Causal Models and Interventions › Causal Representation Learning

Everything above assumed we know the variables. A robot with a camera does not. It gets pixels, and the questions become: what should the latent state be so that causal reasoning over latents is valid? Can we learn latent variables that correspond to stable mechanisms, so that interventions on the world correspond to interventions on specific latents?

The stakes of this question are easy to state. Every result in this chapter, every adjustment formula, every transportability computation, every abduction step, presupposes a vocabulary of variables with the right causal relationships among them. If the latents are entangled, so that one latent coordinate mixes the heat load with the cooling effort and another mixes both with the time of day, then an intervention on the world moves several latents at once, and a single-coordinate edit such as $\mathrm{do}(Z_j=z)$ need not correspond to a realizable, localized physical intervention. The formal machinery can then answer a precisely posed question about the learned variables while that question fails to match the physical action the planner intended.

This is the program of causal representation learning, crystallized by Schölkopf and colleagues (2021). It combines the latent-variable methods of Part III with the causal machinery of this chapter, and its central result is sobering first, hopeful second.

First, the sobering part. Unrestricted nonlinear independent component analysis is not identifiable from i.i.d. observations alone: observationally equivalent nonlinear reparameterizations can yield incompatible latent coordinates when the decoder and latent law transform with them. An equally predictive representation can therefore remain an entangled mixture of causal variables. Temporal, multi-view, nonstationary, or other auxiliary structure can change that conclusion, so the impossibility belongs to the unrestricted observational setting rather than to every objective that lacks explicit interventions.

Second, the hopeful part. Identifiability results become possible when a particular model class is paired with sufficient auxiliary structure and assumptions. Embodied interaction can supply some of that structure, but none of the following ingredients is sufficient by itself:

• Temporal and intervention structure. Slow or sparse transitions can be useful assumptions in some domains, but they are not automatic properties of sequential data. CITRIS, for example, uses temporal intervened sequences together with observed intervention-target indicators and assumptions including invertible observations, stationarity, and no instantaneous effects. Its identification result does not follow from transition sparsity alone.
• Interventions and actions. Deliberately varied, well-characterized actions can provide interventional supervision when targets are known, interventions are sufficiently diverse, and the observation and dynamics assumptions support identification. Ordinary curiosity-driven exploration does not guarantee these conditions: actions may affect multiple unknown targets, be mediated by hidden state, or leave important factors untouched. Interaction is therefore a promising data source, not identifiability for free.
• Controllability structure. In some domains it is useful to distinguish factors the available actions can influence from nuisance factors they cannot. This is a modeling decomposition rather than a universal content-style split. When it is justified, training can encourage action-conditioned dynamics to represent controllable factors without treating every source of visual variation as a planning variable.
• Sparsity and modularity priors. Assuming that each mechanism depends on few variables can improve identifiability in specified model classes. Object-centric representations, covered in Object-Centric and Relational Worlds, provide useful candidates for groups of causal variables, but objects are not automatically mechanisms and an object-centric representation does not inherit causal modularity without further evidence.

For a world model builder, an ordinary i.i.d. predictive loss alone does not guarantee causal latents. Actions, time, multiple environments, or auxiliary variables can add the structure needed by a particular identification result. Action-conditioned latent dynamics can still support planning without coordinate-wise disentanglement when planners optimize realizable action sequences rather than editing latent coordinates directly. The stronger causal-latent goal remains valuable for interpretable interventions, transfer, and diagnosis, but it is a method-specific guarantee rather than a universal prerequisite for predictive-embedding or JEPA-style planning.