Coarse-graining as a downward causation mechanism

Downward causation is the controversial idea that ‘higher’ levels of organization can causally influence behaviour at ‘lower’ levels of organization. Here I propose that we can gain traction on downward causation by being operational and examining how adaptive systems identify regularities in evolutionary or learning time and use these regularities to guide behaviour. I suggest that in many adaptive systems components collectively compute their macroscopic worlds through coarse-graining. I further suggest we move from simple feedback to downward causation when components tune behaviour in response to estimates of collectively computed macroscopic properties. I introduce a weak and strong notion of downward causation and discuss the role the strong form plays in the origins of new organizational levels. I illustrate these points with examples from the study of biological and social systems and deep neural networks.

This article is part of the themed issue ‘Reconceptualizing the origins of life’.

Downward causation is among the most controversial and obscure concepts in evolutionary biology. Simply stated it is the idea that higher-level features can be a cause of behaviour by lower-level components [1,2] (see also [3–7]). On the one hand, this seems self-evident. Governments make laws and laws constrain individual behaviour, more or less forcing individuals to act in certain ways—stopping at a stop sign, for example. There are many similar colloquial examples to be found in the biological and social sciences. However, as soon as one spends a little time considering how this causality works trouble arises.

To summarize a long and convoluted debate (a bibliography: https://philpapers.org/browse/downward-causation), downward causation suffers from the criticism that it is not materialist. As the argument goes, higher levels of organization are ‘just’ temporal and spatial patterns that are the outcome of dynamics at a lower level. As patterns, they have neither material instantiation nor agency and hence cannot be causes. Of course this criticism suffers itself from a criticism: the ‘turtles all the way down’ problem.

Here I suggest we can reconcile this conflict by being operational and examining how adaptive systems identify regularities in evolutionary or learning time and use these perceived regularities to guide behaviour. I propose we move from simple feedback to downward causation when components tune behaviour in response to estimates of coarse-grained, aggregate properties. Elsewhere I have suggested that for tuning to be possible the coarse-grained variables need to have a slow time scale compared with (i) the microscopic behaviour producing them and (ii) the computation used to estimate them [8–10]. I will make these ideas concrete with examples from the biological and artificial intelligence literatures, but before I do, there are some additional issues worth emphasizing.

Adaptive systems generally are collective—meaning that there are multiple, semi-independent components making decisions and contributing to system dynamics [11]. It is not necessarily (it is perhaps rarely) the case that all components perceive similarly the aggregate properties describing the system or tune to them in the same way. This heterogeneity in tuning to aggregate properties is particularly likely in adaptive systems in which learning plays a big role. Hence a useful distinction, which I will come to in a moment, is between what we might call weak and strong forms of downward causation. Recognizing that adaptive systems tend to be intrinsically heterogenous, noisy, and collective brings into focus the reason why this tricky concept is worth arguing about—in its strong form, as I will illustrate through an example, it locally reduces entropy and creates order, which facilitates extraction of energy to do work.

I use the term apparent downward causation when tuning is partial and imprecise. In this weak or minimal form, only a few components need to be tuning their behaviour to estimates of aggregate properties for there to be some downward causation in the system. Apparent downward causation does not demand that estimates of aggregate properties be correct or even good predictors of the system’s future state or successful strategies (although that would be useful). Furthermore, components do not need to agree in their estimates of the variables. To reiterate, what matters is just that some components are tuning. This allows exploration of how the strength of the downward causation changes as a function of system dynamics and contributes to system performance.

Apparent downward causation becomes effective downward causation—the strong form—when [8–10]: — aggregate properties are predictive of the future state of the system (slow variables);— aggregate properties are robust to small perturbations;— estimates of these variables are used nearly universally by all components to tune decision-making;— components largely agree in their estimates of these variables; and— as estimates converge there should be an increase in mutual information between the microscopic behaviour and the macroscopic properties.

As with apparent downward causation, under effective downward causation, components need not be in agreement about how to best to tune to these variables. The degree of agreement will depend on whether decision-making—in learning or evolutionary time—is influenced by other types of heterogeneity in the system (for example, resource heterogeneity), which by influencing cost may place strong constraints on component decision-making, and also on robustness-adaptability tradeoffs. High agreement—high homogeneity—in strategy would likely make the system sensitive to perturbations and move it towards a critical point, which can have costly robustness implications [12].

Notice that by operationalizing apparent and effective downward causation as described above, we avoid violating the materialist requirement because the components are tuning to patterns they perceive and hence are ‘doing the work’. I will not discuss in this paper when the operational concept of downward causation I am proposing conforms to strict definitions of causality (e.g. [13,14]). However, I will discuss (§6 how the causal contributions of the environment and collective behaviour to the aggregate properties can be roughly quantified, and I will propose that from an operational perspective it makes sense to start talking of a new level of organization when the criteria for effective downward causation are met. I explore this further in §7. Because the conceptual framework I am developing here rests in part on the concept of coarse-graining, in §2, I give a brief review of coarse-graining in physics and introduce the concept of endogenous coarse-graining–coarse-graining performed by the system (as opposed to a scientist) as an inference mechanism [8–10]. In §3, I show through an example how coarse-graining can produce effective downward causation. In §6 I discuss challenges, focusing in particular on how the collective and noisy character of adaptive systems impact coarse-graining and downward causation.

The second law of thermodynamics states that the entropy of the Universe is increasing [15]. In apparent contrast to the second law, matter and radiation appear have started out in thermodynamic equilibrium—a high entropy state [16,17]. In addition, the gravitational field at the birth of the Universe was highly structured (low entropy yet also smooth and featureless) but is becoming less ordered [18]. These two facts coupled to confusing use of the terms, ‘entropy’, ‘structure’, ‘order’, ‘uniformity’, etc. have led to a variety of at odds or unclear positions on what it means to say that entropy is increasing. As I am by no means an expert on this topic, I, with gratitude to Sean Carroll, refer the reader to Wallace [17], who nicely summarizes the conventional thinking and space of positions. He offers a restatement in which he emphasizes that the early Universe was not at global thermal equilibrium, only local thermal equilibrium, and gives the reasons why.

For our purposes here, the important point is that entropy is increasing and, as it does, at least some of the detailed information we initially had about the system is lost, making prediction about the behaviour of the system difficult. My interest in this is twofold. First, a point which i will get to in a moment, is how we can improve our capacity to make predictions under this condition. Second, a point which I get to in §3 is how we can reduce entropy locally to increase capacity for prediction locally.

Additionally, classical fluctuations at the microscopic scale—small, fast-timescale (non-directional) changes in component behaviour—can make reliance on microscopic behaviour for macroscopic predictions difficult. And, relying on the microscopic behaviour for prediction can require specifying many details. Ideally, we would like our prediction to be based on a compact description of system behaviour.

For these reasons, to make good predictions we can move to what is called a coarse-grained description in which some of the microscopic detail has been smoothed out. To make this more concrete, think about temperature [19].

Temperature is the average speed of particles in a system. Temperature is a coarse-grained representation of all of the particles’ behaviour—the particles in aggregate. When you know the temperature you can use that to predict the system’s future state better than you could if you actually measured the speed of an individual particle. Temperature can predict the future state of the system (assuming it is at equilibrium) more computationally efficiently because it requires fewer degrees of freedom.

This is why coarse-graining is so important. It gives us what is called in physics and biology the basis for an effective theory. An effective theory allows us to model the behaviour of a system without specifying all of the underlying causes that lead to system state changes. Effective theories by definition are agnostic to system mechanics. Some effective theories are even at odds with the mechanics—for example, the Bardeen–Cooper–Schrieffer (BCS) theory of high temperature superconductivity (discussed in [20]). The effective theories of interest here are those that have a basis in mechanism but nonetheless ignore many of the details.

Having a basis in mechanism is a critical property of a coarse-grained description—it is ‘true’ to the system. It is a simplification of the microscopic details. In principle, a coarse-grained description does not introduce any outside information to the subset of microscopic interactions over which it is performed (but see for examples of technical exceptions [21,22]). This ‘lossy but true’ property is one factor that distinguishes coarse-graining from other types of abstraction.

A second property of coarse-graining is that it is an integration over component behaviour. An average is a simple example but more complicated computations are also possible, as discussed in §3. I emphasize this property of integration to distinguish coarse-graining from other forms of regularity extraction like such as loss-less compression in which noise and redundancies are removed from the dataset but where the compressed output is not itself the result of an integration.

Normally when we talk of coarse-graining, we mean coarse-grainings that we as scientists impose on the system to find compact descriptions of system behaviour sufficient for good prediction. However, we can also ask how adaptive systems identify regularities and build effective theories to guide adaptive decision-making and behaviour [8–10,23]. To distinguish coarse-graining in Nature from coarse-graining by scientists, we call coarse-graining in Nature endogenous coarse-graining [8] (see also [24,25]). I now go through an example of endogenous coarse graining in an animal social system. To give a sense of the range of applicability of this concept I also very briefly discuss related concepts in molecular biology and neural networks.

Our coarse-graining example comes from the study of the dynamics producing power structure in a well-study macaque society model system. The review below is brief, serving to illustrate a few critical points. For further important detail, I refer the reader to [9,10].

In this system power is operationalized as the degree of consensus among group members that an individual can win fights (see [26] and references therein). The degree to which the group perceives an individual capable of winning fights is encoded in a network of subordination signals. An individual sends a subordination signal during peaceful interactions to a receiver it perceives, through a history of fighting, as likely to win fights—fighting is necessary because temporally stable factors such as experience and size of the alliance network, not just body size, influence fight outcomes. Subordination signals formalize agreement to the subordinate role in a dominance relationship, which is a kind of proto-contract. The signal is unidirectional (nearly always emitted by the same individual until the underlying asymmetry grows small or is reversed) and emitted in peaceful settings rather than during conflicts so it is less likely to be perceived by the receiver as meaning only submission in the current conflict.

Subordination signals are only emitted when the sender perceives a large asymmetry in fighting ability in its opponent’s favour. In other words—when it perceives that the cost of continued aggression is greater than the cost of subordination (in this case, signalling is the optimal strategy [27]). The decision to send the signal is the output of an individual level computation. The computation involves integrating over a history of fight outcomes in order to compute an estimate of the magnitude of asymmetry. The subordination signal serves as a coarse-grained representation of the history of fight outcomes over some period.

Fighting continues after the subordination contract has been formalized through signal exchange but at a reduced rate. This provides a mechanism by which the relationship might reverse in the future and is roughly analogous to a ‘background process’ running on your computer.

Individuals appear to roughly track the number of signals they have received from particular individuals, as well as the identity of signal senders. An individual computes its power—the degree to which it is collectively perceived as capable of using force successfully in fights—by coarse-graining the network of status signalling interactions (algorithms described in [26]) to compute the collective perception. Hence the aggregate variable individuals are estimating here is the degree of consensus in the group that they can win fights. The power distribution (DSP) results from the collective computation by all individuals of their power scores.

Whereas the dominance relationship formalized by subordination signal exchange is a course-grained representation of fight outcome history, a power score is a course-grained representation of the signalling network, which encodes an individual’s fighting ability as collectively perceived by the group. The direction of signal exchange and the power score both constitute for each individual effective theories that respectively predict, in the case of the dominance relationship and the power score, social tolerance from the signal receiver and the average cost of social interaction. Finally, in case it is not obvious it is worth noting that the collective computation in this example has two phases—an information accumulation phase in which the individuals, like sensors, gather information semi-independently about who is capable of winning fights, and a consensus or aggregation phase, in which that information is shared in a signalling network that encodes the power distribution [26,27] (also applies in neural systems [28]).

Coarse-graining, which happens both during the information accumulation phase and also during information aggregation phase of the collective computation, is advantageous for at least two reasons. One reason is that coarse-graining allows individuals to make predictions without requiring they indefinitely store all of the details of their interactions. Once they have signalled, the time series of fights leading up to the signal can (in principle, we do not yet know exactly how this works) be deleted from memory. Going forward individuals only need retain the signal, which summarizes the history of fights leading up to signal exchange, and the outcome of any new fights. Hence coarse-graining may allow memory minimization.

A second reason coarse-graining is advantageous is it allows individuals to identify slowly changing regularities that may not be evident in the fine-grained social interactions if these fluctuate for transient and/or contextual reasons, as fights do. Coarse-graining by smoothing out noise improves predictions. Hence coarse-graining results in uncertainty reduction through slow variable construction. An important subtlety is that even though the coarse-graining is lossy, from a functional perspective information is gained because the signal to noise ratio is higher and the uncertainty about what constitutes a ‘good’ strategy decreases. There is not yet a good language for discussing this transition. This point may be similar to the idea that in the normal derivation of an arrow of time, coarse-graining over microstates loses information, but information is gained about the arrow of time (anonymous reviewer 2017, personal communication).

Both the accuracy with which the DSP reflects true fighting abilities and the skewness of the DSP are functionally important. A DSP will be a reliable predictor of interaction cost if it has mutual information with the underlying (and not directly observable) distribution of fighting abilities and changes slowly [27]. The right skewness of the DSP influences conflict management. For example, heavy-tailed distributions make otherwise costly conflict-management strategies, such as policing, accessible to individuals who occupy the tail of the distribution of power. The reason for this is that individuals in the tail are perceived to be disproportionately powerful and are unchallenged when they intervene.

The system exhibits apparent downward causation when the DSP has consolidated enough so that it changes more slowly than the microscopic fight behaviour producing it and at least one individual uses estimates of its power scores or other properties of the DSP, like skewness, to make predictions about interaction cost and tune behaviour. The system begins to show effective downward causation when/if (i) the collectively estimated DSP is robust to small perturbations in signalling patterns and has a slower time scale than the fight outcome network (many fights per hour with a per individual time scale on the order of hours [29]) underlying it and the signalling network used to compute it, (ii) the DSP predicts the cost of social interaction, (iii) individuals’ estimates of properties of the DSP begin to converge—in other words over time individuals come agree through learning and increasing sample size who is powerful and who is weak and roughly by how much and (iv) the mutual information between DSP and the underlying distribution of fighting abilities is high—meaning that DSP is capturing regularities in the system.

With respect to (iii), the probability of convergence on similar estimates increases as the fight outcome network becomes fully connected—meaning all individuals have fought each other, as individuals come to have similarly sized datasets on fight outcomes, when there is social learning (correlated learning), when there is disparity in fighting ability—in other words, when regularities can be easily learned and are costly not to learn—in other words, when individuals have an incentive to accurately estimate regularities [27], when the computational capacity of components is similar, and as a result of positive feedback induced by the downward causation itself.