The free-energy principle subsumes the Bayesian brain hypothesis[6] (cf. Friston 2009, p. 294). According to this view, processing in the brain can usefully be described as Bayesian inference. This means that the brain implements a probabilistic model that is updated in light of sensory signals using Bayes’ theorem. More specifically, the brain combines prior knowledge about hidden causes in the world with a measurement of likelihood describing how probable the observed (sensory) evidence is, given various possible hidden causes. The result is a distribution (posterior) that describes how probable various possible causes are, given the obtained evidence. The process of determining the posterior is often called model inversion. In FEP, this type of inference is approximated using variational Bayes, which establishes the connection to predictive processing (cf. footnote 2 above). FEP can thus either be seen as a particular instance of the Bayesian brain hypothesis, or as a generalization.
As mentioned above, it is often pointed out that perceptions in PP are analogous to scientific hypotheses. The Bayesian brain is thus a hypothesis-testing brain (this analogy is also referred to in titles of papers by Jakob Hohwy, see Hohwy 2010, 2012). Thanks to active inference, the Bayesian brain performs an active kind of hypothesis testing. The three types of active inference distinguished by Seth assign a role to both confirmation and disconfirmation (falsification). This dual role of active inference is also emphasized by (Friston et al. 2012, p. 19):
The resulting active or embodied inference means that not only can we regard perception as hypotheses, but we could regard action as performing experiments that confirm or disconfirm those hypotheses.
Further exploration of the analogy to theory of science reveals a puzzle: as we will see, doubts can be raised regarding the idea that a theory gains merit when it is confirmed (or even regarding the very notion of theory confirmation). Does this mean that the Bayesian brain generates hypotheses in an unscientific way?
According to Popper, science advances mainly by seeking falsifying evidence. In fact, falsifiability is Popper’s proposed solution to the demarcation problem, i.e., the problem of specifying the difference between science and pseudo-science. Scientific theories posit universal propositions (scientific laws) that can never be proven in a strict sense, because only finite observations can be made. The next observation could, in principle, always disconfirm a universal empirical hypothesis. Hence, being verifiable cannot be a criterion for being scientific, because theories cannot be empirically verified (cf. Popper 2005[1934], pp. 16-17.). Conversely, it is possible to falsify a universal statement using a single empirical proposition:
Diese Überlegungen legen den Gedanken nahe, als Abgrenzungskriterium nicht die Verifizierbarkeit, sondern die Falsifizierbarkeit des Systems vorzuschlagen; […] Ein empirisch-wissenschaftliches System muß an der Erfahrung scheitern können. (Popper 2005[1934], p. 17)[7]
Scientific theories thus cannot, according to Popper, be verified, but only falsified. However, when attempts to falsify a hypothesis have failed, we can say that the theory has been corroborated—which still means that the theory could be falsified in the future (cf. Popper 2005[1934], ch. X).
How can we apply these ideas to predictive processing? First, we have to find an analogon to scientific theories. I suggest that models can be treated analogously to theories, because in PP, predictions or hypotheses are derived from models and then compared to bottom-up signals. This also fits the way in which Seth describes the starfish example (namely in terms of model selection). What does it mean that a model is falsified in PP?
The question is not a trivial one, as there seems to be a crucial disanalogy between hypothesis-testing in Popper’s sense and hypothesis-testing in the Bayesian brain. The reason why scientific theories are falsifiable is that they allow deriving hypotheses deductively. This means if a hypothesis is falsified, the theory is falsified as well. By contrast, hypotheses in the Bayesian brain are not deductively entailed by the models from which they are derived: the relation between model and hypothesis is probabilistic (the hypothesis is more or less probable, given the model). Hence, when a hypothesis or prediction elicits a large prediction error, this does not falsify the model; rather, it calls for an update to the effect that the model becomes less likely. Furthermore, according to Popper, it does not make sense to say that such hypotheses are corroborated to a greater or lesser extent. For being corroborated means that attempts at falsification have failed. But if it is in principle impossible to falsify a hypothesis, then saying that it has been corroborated becomes empty—worse, such hypotheses are not even scientific hypotheses (cf. Popper 2005[1934], pp. 248-249.). This, then, constitutes the puzzle mentioned above: if hypotheses in PP are not falsifiable, does this mean the Bayesian brain is unscientific?
This conclusion—that no useful analogy to Popper’s theory of science can be drawn—rests on a naïve understanding of falsification (as emphasized by Imre Lakatos, cf. Lakatos 1970).[8] A closer look at the notion of falsification reveals that the analogy can be upheld. Furthermore, it helps us gain a better grasp of the notion of falsification in the context of PP.
First of all, we can note that in actual scientific practice, it is not the case that scientists attempt to falsify an isolated, single hypothesis—and then try to come up with a new theory when the hypothesis has been falsified. Rather, scientists often operate with different versions of a theory at the same time, or seek to find the best parameters for a model. The outcomes of an empirical study are then used to eliminate some of the different theories or parameter ranges. This has already been acknowledged by Popper (cf. 2005[1934], p. 63., fn. 10). As Thomas Nickles puts it:
According to Popper, at any time there may be several competing theories being proposed and subsequently refuted by failed empirical tests—rather like balloons being launched and then shot down, one by one. (2014)
The result of this falsification procedure is that some of the competing theories are eliminated. This can already be seen as a slight departure from what Imre Lakatos calls naïve falsificationism: for the elimination may be based on a comparison, not on an isolated falsification procedure. If some of the theories are in some sense better than the others (for instance, by making more empirical predictions, or by being less complex), then they can be preferred without having independent reasons to reject the eliminated theories. However, Popper’s falsificationism is even more sophisticated.
Popper noted that there were no theory-neutral empirical propositions. Descriptions of empirical facts are not immediately given, they are based on observations and involve interpretations (cf. Popper 2005[1934], p. 84, fn. 32). This means it is always possible to add auxiliary hypotheses to a theory, and thereby make the theory compatible with seemingly falsifying evidence. As a consequence, when it comes to determining whether a theory is scientific or not, we cannot consider an isolated theory, but must assume a diachronic stance, in which we consider how a theory is modified in the light of new evidence. Such modifications (e.g., auxiliary hypotheses) increase the empirical content of the theory (cf. Lakatos 1970, p. 183). As Popper puts it:
Bezüglich der Hilfshypothesen setzen wir fest, nur solche als befriedigend zuzulassen, durch deren Einführung der ‘Falsifizierungsgrad’ des Systems […] nicht herabgesetzt, sondern gesteigert wird; in diesem Fall bedeutet die Einführung der Hypothese eine Verbesserung: Das System verbietet mehr als vorher.[9] (Popper 2005[1934], p. 58)
When confronted with evidence that contradicts predictions, we are thus never forced to reject the theory from which the prediction has been derived. We may always modify the theory. But this modification must not be ad hoc. Auxiliary hypotheses that only make the theory compatible with the evidence, without having any additional value (without allowing new predictions), are not scientific.
Lakatos (1970) emphasizes that this entails a refined notion of falsificationism. He calls this sophisticated falsificationism (or sophisticated methodological falsificationism). A theory can only be falsified in this “sophisticated” manner when it has been replaced by a theory that:
has more empirical content (makes new predictions), and
makes at least one prediction that is empirically corroborated (cf. Lakatos 1970, pp. 183-184.).
Popper’s sophisticated falsificationism[10] can more easily be applied to predictive processing, because it does not require that we reject a model whenever its predictions yield large prediction errors. Instead, the model can be updated to achieve a better fit with the data. Furthermore, we find a counterpart for the insight that there are no theory-neutral observations: bottom-up signals are never treated as raw data, but as being (more or less) noisy. Hence, prediction errors are weighted by expected precisions. When the expected precision is extremely low, prediction errors will be attenuated. A low expected precision can thus be seen as analogous to an auxiliary hypothesis that makes the model compatible with otherwise contradicting evidence. What is more, it is not an ad hoc move, because the precision estimate itself is also constantly being updated in light of the evidence. Similarly, when a model generates a significant amount of prediction error, but is strongly supported by a higher-level model with high prior probability, a relatively high amount of prediction error may not lead to a major revision of the model.
Model competition in PP can also be seen as an instance of sophisticated falsificationism. Competition need not be resolved by eliminating those models that yield the largest prediction errors (as in the starfish robot). Instead, it may be that some models make more specific counterfactual predictions. Indeed, this seems to be the main rationale behind active inference in FEP.
According to the formalization provided in Friston et al. (2012, p. 4), active inference involves minimizing the entropy of a counterfactual density. This density links future internal states and hidden controls to hidden states, which cause sensory states; hidden controls are hidden states that can be changed by action (Friston et al. 2012, p. 3). A density has low entropy, roughly, if it assigns high values to a relatively small subset of states, and low values to most other sets of states. Predictions based on a probability density with very low entropy can thus be made with a high level of confidence, because most other possibilities are more or less ruled out (due to the low values assigned to them by the density). Formally, this is reflected in the proposition that the negative entropy of the counterfactual density is a monotonic function of the precision of counterfactual beliefs (Friston et al. 2012, p. 4).
The entropy of the counterfactual density is minimized with respect to hidden controls. In effect, this is a selection process, in which a model (here: a counterfactual density) is selected that has minimal entropy. The other models are eliminated, because they have higher entropies. We can say they are falsified in the sense of sophisticated falsificationism (but not in the sense of naïve falsificationism).
Another way in which model competition can be resolved without naïve falsification can be illustrated by the famous “wet lawn” example (cf. Pearl 1988). Suppose you enter your garden and find that the lawn is wet. There are at least two models that can explain this: either your sprinkler has been on during the night or it has rained. Let us assume that both models are initially equally likely (i.e., they have the same prior probability). When you now observe that your neighbor’s garden is also wet, the rain model is corroborated, because it makes the strong prediction that the neighbor’s lawn is wet (i.e., the conditional probability that the neighbor’s lawn is wet, given that it has rained, is high). The other model is not incompatible with this evidence, but it is not supported by it as much (because the conditional probability that the neighbor’s lawn is wet, given that your sprinkler has been on, is not as high). In other words, it has been explained away. As Jakob Hohwy puts it:
The Rain model accounts for all the evidence leaving no evidence behind for the Sprinkler model to explain. Even though the Sprinkler model did increase its probability in the light of the first observation, it seems intuitive right to say that its probability is now returned to near its prior value. The model has been explained away. (2010, p. 137)
Explaining away is another example of sophisticated falsification. Even when two or more models are compatible with the evidence (and with each other), there can be reason to prefer one of them and reject the others.
The clarification in this section should have shown that there is more to falsification than just “disconfirming” a hypothesis, and that competition between models can be resolved in different ways, not only in the way exemplified by the starfish robot. Furthermore, different types of sophisticated falsificationism are part and parcel of predictive processing.
Does this mean that the Bayesian brain is Popperian? This conclusion would be premature. The above can at best show that there are many situations in which the Bayesian brain is a sophisticated falsificationist. But there may be situations in which not even sophisticated falsification is possible or necessary. In the following section, I will argue that predictive processing also has Kuhnian aspects.
According to Kuhn, scientific research develops in different recurring phases. Most of the time, scientists work within an established paradigm, in which implications of theories are explored and puzzles are solved (cf. Kuhn 1962, ch. IV). In this phase, falsification or confirmation do not play a role:
Normal science does and must continually strive to bring theory and fact into closer agreement, and that activity can easily be seen as testing or as a search for confirmation or falsification. Instead, its object is to solve a puzzle for whose very existence the validity of the paradigm must be assumed. Failure to achieve a solution discredits only the scientist and not the theory. (cf. Kuhn 1962, p. 80)
At some stage, however, there will be anomalies, i.e., empirical observations that cannot be explained within the current paradigm. When these anomalies accumulate, scientists will try to explore new concepts and methods. If, using new concepts and methods, previously unexplainable anomalies can be accounted for, a scientific revolution can result, through which a new paradigm is established. Kuhn shares the sophisticated falsificationist’s insight that theories are never rejected in isolation:
[…] the act of judgment that leads scientists to reject a previously accepted theory is always based upon more than a comparison of that theory with the world. The decision to reject one paradigm is always simultaneously the decision to accept another, and the judgment leading to that decision involves the comparison of both paradigms with nature and with each other. (cf. Kuhn 1962, p. 77)
This shows that Kuhn’s theory is in some respects in line with sophisticated falsificationism—but he goes beyond it, in that he doubts that a paradigm that has been adopted instead of another is always better or closer to the truth. The reason for this is that he claims competing paradigms to be incommensurable (cf. also Feyerabend 1962), which means that they typically use radically different concepts and methods (cf. Oberheim & Hoyningen-Huene 2013, §1). A new paradigm that becomes dominant is thus not marked by being closer to the truth, but mainly by constituting a departure from the old paradigm (cf. Kuhn 1962, pp. 170-171). This seems to entail that scientific progress need not be a process in which theories approximate the truth to an ever higher degree.
Can we find an analogon for such a transition from one paradigm to the other in predictive processing? Above, we saw that the sophisticated falsificationist assumes that scientific progress happens only when a theory makes new predictions, and thereby leads to the discovery of new states of affairs. This need not always be the case in the Bayesian brain. When a model is changed to minimize free-energy, this does not mean that the empirical content or predictive power has been increased. A particularly clear example of this can be found in perceptual phenomena like binocular rivalry.
In binocular rivalry (cf. Blake & Logothetis 2002), subjects are presented with two different images, one to the left eye, the other to the right eye, e.g., a face and a house. According to a predictive coding account put forward by Jakob Hohwy, Andreas Roepstorff & Karl Friston (2008), the brain generates two main competing models of what the stimuli depict, one corresponding to the face, the other corresponding to the house. However, only one of these models is consciously experienced at any given time (although there can be intermittent phases in which subjects report seeing a mixture of both stimuli, i.e., parts of the house and parts of the face at the same time, but usually non-overlapping). This means that the brain will tend to settle into one of two classes of states (one corresponding to perceiving the house, the other to perceiving the face). Since each of the models can only account for part of the visual input, both cause a significant amount of prediction error (cf. Hohwy et al. 2008, p. 691). Over time, the prior probability of the currently assumed model (house or face, respectively) will decrease, leading to a revision of the hypothesis, until the brain settles into a state corresponding to the other percept, at least temporarily (cf. Hohwy et al. 2008, pp. 692–694).[11] The crucial difference between this and cases like the wet lawn example or model selection in the starfish robot is that neither of the two competing models is in any sense better than the other (in terms of empirical content, simplicity, predictive power, etc.).
We can recast binocular rivalry in terms of Kuhnian paradigm changes. If we liken each of the two models (house/face) to a paradigm, we can say that perceiving a single object in binocular rivalry corresponds to the phase of normal science, in which many phenomena (inputs) can be explained. After some time, however, there are anomalies (increasing prediction error), which leads to a scientific crisis in which new directions are explored (intermittent phase in which no unified percept is generated), until a new form of scientific practice becomes dominant (scientific revolution), and a new phase of normal science (temporarily stable perception) is reached. The transition from one percept to the other does not go along with increased veridicality: neither of the two percepts is closer to the truth than the other.[12] This may also support the cybernetic idea that internal models are used in the pursuit of homeostasis, not to approximate the truth (as also noted by Seth this collection, p. 15).
There is another analogy between the Bayesian brain and Kuhn’s theory of science. According to Kuhn, it is indeterminate whether an anomaly (an unexpected experimental result, for instance) is something that should be regarded as just another puzzle or as a reason to reject the whole paradigm:
Excepting those that are exclusively instrumental, every problem that normal science sees as a puzzle can be seen, from another viewpoint, as a counterinstance and thus as a source of crisis. (Kuhn 1962, p. 79)
If it is treated as a puzzle, it yields questions like: how can we account for this phenomenon within our established framework? If it is treated as a counterinstance, a more fundamental solution is needed. This is analogous to the fact that whether two models in predictive processing are compatible or not depends on (hyper)priors (cf. FitzGerald et al. 2014, p. 2). When a hyper-prior has it that two models are incompatible, this can either lead to a competition, in which one of the models is eliminated, or it can lead to a revision of the hyper-prior. (Which of the two possibilities corresponds more to puzzle solving, and which to something more fundamental will depend on whether the lower-level models or the high-level prior initially have a higher probability.) This is illustrated by the RHI (rubber hand illusion).
In the RHI (Botvinick & Cohen 1998), the brain harbors two contradictory sensory models. According to the visual model, tactile stimulation occurs on the surface of the rubber hand. According to the proprioceptive model, the felt strokes occur at a different location (i.e., where the real hand is located). While there is, in and of itself, no contradiction between these models, it is likely that the brain has a prior that favors common-cause explanations of sensory signals. Relative to this prior, there is a tension between the models: they seem to indicate that the seen stroking and the felt touch occur at distinct locations, which is odd, because they occur synchronously (and the prior has it that synchronous effects have a common cause, which speaks against two distinct locations). As Jakob Hohwy puts it:
[...] we have a strong expectation that there is a common cause when inputs co-occur in time. This makes the binding hypothesis of the rubber hand scenario a better explainer, and its higher likelihood promotes it to determine perceptual inference and thereby resolve the ambiguity. (2013, p. 105)
Notice that the common-cause hypothesis (that the touch is felt where it is seen) only becomes the dominating hypothesis because the design of the study prevents subjects from confirming the distinct-causes hypothesis (e.g., by looking at their real hands). Because of the common-cause hypothesis, there is an ambiguity in the percepts. This ambiguity can be resolved in at least two ways: either by adjusting the lower-level (perceptual) models (to the effect that the felt touch occurs at the same location as the seen stroking); or by active inference (which in this case would lead to a rejection of the higher-level model corresponding to the common-cause hypothesis). The first way corresponds to puzzle solving, the second more closely to a paradigm change. Note that the analogy will be the stronger the more remote the hyper-prior is from the perceptual models.
I hope to have shown that the Bayesian brain has aspects that make it Popperian, as well as aspects that make it Kuhnian. At the very least, it should have become clear that falsification is a more complex concept than depicted in Seth’s target paper (which seems to tend towards a more naïve form of falsificationism).