Successful perception in humans clearly relies on both top-down and bottom-up signals. Top-down information encodes relevant context, priors and preconceptions about the current scene: for example, what we might expect to see when we enter a familiar place. Bottom-up signals consist of what is literally observed through sensation.

The best way to combine top-down and bottom-up signals remains an open question, but it is clear that these signals need to be combined in a way which is dynamic and depends on context - in particular top-down signals are especially important when stimuli are noisy or hard to interpret by themselves (for example walking into a dark room).

Additionally, which top-down signals are relevant also changes depending on the context. It is possible that combining specific top-down and bottom-up signals that can be weighted dynamically (for example using attention) could improve robustness to distractions and noisy data.

In addition to the general requirement of dynamically combining top-down and bottom-up signals, it makes sense to do so at every level of the processing hierarchy to make the best use of both sources of information at every stage of that computation, as is observed in the visual cortex (with very rich top-down signals influencing the activity at every level).

Dynamic Integration of Bottom-up and Top-Down Information. In favour of architectures in which top-down contextual information is dynamically combined with bottom-up sensory signals at every level of the hierarchy of computations relating low-level and high-level representations.

Whereas a statistical model captures a single joint distribution, a causal model captures a large family of joint distributions, each corresponding to a different intervention (or set of interventions), which modifies the unperturbed or default distribution (e.g., by removing parents of a node and setting a value for that node).

Whereas the joint distribution P(A,B) can be factored either as P(A)P(B|A) or P(B)P(A|B) (where in general both graph structures can fit the data equally well), only one of the graphs corresponds to the correct causal structure and can thus consistently predict the effect of interventions. The asymmetry is best illustrated by an example: if A is altitude and B is average temperature, we can see that intervening on A will change B but not vice-versa.

Preliminaries. Given a set of random variables Xᵢ, a Bayesian network is commonly used to describe the dependency structure of both probabilistic and causal models via a Directed Acyclic Graph (DAG). In this graph structure, a variable (represented by a particular node) is independent of all the other variables, given all the direct neighbors of a variable. The edge direction identify a specific factorization of the joint distribution of the graph's variables: p(X₁,...,Xₙ) = Πᵢ p(Xᵢ | PAᵢ).

Structural causal models (SCMs). A Structural Causal Model (SCM) over a finite number M of random variables Xᵢ given a set of observables X₁,...,Xₘ (modelled as random variables) associated with the vertices of a DAG G, is a set of structural assignments Xᵢ := fᵢ(X_{pa(i,C)}, Nᵢ), ∀i ∈ {1,...,M}, where fᵢ is a deterministic function, the set of noises N₁,...,Nₘ are assumed to be jointly independent, and pa(i,C) is the set of parents (direct causes) of variable i under configuration C of the SCM directed acyclic graph.

Causal structure learning is the recovery of the ground-truth C from observational and interventional data, possibly yielding a posterior distribution over causal structures compatible with the data, and a neural network can be trained to generate graphs from that posterior.

Interventions. Without experiments, or interventions i.e., in a purely-observational setting, it is known that causal graphs can be distinguished only up to a Markov equivalence class, i.e., the set of graphs compatible with the observed dependencies. In order to identify the true causal graph, the learner needs to perform interventions or experiments i.e., interventional data is generally needed.

A powerful assumption about how the world works which arises from research in causality and briefly introduced earlier is that the causal structure of the world can be described via the composition of independent causal mechanisms.

Independent Causal Mechanisms (ICM) Principle. A complex generative model, temporal or not, can be thought of as composed of independent mechanisms that do not inform or influence each other. In the probabilistic case, this means a particular mechanism should not inform (in the information theory sense) or influence the other mechanisms.

This principle subsumes several notions important to causality, including separate intervenability of causal variables, modularity and autonomy of subsystems, and invariance.

This principle applied to the factorization in equation 1, tells us that the different factors should be independent in the sense that (a) performing an intervention on one of the mechanisms p(Xᵢ|PAᵢ) does not change any of the other mechanisms p(Xⱼ|PAⱼ) (i≠j), (b) knowing some other mechanisms p(Xᵢ|PAᵢ) (i≠j) does not give us information about any another mechanism p(Xⱼ|PAⱼ).

Nature doesn't shuffle examples. Real data arrives to us in a form which is not iid, and so in practice what many practitioners of data science or researchers do when they collect data is to shuffle it to make it iid. "Nature doesn't shuffle data, and we should not" (Bottou, 2019). When we shuffle the data, we destroy useful information about those changes in distribution that are inherent in the data we collect and contain information about causal structure. Instead of destroying that information about non-stationarities, we should use it, in order to learn how the world changes.

To illustrate the link between meta-learning, causality, OOD generalization and fast transfer learning, consider the example from (Bengio et al., 2019). We consider two discrete random variables A and B, each taking N possible values. We assume that A and B are correlated, without any hidden confounder. The goal is to determine whether the underlying causal graph is A → B (A causes B), or B → A.

Note that this underlying causal graph cannot be identified from observational data from a single (training) distribution p only, since both graphs are Markov equivalent for p, i.e. consistent with observational data of any size. In order to disambiguate between these two hypotheses, (Bengio et al., 2019) use samples from some transfer distribution p̃ in addition to our original samples from the training distribution p.

Without loss of generality, they fix the true causal graph to be A → B, which is unknown to the learner. Moreover, to make the case stronger, they consider a setting called covariate shift, where they assume that the change (again, whose nature is unknown to the learner) between the training and transfer distributions occurs after an intervention on the cause A. In other words, the marginal of A changes, while the conditional p(B|A) does not, i.e. p(B|A) = p̃(B|A). Changes on the cause will be most informative, since they will have direct effects on B.

(Bengio et al., 2019) find experimentally that this is sufficient to identify the causal graph, while (Priol et al., 2020) justify this with theoretical arguments in the case where the intervention is on the cause.

In order to demonstrate the advantage of choosing the causal model A → B over the anti-causal B → A, (Bengio et al., 2019) compare how fast the two models can adapt to samples from the transfer distribution p̃. They quantify the speed of adaptation as the number of samples from p̃ needed to adapt. This exemplifies the key point: learning the correct causal structure allows faster adaptation to new distributions, which is the essence of the connection between causality and fast transfer learning / OOD generalization.

Understanding causes and effects is a crucial component of the human cognitive experience. Humans are agents and their actions change the world (sometimes only in little ways), and those actions can inform them about the causal structure in the world. Understanding that causal structure is important in order to plan further actions in order to achieve desired consequences, or to attribute credit to one's or others' actions, i.e., to understand and cope with changes in distribution occurring in the world.

However, in realistic settings such as those experienced by a child or a robot, the agent typically does not have full knowledge of what abstract action was performed and needs to perform inference over that. The agent would thus have a causal model of latent causal variables (how they influence each other and relate to each other), an intervention model relating low-level actions with interventions (or intentions to change specific high-level variables), as well as an observation model (relating high-level causal variables and sensory observations).

In addition to these models, it would have inference machinery associated with them, including a high-level policy generating goals (i.e. intentions to intervene in a particular way).

A human-centric version of this viewpoint is the psychological theory of affordances that can be linked to predictive state representations in reinforcement learning: what can we do with an object? What are the consequences of these actions? Learning affordances as representations of how agents can cause changes in their environment by controlling objects and influencing other agents is more powerful than learning a data distribution.

It would not only allow us to predict the consequences of actions we may not have observed at all, but it also allows us to envision which potentialities would result from a different mix of interacting objects and agents. This line of thinking is directly related to the work in machine learning and reinforcement learning on controllability of aspects of the environment.

A clue about a good way to define causal variables is precisely that there exist actions or skills to control one causal variable while not directly influencing most others (i.e., except as an effect of the causal variable which is being controlled). A learner thus needs to discover an intervention model (what actions give rise to what interventions), but the locality of interventions in the causal graph can also help the learner figure out a good representation space for causal variables.