Really radical?

Abstract

I enjoyed reading this compelling account of Conviction Narrative Theory (CNT). As a theoretical neurobiologist, I recognised – and applauded – the tenets of CNT. My commentary asks whether its claims could be installed into a Bayesian mechanics of decision-making, in a way that would enable theoreticians to model, reproduce and predict decision-making.

Conviction Narrative Theory (CNT) (target article) is both a “theory of narratives” and a “narrative theory” that precludes mathematical or numerical analysis. This commentary reviews the commitments of CNT through the lens of active inference and self-evidencing (Hohwy, 2016), asking whether CNT could lend itself to a formal (Bayesian) treatment.

Box 1 summarises the fundaments of active inference, as it relates to decision-making under uncertainty. With these fundaments, one can simulate the kind of decision-making addressed by CNT. For example, active inference reproduces decision-making under unknowable circumstances (Friston et al., 2016); it dissolves the exploration–exploitation dilemma and provides a principled account of affordances (Schwartenbeck et al., 2019). It can model the spread of ideas (Albarracin, Demekas, Ramstead, & Heins, 2022) and has been applied to cultural niche construction and social norms (Veissiere, Constant, Ramstead, Friston, & Kirmayer, 2019).

Box 1. Active inference

Recent trends in theoretical neurobiology, machine learning and artificial intelligence converge on a single imperative that explains both sense-making and decision-making in self-organising systems, from cells (Friston, Levin, Sengupta, & Pezzulo, 2015) to cultures (Veissiere et al., 2019). This imperative is to maximise the evidence (a.k.a. marginal likelihood) for generative (a.k.a., world) models of how observations are caused. This imperative can be expressed as minimising an evidence bound called variational free energy (Winn & Bishop, 2005) that comprises complexity and accuracy (Ramstead et al., 2022):

$${\rm Free\ energy} = {\rm model\ complexity\,\ndash\, model\ accuracy}$$

Accuracy corresponds to goodness of fit, while complexity scores the divergence between prior beliefs (before seeing outcomes) and posterior beliefs (afterwards). In short, complexity scores the information gain or cost of changing one's mind (in an information theoretic and thermodynamic sense, respectively). This means Bayesian belief updating is about finding an accurate explanation that is minimally complex (c.f., Occam's principle). In an enactive setting – apt for explaining decision-making – beliefs about “which plan to commit to” are based on the free energy expected under a plausible plan. This implicit planning as inference can be expressed as minimising expected free energy (Friston, Daunizeau, Kilner, & Kiebel, 2010):

$${\rm Expected\ free\ energy} = {\rm risk\ }( {{\rm expected\ complexity}} ) {\rm} + {\rm ambiguity\ }( {{\rm expected\ inaccuracy}} ) $$

Risk is the divergence between probabilistic predictions about outcomes, given a plan, relative to prior preferences. Ambiguity is the expected inaccuracy. An alternative decomposition is especially interesting from the perspective of CNT:

$${\rm Expected\ free\ energy} = {\rm expected\ cost\,\ndash\, expected\ information\ gain}$$

The expected information gain underwrites the principles of optimal Bayesian design (Lindley, 1956), while expected cost underwrites Bayesian decision theory (Berger, 2011). However, there is a twist that distinguishes active inference from expected utility theory. In active inference, there is no single, privileged outcome that furnishes a utility or cost function. Rather, utilities are replaced by preferences, quantified by the (log) likelihood of encountering every aspect of an observable outcome. In short, active inference appeals to two kinds of Bayes optimality and subsumes information and preference-seeking behaviour under a single objective.

What prevents CNT from using active inference for simulation, scenario modelling or computational phenotyping (Parr, Rees, & Friston, 2018)? One answer is that the requisite generative models are too complex and difficult to specify. However, there may be some commitments of CNT that could be usefully dismantled, enabling its claims to be substantiated with simulations and implicit proof of principle.

In active inference, narratives feature as prior beliefs. Indeed, the plans – that underwrite policy selection – are often described as narratives (Friston, Rosch, Parr, Price, & Bowman, 2017b). So, could one cast CNT in terms of narrative (i.e., policy) selection and “planning as inference” (Attias, 2003; Botvinick & Toussaint, 2012; Matsumoto & Tani, 2020)? In what follows, five arguments against formalising CNT in this fashion are considered and countered.

1. (1) Radical uncertainty does not admit any Bayesian mechanics because the requisite probabilities do not have a well-defined outcome space.

Radical uncertainty rests upon an unknowable outcome (e.g., John Kay's wheel example). However, outcomes are known quantities that are observed. Technically, radical uncertainty refers to unknowable (i.e., hidden) causes of outcomes. However, finding the right causal explanation just is the problem of Bayesian inference. So what is radical about radical uncertainty? The answer might lie in the hierarchical nature of belief updating and implicit generative models. Given the parameters of a generative model, I can be uncertain about hidden states generating my observations. However, I can also be uncertain about the parameters, given a model. Finally, I can have uncertainty about my model. Radical uncertainty seems to concern the model structure.

Resolving the three kinds of uncertainty above corresponds to inference, learning and model selection, respectively. All entail maximising marginal likelihood or minimising free energy, with respect to posteriors over states, parameters and models, respectively. Model selection is known as structure learning in Radical Constructivism (Salakhutdinov, Tenenbaum, & Torralba, 2013; Tenenbaum, Kemp, Griffiths, & Goodman, 2011; Tervo, Tenenbaum, & Gershman, 2016). Structure learning is a partly solved problem, through Bayesian model reduction (Friston, Parr, & Zeidman, 2018), where redundant components are removed from an overly expressive model to maximise model evidence (e.g., Smith, Schwartenbeck, Parr, & Friston, 2020). This reductive approach complements non-parametric Bayes, which formalises the inclusion of new narratives (Gershman & Blei, 2012). In light of Bayesian model selection, one could argue that radical uncertainty admits a Bayesian mechanics.

1. (2) The utilities of different kinds of outcomes cannot be compared in a meaningful way.

This is only a problem if one subscribes to Bayesian decision theory as a complete account. Active inference vitiates this objection because to be Bayes optimal is to resolve uncertainty in the context of securing preferred outcomes (i.e., minimise expected free energy; see Box 1). Crucially, expected utility and information gain (Howard, 1966; Kamar & Horvitz, 2013; Moulin & Souchay, 2015) share the same currency; namely, natural units (when using natural logarithms of prior preferences). This lends a quantitative and comparable meaning to the value of information and preferences.

1. (3) Certain outcomes are so fuzzy they are impossible to predict and therefore one has to use heuristics.

Knowing something is unpredictable is itself an informative prior that can be installed into hierarchal generative models: c.f., Jaynes' maximum entropy principle (Jaynes, 1957; Kass & Raftery, 1995; Sakthivadivel, 2022). So, how do “fast and frugal” heuristics fit into active inference? Heuristics are generally considered as priors that comply with complexity minimising imperatives (Box 1), for example, habitisation (FitzGerald, Dolan, & Friston, 2014) or the minimisation of perceptual prediction errors (Mansell, 2011). In short, heuristics are exactly what active inference – under hierarchal generative models – is there to explain. On this reading of active inference, self-evidencing just is satisfising (Gerd Gigerenzer, personal communication).

1. (4) But people don't behave as if they were rational, or even with bounded rationality.

Many careful studies in cognitive neuroscience are concerned with how people deviate from Bayes optimality. However, this overlooks the complete class theorem (Brown, 1981; Wald, 1947). The complete class theorem says that for any pair of choice behaviours and cost functions, there are some priors that render the decisions Bayes-optimal. This has the fundamental implication that Bayesian mechanics cannot prescribe optimal (i.e., rational) decision-making. It can only describe rationality in terms of the priors a subject brings to the table. This insight underwrites the emerging field of computational psychiatry, where the game is to estimate the prior beliefs of patients that best explain their decision-making (Schwartenbeck & Friston, 2016; Smith, Khalsa, & Paulus, 2021).

1. (5) But the dimensionality and numerics of belief updating in realistic generative models are beyond the capacity of any computer, human or otherwise.

This argument rests on the use of sampling procedures to approximate posterior distributions, for example, likelihood free methods or approximate Bayesian computation (Chatzilena, van Leeuwen, Ratmann, Baguelin, & Demiris, 2019; Cornish & Littenberg, 2007; Girolami & Calderhead, 2011; Ma, Chen, & Fox, 2015; Silver & Veness, 2010). However, active inference rests on variational schemes found in physics, high-end machine learning (Marino, 2021) and (probably) the brain (Friston, Parr, & de Vries, 2017a). Variational Bayes eschews sampling by committing to a functional form for posterior beliefs; thereby converting an impossible marginalisation problem into an optimisation problem; namely, minimising variational free energy (Feynman, 1972). In summary, some people may think generative models with realistic narratives cannot be inverted; however, they (i.e., these people) are are existence proofs that such models can be inverted.