Hierarchical and temporal causation: what changes when causes live at different scales?

In brief

• Many real systems contain nested causal structure: parts affect wholes, and wholes constrain parts.
• Temporal causation adds a second difficulty: causes can act with delay, persistence, feedback and changing context.
• A useful world model should therefore recover causal variables at multiple levels and represent how interventions propagate across time.

A large fraction of causal modelling assumes a relatively flat set of variables observed at one level of abstraction. Real systems are rarely organised this way.

A port contains berths, vessels and service processes. A fishery contains vessels, trips, sets, catches and management rules. A medical image contains tissues, lesions, cells and acquisition effects. At the same time, the relevant mechanisms unfold over minutes, hours, days or years.

This creates two coupled questions:

1. At which level does a cause act?
2. Over which timescale does its effect become visible?

I refer to these as hierarchical causation and temporal causation.

Hierarchical causation

A hierarchical causal system contains variables at multiple levels of abstraction.

A vessel-level decision can affect a port-level queue. Port-level congestion can in turn alter vessel behaviour. In a fishery, trip-level effort aggregates into fleet-level pressure, while fleet-level policy changes constrain trip-level decisions.

The key point is that causal influence can move up and down the hierarchy.

A flat model that replaces lower-level structure with one aggregate variable may therefore lose information required for identification. Recent hierarchical causal models formalise this by extending structural causal models to nested data and show that subunit-level observations can enable causal identification that would be impossible from aggregated unit-level summaries alone.

This immediately raises a representation-learning question:

Which latent variables should exist at each level, and which relations between levels are identifiable from observations?

That is closely related to object-centric learning. Objects provide one level of decomposition, but causal reasoning may require additional structure above and below the object level: parts, interactions, groups, systems and environments.

Temporal causation

Temporal structure introduces a different ambiguity.

Suppose vessel speed falls before berth congestion rises. The ordering is consistent with several explanations:

• vessels slowed because congestion was already anticipated;
• congestion caused vessels to slow;
• weather caused both;
• a policy intervention changed arrival behaviour and congestion later;
• the observed relation is only predictive.

Time ordering constrains causal explanations, but does not determine them.

Temporal causal discovery therefore has to represent lagged effects, event sequences, feedback, non-stationarity and missing observations. Recent surveys distinguish multivariate time-series causality from event-sequence causality precisely because the structure of the data changes what can be identified.

A temporal causal model should answer more than:

What happens next?

It should support:

What changes later if I intervene now?

When hierarchy and time interact

The difficult case is not hierarchy alone or time alone. It is their interaction.

Consider port congestion.

At a short timescale, berth occupancy affects an arriving vessel’s waiting time. At a longer timescale, repeated queueing changes carrier arrival strategies. At a higher level, those strategies change the port-level arrival process. A policy introduced at the port level then changes future vessel-level behaviour.

The causal loop spans:

vessel → berth → port → policy → future vessel

and multiple timescales.

A model that predicts the next vessel state can perform well while failing to represent this mechanism.

This is where hierarchical temporal causal representation learning becomes important. Recent work such as CHiLD studies identifiability of multi-layer latent causal dynamics from temporal observations, explicitly targeting hierarchical latent variables that evolve over time.

What should a causal world model represent?

For me, a useful causal world model should separate at least four components.

1. Entities

Objects or agents that persist through time.

Examples:

• vessel;
• berth;
• fish;
• camera;
• port;
• fleet.

2. Hierarchical state

Variables defined at different levels.

Examples:

• vessel speed;
• berth availability;
• port congestion;
• fleet effort;
• ecosystem pressure.

3. Temporal mechanisms

How those variables evolve and influence one another over time.

Examples:

• delayed effects;
• accumulation;
• feedback;
• recovery;
• regime change.

4. Intervention semantics

What it means to change one variable while holding the relevant mechanisms fixed.

Without this last component, a world model remains primarily predictive.

Identifiability matters

A hierarchical latent model can always invent variables. The scientific question is whether the recovered variables correspond, up to a meaningful equivalence, to the mechanisms that generated the data.

This is why identifiability is central.

If several latent decompositions explain the same observations equally well, then downstream causal reasoning may depend on arbitrary representation choices.

For hierarchical temporal models, the challenge becomes stronger: we need to know whether both the layer structure and the dynamics within and across layers can be recovered from observations.

That connects directly to my broader interest in identifiable object-centric representations. Before asking whether a model reasons causally, we should ask whether the representation on which that reasoning operates is itself recoverable.

Causal abstraction

Hierarchy is also an abstraction problem.

A high-level variable such as congestion is not simply another sensor measurement. It summarises many lower-level processes: arrivals, berth service, priorities, delays and local interactions.

For that abstraction to be causally meaningful, interventions at the high level should correspond consistently to transformations of lower-level mechanisms.

This is the core motivation behind causal abstraction: a useful high-level model should preserve the intervention structure of the lower-level system, rather than merely compress its observations.

The implication for AI is important:

A representation is not useful because it is compact. It is useful when the interventions we care about remain meaningful after abstraction.

Feedback should not be treated as an exception

Many real systems contain feedback.

Congestion changes arrival behaviour; arrival behaviour changes congestion. Management interventions alter vessel behaviour; those behavioural changes alter the data used for later management.

Classical recursive structural models often avoid cycles for mathematical convenience. Recent temporal causal reasoning work shows that causal reasoning can be extended to non-recursive settings where feedback and mutually dependent processes are explicit.

For world models, feedback is not a corner case. It is part of the environment dynamics.

A practical modelling direction

I would formulate hierarchical temporal causation as a latent state-space problem:

z_t = {z_t^(1), z_t^(2), …, z_t^(L)}

where each layer represents a different causal scale.

Within each layer:

z_t^(l) = f_l(z_{t-1}^{(l)}, pa_t^(l), ε_t^(l))

and cross-level mechanisms connect layers:

z_t^(l+1) = g_l(z_t^(l), z_{t-1}^{(l+1)}, η_t^(l))

The objective is not only to predict observations x_t, but to recover a representation in which:

• latent variables are identifiable under explicit assumptions;
• temporal dependencies are structurally meaningful;
• cross-level relations are sparse and interpretable;
• interventions propagate consistently through the hierarchy.

Evaluation

A hierarchical temporal causal model should be evaluated at more than one level.

Representation

• latent identifiability;
• separation of causal factors;
• stability across domains.

Temporal structure

• lag recovery;
• transition prediction;
• feedback reconstruction.

Hierarchy

• correct cross-level dependencies;
• robustness to aggregation;
• intervention consistency between levels.

Causal reasoning

• counterfactual accuracy;
• interventional prediction;
• treatment-effect recovery.

Human contestability

• can a user intervene at one level and inspect how the consequence propagates across levels and time?

The last criterion matters for human-centred AI. Contestability is difficult when the system’s representation has no meaningful hierarchy or temporal semantics.

Why this matters

Flat causal graphs are useful abstractions, but many scientific and operational systems require more.

A vessel is embedded in a port.
A port is embedded in a logistics network.
A decision made now changes what becomes observable later.

The research problem is therefore not simply causal discovery over more variables.

It is to learn which variables belong at which level, how mechanisms connect those levels, how those mechanisms evolve through time, and which parts of that structure remain identifiable from observation.

That is the direction in which I think causal world models need to move.

References

• Weinstein, E. N. & Blei, D. M. Hierarchical Causal Models. JMLR, 2026.
• Li, Z. et al. Towards Identifiability of Hierarchical Temporal Causal Representation Learning. NeurIPS, 2025.
• Gong, C. et al. Causal Discovery from Temporal Data: An Overview and New Perspectives. ACM Computing Surveys, 2024/2025.
• Assaad, C. K., Devijver, E. & Gaussier, E. Survey and Evaluation of Causal Discovery Methods for Time Series. IJCAI, 2023.
• Gladyshev, M. et al. Temporal Causal Reasoning with (Non-Recursive) Structural Equation Models. AAAI, 2025.
• Geiger, A. et al. Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretability. JMLR, 2025.