Frontier Questions and Research Roadmaps › Causal, Compositional, and Persistent Structure

The second frontier question concerns structure: what kind of structure can learned world models acquire, and what does acquiring it require?

"Structure" is not a single property that a model either has or lacks. Temporal structure, causal structure, compositional structure, and persistent-memory structure are different properties with different requirements. A model can have one and lack another. Evidence for one property alone need not establish the others, although a well-designed test may support more than one. The next three subsections separate these questions.

An observational conditional describes the sampled data-generating process. Without additional assumptions, it need not identify an intervention distribution. More observations from that same process do not resolve an ambiguity between observationally equivalent causal models. Known structure, suitable adjustment variables, randomized actions or other identification assumptions can change what the data establish.

Three distinct notions get merged in casual discussion, and Pearl's causal ladder gives the standard separation:

• Association. "Given that the agent has been moving right, what comes next?" Temporal prediction is one example of an associational query. This is the lowest level in the causal-information hierarchy, not necessarily the easiest prediction problem computationally.
• Interventional prediction. "If I force the agent to move left, what happens?" Identifying this effect requires appropriate assumptions: randomized actions, valid adjustment for confounding, or other justified structure. An explicit causal diagram alone need not identify the effect.
• Counterfactual inference. "Given what actually happened, what would have happened had I acted differently?" This also requires a justified account of the individual circumstances or latent disturbances shared across the factual and counterfactual scenarios. Observational fit alone does not generally identify it.

Imagine a manipulation dataset collected by an expert that only pushes toward the goal. Accuracy on that distribution does not validate predictions for pushing away from it. Those predictions can be wrong or miscalibrated; confidence and error are not inevitable, since structural assumptions may support extrapolation. Coverage, architecture, uncertainty estimation and evaluation all influence the outcome. An independent intervention test makes this unsupported action query explicit (Part XII, Chapter 1).

Training loss on expert trajectories need not reveal errors at actions those trajectories never cover. A model can fit the observed distribution while extrapolating poorly elsewhere. A deterministic planner that treats its predictions as exact can then exploit those errors. Broader action coverage, calibrated uncertainty, conservative planning and appropriate structural assumptions are possible remedies. None guarantees correctness outside the conditions under which it was validated; changing the architecture alone does not supply missing evidence.

Causal representation learning attempts to recover variables that behave causally, so that interventions and counterfactuals become well defined. The program is laid out in Schölkopf et al., "Towards Causal Representation Learning", and interventional approaches such as Ahuja et al. show identifiability results under explicit assumptions.

State the assumptions of the particular result. Ahuja et al.'s Theorem 5.3 uses a polynomial decoder with full-column-rank coefficients, support regularity, a hard intervention fixing one latent coordinate, and nonempty interior for the remaining intervention support. The learned decoder has the prescribed polynomial degree, the encoder does not collapse the support, reconstruction is exact on observational and interventional supports, and one encoded coordinate is fixed on the intervention support. Under these conditions, that intervened latent is identified up to shift and nonzero scaling. Their block-affine result uses different intervention-support and representation constraints. These are conditional coordinate-identification results, not proof that arbitrary robot latents recover complete causal dynamics. Check the particular theorem rather than applying one generic checklist to every approach.

The blunt consequence: a learned disentangled representation is not causal evidence. If you train a $\beta$-VAE and the latent dimensions align with your factors, or if an object-centric slot attention module produces one slot per object, you have found a representation with a certain factorization. You have not shown that intervening on the object corresponding to slot 3 will change the state in the way your model predicts, because you have not run the intervention. The claim and the evidence are different objects.

Separating a representation into components does not establish how interventions work. Even a probability factorization need not imply independence: the chain rule $p(x,y)=p(x)p(y\mid x)$ also holds for dependent variables. An independent product makes an additional statistical claim, but neither separation nor independence alone identifies the effect of forcing a component to change. A representation can align with observed factors while leaving their intervention behavior unidentified. The assumptions of a particular causal-identification result, rather than the factorization alone, establish what intervention claims it supports.

The next cell constructs a linear confounded system. The associational predictor sees only $X$. An information-advantaged structural reference also observes the common cause $Z$. This is not identification with an unobserved confounder. We report two distinct estimands: noisy individual-outcome error on held-out observational samples, and error in the interventional mean averaged over $Z$ at three fixed intervention values. Their absolute magnitudes are not directly comparable.

Planners select actions, and their model queries can include actions absent from the recorded data. Test the claimed action effects with an appropriate intervention protocol: apply specified actions and compare repeated outcomes with the corresponding predicted quantities. A discrepancy challenges the prediction or its assumptions; it does not identify whether the cause is a wrong causal coefficient, unmodeled context, sampling error or another failure. Agreement on the tested interventions supplies scoped evidence, not proof of every structural claim.

Compositional generalization is the ability to handle novel combinations of factors that were each observed separately. The clean experimental design is a held-out-combination split: every factor level appears in training, but selected combinations do not.

Sequence-to-sequence studies found substantial generalization gaps under compositional evaluations (Keysers et al.; Hupkes et al.; Lake and Baroni). Their protocols differ: compound-divergence splits, excluded function-pair combinations, and primitive or length splits are not identical tests. An analogous factor-combination split can be designed for dynamics learning: cover each factor level in training, hold out selected friction–payload or shape–surface pairs, and evaluate damping, contact or action-effect predictions separately on the held-out cells. This is a proposed dynamics evaluation, not a dynamics-transfer result from those sequence studies.

Two questions keep the interpretation of this split clear:

1. Are separate factor effects identifiable under the stated model and assumptions? If payload co-varies perfectly with friction, their separate effects need not be identifiable without additional assumptions. For a specified linear-in-parameters family, full column rank establishes coefficient uniqueness and conditioning diagnoses numerical or noise sensitivity; neither establishes identifiability for every nonlinear model. This question matters when interpreting recovered factor effects, but separate-effect identification is not a prerequisite for every held-out-combination performance test: a known structural law can supply those effects without estimating them from the training split.
2. The evaluation must distinguish seen from unseen combinations. Report both separately. A single aggregate over seen and unseen cells can conceal their contrast, even when it shows some overall performance change.

The interesting failure mode is when an additive inductive bias is wrong. If the true dynamics multiply two context factors, an additive model can fit the training combinations well and be systematically wrong off the diagonal. The second experiment below constructs exactly this case, and then deliberately breaks the multiplicative assumption too, so that the interaction model's success is not unconditional either.

A held-out-combination split probes the interaction of data coverage, model capacity, and inductive bias. A misspecified restricted family can retain error even with more samples, whereas a richer family may represent the interaction. Rank checks establish identifiability only within the chosen feature family. Additional structural assumptions can resolve ambiguities that the observed combinations alone do not resolve, but those assumptions must be stated and tested.

"Memory" in world models covers at least four mechanically distinct mechanisms. Conflating them makes it impossible to say what an ablation measured.

• Recurrent hidden state. The internal state of an RNN or a recurrent state-space model (Part V, Chapter 1). It carries a compressed summary of history, with no guaranteed storage policy and no explicit retrieval.
• A belief state. The sufficient statistic of the history for the current latent state under the model's assumptions (Part II, Chapter 2). A belief is a filtered, uncertainty-aware summary. Under particular models a compact parametric belief can be much smaller than the stored history; a general continuous-state posterior need not have a fixed-size representation.
• External memory. This includes distinct mechanisms, not just one episodic database. Graves et al. introduced Neural Turing Machines with differentiable external memory and a learned read/write controller. Blundell et al. used non-parametric episodic state-action return memory for control. Lewis et al. provide a retrieval-augmented generation example in NLP, not a control result or an origin claim for all retrieval augmentation. A key-value or vector store can retain experience without updating model weights, but retrieval errors, staleness and storage costs still need evaluation.
• Causal finite-window transformer context. Past tokens inside a configured window are attended over directly (Part V, Chapter 2). This is one implementation, not a definition of all transformer attention. Access does not guarantee reliable retrieval. Tokens outside the window are not directly attended to unless another mechanism, such as a summary, recurrent state, or external store, retains their information.

Each mechanism has possible failure modes. A learned recurrent state can drift and can be difficult to inspect; that difficulty depends on the representation. Beliefs can be systematically miscalibrated if the model is wrong. External stores can retrieve the wrong entry, or the right entry from the wrong episode. Dropping a token removes its direct attention path; the effect on a decision depends on redundancy and any retained summaries, so behavioral forgetting need not be a hard discontinuity.

Four questions should accompany any memory claim:

1. What information is retained? Episode identity, hidden context, task goal, object permanence, a recently observed cue.
2. How is it refreshed? Never? On a schedule? When prediction error rises? Is there a hazard rate for context change? The third experiment shows that a memory without a refresh mechanism is worse than no memory at all once the context changes.
3. How much does it cost? Storage, retrieval latency, and the compute and energy per decision (Part XII, Chapter 4).
4. What are the reset semantics? When does memory clear? At episode boundaries, at task changes, at a detected distribution shift? Retention across a reset can carry stale evidence when the reset changes that information's validity. Other retained facts, such as unchanged robot geometry, may remain useful.

The four mechanisms differ not just in what they retain but in how they fail to be updated:

• A recurrent state is updated at each invoked recurrent step, which need not be every environment step. Its learned update rule may be poorly matched to the rate at which the world changes.
• A belief is updated by a filter whose assumptions may be wrong.
• A standard rolling FIFO context window drops tokens as new ones arrive, without a relevance judgment. Selective retention policies can use relevance instead.
• An external store changes through its configured write, eviction, and retention rules; an agent need not control every update. Stored information can outlast the context in which it was valid.

Each mechanism needs an explicit retention and refresh policy. The third experiment isolates fixed and updating beliefs rather than comparing these storage architectures.

More retained information need not improve the decisions of a fixed learned agent. The following possible failures show why retention and use must be evaluated together.

• Stale context. The goal or physics changed and memory did not. Part VI, Chapter 5 and Part XII, Chapter 5 discussed continual correction in this setting.
• Retrieval of wrong evidence. A nearest-neighbor retrieval returns a transition from a visually similar but dynamically different situation.
• Distractor amplification. Memory preserves salient but irrelevant evidence, and a learned policy trained to attend to memory can over-weight it.
• Compression loss. Summarizing history discards exactly the rare detail that made the current situation special.

For this toy, memory is an estimate of a task-relevant belief. Other memory systems may retain raw history rather than estimate a sufficient statistic. Evaluate the retained information and update mechanism under the context changes they will actually face. For an ablation of history access, match current, nonhistorical inputs and training and compute budgets as far as the design permits. Historical information is the intended treatment, not an input confound to remove. Extra parameters or different training can change the comparison; document such differences and use additional controls before attributing the effect to history access alone.

A lossy history summary can discard information; lossless coding or an invertible representation need not do so. If the discarded information is irrelevant to the declared task, a summary can reduce storage while preserving what that task needs, but computing and maintaining it also costs resources. If an omitted detail matters under a later condition, the summary may no longer be sufficient. Report performance across the expected conditions and their frequencies, alongside retention and update costs, rather than relying on an average alone.