Active Inference and Cognitive Consistency

I know little about social psychology and less about cognitive consistency theory; however, I greatly enjoyed reading the deconstruction of this paradigm by Kruglanski et al. (this issue). I learned a lot and was struck repeatedly by the consilience between their treatment and complementary formulations in theoretical neurobiology. The underlying tenets of their argument emerge—in my world—from a Bayesian or variational treatment of perception and self-organized behavior. This is variously known as the free energy principle, active inference, predictive processing, or self-evidencing (Clark, 2013, Friston, 2010; Friston, FitzGerald, Rigoli, Schwartenbeck, & Pezzulo, 2017; Hohwy, 2016). Particular flavors of this formulation have dominated cognitive neuroscience and aspects of philosophy for the past decade. For example, the Bayesian brain hypothesis (Kersten, Mamassian, & Yuille, 2004; Knill & Pouget, 2004) and predictive processing (Barrett & Simmons, 2015; Michael & De Bruin, 2015; Rao & Ballard 1999; Seth, 2013) are now predominant paradigms in cognitive neuroscience. Active inference generalizes this approach to provide an enactive or embodied treatment of action and perception. This resulting treatment bears some remarkable similarities to the ideas reviewed in Kruglanski et al. This commentary tries to establish the formal links between active inference and constructs in cognitive consistency theory in the hope that there may be some useful cross-fertilisation. In what follows, I briefly overview active inference with a special focus on the quantities needed to describe affective responses to new information and then unpack some key dialectics that speak to cognitive consistency, epistemic and motivational value, specific and nonspecific closure, and so on.

In brief, active inference explains everything we perceive and do in terms of one imperative, namely, the minimization of variational free energy (Friston, 2013). Variational free energy is an upper bound on surprise, where surprise (the negative log probability of sensory samples) corresponds to negative Bayesian log evidence. This means that everything we infer (and do) is in the service of minimizing surprise or maximizing the evidence for our internal or generative models of the world. By maximizing the evidence for our models of the world (i.e., selfevidencing), we come to infer hidden or latent states of the world "out there" that generate our sensations. This formulation of "perception as inference" has a long pedigree and was arguably best articulated by Helmholtz (Helmholtz, 1878(Helmholtz, /1971: "Objects are always imagined as being present in the field of vision as would have to be there in order to produce the same impression on the nervous mechanism." Crucially, in active inference, we also have to consider beliefs about action or behavior. These (posterior) beliefs depend upon the degree to which a course of action will minimize expected free energy in the future. The notion of expected free energy, given a particular action, is key here. This follows because expected surprise corresponds to uncertainty. This means that everything we do is in the game of resolving uncertainty or ambiguity about states of affairs "out there," that is, beyond our sensory impressions. These states of affairs are often referred to as hidden or latent states because they cannot be observed directly, only inferred on the basis of observations or sensory evidence.
Technically, free energy can always be expressed as a divergence minus log evidence. This means that minimizing free energy reduces the divergence or difference between our current belief and the true posterior belief (because beliefs cannot change sensory evidence). In other words, our beliefs about states of the world are as close as possible to the true state of affairs, given the sensory evidence at hand. 1 Based on these beliefs, we can then form beliefs about "what to do" by choosing those actions that minimize expected free energy. The important move here is to separate the divergence and evidence parts of free energy and understand what their expected values mean. It turns out that they correspond to epistemic and pragmatic (i.e., motivational) value respectively. This is remarkable because exactly the same separation emerges from the treatment of cognitive consistency, namely, into epistemic and motivational value. Furthermore, these two components appear to underpin nonspecific and specific closure. In other words, the maximization of epistemic value offers a formal description of nonspecific closure, whereas the maximization of motivational (pragmatic) value corresponds to specific closure.
The mathematical form of this separation can be expressed in terms beliefs Q about states of the world and choices or policies, where beliefs about states of the world under a particular policy minimize free energy F, whereas beliefs about policies minimize expected free energy G: Equation 1 provides a detailed description of these mathematical expressions for readers familiar with Bayesian or variational treatments. The variable c is a constant of proportionality that will play an important role later in terms of affective responses to beliefs about action.
Pragmatic value acquires the semantic "motivational" because it is the expected log probability of prior beliefs about outcomes. In other words, if we treat beliefs about the consequences of behavior as prior preferences, then we will choose those behaviors that lead to goals or preferred outcomes. However, this is always in the context of reducing uncertainty (that can be also expressed in terms of ambiguity and risk; see Equation A.1 in the appendix). This is the epistemic part of expected free energy-variously known as Bayesian surprise, information gain, the value of information, intrinsic motivation, and so on (see Equation 1). In summary, the interaction between motivational and epistemic value appears to underpin the deconstruction of cognitive consistency and plays a central role in active inference. Note that pragmatic and epistemic values are log probabilities. This means that there is exactly the same sort of interaction in terms of probabilities per se suggested by Kruglanski et al. (this issue). In other words, our prior preferences contextualize attempts to resolve uncertainty. So how can this formalism used to understand "the affective response to new information" and, more specifically, how does it address "people's reactions to awkward news" (Kruglanski et al., this issue, p. 54)?
The important thing that active inference brings to the table is the distinction between beliefs about states of the world and beliefs about "what I am going to do." Expected free energy is a functional 2 of beliefs about states of the world and therefore determines (posterior) beliefs about "what to do" based on motivational (pragmatic) and epistemic value. So where does the affective bit come in? Generally, people describe affective or hedonic attributes to the beliefs about "what to do," as opposed to the "states of affairs." In particular, a positive valence is associated with precise, confident (low entropy) beliefs about action, and conversely, negative affect is associated with uncertainty and confusion about what to do next (Gu, Hof, Friston, & Fan, 2013;Seth & Friston, 2016). This distinction between beliefs about states and beliefs about action comfortably accommodates the key dialectics in the target article, as follows.

Trivial and Nontrivial Inconsistency
First, it distinguishes between trivial and nontrivial inconsistencies, in the sense that trivial inconsistencies can be associated with belief updates about latent states of the world and nontrivial inconsistencies change beliefs about behavior, "that is, relevant to individuals' goals in the situation" (Kruglanski et al., this issue, p. 54). Furthermore, a separation into beliefs about states and action offer a simple definition of consistency namely, the confidence or precision of beliefs about behavior. In other words, a consistent belief about what to do identifies one course of action unambiguously over all plausible alternatives. Conversely, inconsistency corresponds to an uncertainty about what to do that is generally associated with negative affect and-in the context of interoceptive inference-stress, anxiety, and negative emotion (Peters, McEwen, & Friston, 2017;Seth, 2013;Stephan et al., 2016).
The interesting thing about associating inconsistency with uncertainty about policies to pursue is that inconsistency becomes proportional to the free energy expected under the policies entertained. Mathematically, this can be expressed as follows: This is remarkable because it is exactly the conclusion offered by Kruglanski et al. (this issue), namely, goal-sensitive or deliberative inconsistency is not a universal construct; it is composed of motivational and epistemic components that contextualize one another. Often, these imperatives can be in opposition. Indeed, a ubiquitous pattern of behavior-seen when simulating active inference-is that epistemic imperatives predominate initially, even at the expense of securing preferred outcomes. Only when the context has been explored sufficiently-and its epistemic value has been exhausted-do (synthetic) subjects exploit their epistemic foraging to pursue preferred outcomes Moulin & Souchay 2015).
Note that this construction necessarily implies that we will try to avoid bad news because we are inherently optimistic (Sharot, 2011;Sharot, Guitart-Masip, Korn, Chowdhury, & Dolan, 2012). This optimism is a necessary aspect of ideal Bayesian (active) inference, in which subjects make choices that are most likely given the sort of subject 2 A function of a function; in this case, a function of a probability distribution they are . Because the posterior probability of a choice rests upon prior beliefs, these prior beliefs bias everything we do. Any epistemic foraging (i.e., information seeking) that that leads to highly unlikely outcomes will therefore not be entertained; for example, we do not seek medical information that leads to a course of action that is so unlikely it is not worth contemplating, namely, dying.
Before turning to some of the implications in terms of affective responses to good and bad information, there is one interesting corollary that endorses the arguments in Kruglanski et al. (this issue)-and allows us to showcase the advantages of formal treatments, like active inference. In brief, the constant of proportionality c above itself has a Bayes optimal (free energy minimizing) solution that turns out to be proportional to cognitive consistency [this can be written mathematically as follows by substituting Equation (2) into the update equations in Figure 1]: This is important because this constant of proportionality behaves in a way that has all the hallmarks of dopaminergic responses in real brains . This speaks to the neuromodulatory correlates of affective reactions to changes in cognitive consistency-and shows how formal treatments can link concepts in social psychology to neurobiological processes. In short, it suggests that whenever there is an increase in epistemic or motivational value during active inference, there will be an increase in consistency that will be reported by increases in dopamine activity. See Figure 1 for an example of phasic dopamine responses to epistemic and motivational value. Indeed, there is an emerging literature on the link between dopaminergic activity, in this setting, that may be usefully migrated to social psychology . Although promising, this formulation of consistency-as the impact of new information on confidence about what to do-does not explain our responses to good and bad news (Kruglanski et al., this issue). Or does it?

Affective Responses and Closure
On the preceding arguments, a negative effective response to bad news would imply that new evidence induces posterior beliefs about the state of the world that induce uncertainty about the course of action. This seems sensible: For example, when opening a letter that contains exam results, one would imagine that this epistemic foraging is driven by the epistemic value (i.e., resolution of uncertainty) about your performance and the sort of person you are. If you have failed, under the belief that you are an overachiever, the overall consequences can be summarized as "What on Earth am I to do now?" In short, bad news almost invariably induces uncertainty about how to realize goals or prior Here, we have associated the Bayesian updates of hidden states of the world with perception, control states (policies) with action selection and expected precision with confidence. In this (purely iconic) schematic, we have associated perception (inference about the current state of the world) with the prefrontal cortex, while assigning action selection to the basal ganglia. Precision has been associated with dopaminergic projections from ventral tegmental area and substantia nigra. Lower panel: This shows the results of a simulation in terms of simulated dopamine discharges. The key thing to note is that the responses to an informative cue (CS) pre-empts subsequent responses to the reward (US). In this simulation, the agent was shown a cue that resolved uncertainty (i.e., had epistemic value) about where to find a reward (i.e., that had motivational value) in a simple T-maze (inset).
preferences, whereas good news signifies a clear path forward, either in the short or long term. This seems to be a plausible explanation for our affective responses to new evidence that incorporates both the affective dimension and the interplay between epistemic affordance and prior preferences, both in resolving uncertainty and inducing it in terms of future prospects. There are more nuanced arguments (that entail the opportunity to resolve uncertainty in the future) that can be applied to the interesting phenomena of not wanting to know the end of a book (Kruglanski et al., this issue) or the final score of a football match before it is watched. See Friston, Lin, et al. (2017) for a discussion of novelty and curiosity in this context.

Conclusion
So is there a universal need for cognitive consistency? In the preceding view, one would argue that consistency is not the primary construct: It is an inevitable consequence of forming posterior beliefs about an active engagement with the world that has epistemic and motivational aspects. This dual-aspect construction has the latitude to dissociate (Bayesian) surprise from prior preference [see Equation (1)], providing an accommodating account of pleasant and unpleasant surprises. For example, the state of mind on opening a gift can place motivational and epistemic imperatives in opposition. Both will reduce uncertainty and afford Bayesian surprise (i.e., be informative); however, the outcome (i.e., the gift) may or may not be what you expected (i.e., preferred). Before closing, I wanted to briefly mention other prescient points of contact between active inference and the Kruglanski et al. (this issue) account. It strikes me that "a reluctance to face ambiguity and uncertainty" (Kruglanski et al., this issue, p. 51) fits comfortably within the epistemic value of certain actions-and the overall propensity to minimize surprise (entailed by the free energy principle). The degree to which one person or another expresses a need for nonspecific closure may translate into the degree to which they, a priori, weight epistemic against pragmatic imperatives. This speaks to characterizing phenotypic traits in terms of priors, which is a prominent direction of research in things like computational psychiatry (Huys, Moutoussis, & Williams, 2011;Wang & Krystal, 2014).
I was also taken with the notion of self-verification. This seems to be almost isomorphic to self-evidencing in its broadest sense (Hohwy, 2016). This becomes particularly interesting in relation to understanding certain psychiatric syndromes. For example, the explanation for depression as self-verification or self-evidencing-in the context of prior beliefs about adverse consequences of behavior-fits perfectly with current formulations of depression in terms of false inference (Stephan et al., 2016). In short, "individuals with such low self-esteem (e.g., depressed people) search for and prefer negative feedback consistent with their self-view" (Kruglanski et al.,this issue,p. 51). This reduces uncertainty about their engagement with the (prosocial) world. There are clear metaphors for this in the behavioral psychology literature, for example, learned helplessness (Hammack, Cooper, & Lezak, 2012;Stephan et al., 2016).
In closing, I refer interested readers to Table 1 and Figure 2 for a summary of the similarity between the paradigm in the target article and active inference. Table 1 attempts to map the concepts and terms used in cognitive consistency theory with the corresponding constructs in active inference. The corresponding process theories are sketched out in Figure 2 using the same format as in Kruglanski et al. (this issue). As intimated in the closing comments of Kruglanski et al., these theoretical formulations will only prove themselves in terms of their predictive The precision of beliefs about policies The consequences of Bayesian belief updating on the confidence placed in policies validity. In this regard, there are some interesting paradigms that are emerging from the active inference literature that could be scrutinized from the perspective of social psychology. I have in mind here explicit tests of choice behavior when motivational and epistemic imperatives are set in opposition. One might even imagine the study of the neuronal correlates of belief updating-along the lines of the dopaminergic responses just described .
The expectancy-value model ..
In short, perception and action are subsumed under planning as inference (Attias, 2003;Botvinick & Toussaint, 2012;Toussaint & Storkey, 2006). Formally, this corresponds to inverting or fitting a generative model, given a sequence of outcomes. Technically, this is equivalent to optimizing the expected hidden states, policies, and precision with respect to variational free energy. These (posterior) estimates constitute posterior beliefs, usually denoted by the probability distribution QðxÞ, where x ¼ e s; p; c are the hidden or unknown variables.

Variational Free Energy and Inference
In variational Bayesian inference, model inversion entails minimizing variational free energy with respect to the sufficient statistics (i.e., expectations) of posterior beliefs: