there. This conditional capacity is called systematic generalization, and it is an important property for world models intended to support planning in novel situations.

The stakes are especially high for world models specifically, as opposed to predictive models in general, because of how agents use them. A planner queries a world model at the states reached by candidate action sequences, and unconstrained candidate rollouts can leave the support of the data-collection policy. Generalization is therefore a core requirement whenever planning induces this distribution shift. Compositional structure is one important response when the assumed mechanisms and composition rule match the world; support constraints, uncertainty-aware objectives, robust planning, and new data address complementary failure modes.

We will build the idea in four steps: why compositionality matters for prediction and control, how factorized mechanisms formalize it, how to recombine objects, relations, and skills, and how to measure whether a model generalizes systematically. Along the way we will implement a small experiment where a factorized model and a monolithic model see identical data but behave completely differently out of distribution.