In his target article, Brette criticized the claim that people have a “Bayesian brain.” This term has been widely adopted to describe the nature of the human brain (Friston Reference Friston2012; Knill & Pouget Reference Knill and Pouget2004; Sanborn and Chater Reference Sanborn and Chater2016). Surprisingly, however, there is no agreed-upon definition of the term. Two rather informal definitions have been offered. First, Knill and Pouget (Reference Knill and Pouget2004) describe the “Bayesian coding hypothesis” as follows: “the brain represents sensory information probabilistically, in the form of probability distributions”; second, according to Friston (Reference Friston2012), the “Bayesian brain says that we are trying to infer the causes of our sensations based on a generative model of the world.” Neither of these definitions even mentions Bayesian computations, which, one may expect, should be central to the idea of a Bayesian brain. So, what then, is exactly meant by the “Bayesian brain?”
Any model of Bayesian computation contains at a minimum a set S of known stimuli, a set r of internal responses, and a known generative model P(r|S) of the response generated by each stimulus. Bayes’ theorem is used to invert the generative model to compute a likelihood function that is then combined with a prior P(S) to obtain a posterior distribution. The result can be used to inform a forthcoming action or simply the percept of the observer.
A Bayesian brain must be implementing such Bayesian computations on some level. One can distinguish between two possible views here (Block Reference Block2018). The “as if” view holds that the brain does not necessarily literally have a generative model and does not literally use Bayes’ theorem to derive a likelihood function. Instead, the computations performed by the brain can be seen “as if” it performs these operations. The “realist” view, on the other hand, holds that a generative model, a likelihood function, and a prior are actually represented in the brain and that the computations performed are literally the computations required by Bayes’ theorem. Unfortunately, most authors do not necessarily commit to one or the other interpretation and, in some cases, appear to make different theoretical commitments in different papers.
Importantly, the “as if” view is typically expressed at Marr's “computational level” with no commitment to brain implementation (Griffiths et al. Reference Griffiths, Chater, Norris and Pouget2012). Consequently, using the term “Bayesian brain” in an “as if” sense appears almost contradictory because this usage is explicitly not about what happens in the brain. Thus, if the “Bayesian brain” is really a claim about the brain, then it has to be reserved for the realist view that the brain literally implements the components of Bayesian computation.
Is there evidence for the claim that humans have a Bayesian brain in the realist sense? No direct evidence has been presented to date. Instead, what is usually offered is an indirect argument from behavior. For example, Knill and Pouget (Reference Knill and Pouget2004) motivated the view that brains are Bayesian by “the myriad ways in which human observers behave as optimal Bayesian observers” (p. 712). The problem is that this argument ignores the fact that findings of suboptimality are at least as common as findings of optimality (Rahnev and Denison Reference Rahnev and Denison2018). Even more importantly, Bayesian optimality can be achieved by non-Bayesian algorithms (Ma Reference Ma2012), and thus. such findings do not imply that brain computations are literally Bayesian.
In fact, as Brette eloquently explains, there are many reasons to doubt that brains are literally implementing Bayesian computations. Here, I formalize some of the issues examined by Brette and discuss some additional problems.
First, as pointed out by Brette, the internal response depends on more than just the stimulus of interest. Instead, the internal response to, for example, a tilted bar is better described not as P(r|S) but as P(r|S, Θ), where Θ is a set of variables that affect neural firing, including the color of the bar, the color of the background, the size of the bar, the level of illumination, contrast, attention, arousal, metabolic state, and so forth. Dozens of such “confounding” variables can easily be present in any real-world situation. Inverting this generative model necessitates the integration (i.e., marginalization) over all possible values of all of these variables. For many forms of the assumed internal response, this computation is infeasible in real brains.
Second, as also discussed by Brette, Bayesian computations depend on the existence of a well-defined response r. However, brain activity is a dynamic, recurrent, never-ending string of action potentials. It is unclear how the Bayesian brain isolates “the response” to any given stimulus to perform the necessary Bayesian computations.
Third, an even more insidious problem that Brette did not examine in the context of the Bayesian brain is that a realist Bayesian brain must already know the set S of possible stimuli and the generative model P(r|S) for each stimulus. However, the brain has to first learn both the stimuli in the world and their associated generative models. A truly Bayesian brain would thus form a probability distribution over the stimuli and generative models, which goes against current models that assume the existence of a predefined set S of stimuli.
Finally, a central tenet of the Bayesian brain – that the brain represents and computes with full probability distributions – has only been supported by theoretical proposals of how this could be achieved. Recent empirical research has, however, challenged this tenet (Yeon and Rahnev Reference Yeon and Rahnev2019).
The idea of the “Bayesian brain” has gained popularity perhaps not despite but because of the fact that it has never been clearly defined. This ambiguity shields it from criticism but it also robs it from any chance of contributing to scientific progress. To be useful, the term should be defined according to its plain meaning of a realist view where the brain literally represents the different components of Bayesian computations and researchers should present evidence for it that goes beyond “some behavior is close to optimal.” Until then, the “Bayesian brain” should be seen for what it is: a theoretical possibility fully divorced and shielded from the empirical reality.
In his target article, Brette criticized the claim that people have a “Bayesian brain.” This term has been widely adopted to describe the nature of the human brain (Friston Reference Friston2012; Knill & Pouget Reference Knill and Pouget2004; Sanborn and Chater Reference Sanborn and Chater2016). Surprisingly, however, there is no agreed-upon definition of the term. Two rather informal definitions have been offered. First, Knill and Pouget (Reference Knill and Pouget2004) describe the “Bayesian coding hypothesis” as follows: “the brain represents sensory information probabilistically, in the form of probability distributions”; second, according to Friston (Reference Friston2012), the “Bayesian brain says that we are trying to infer the causes of our sensations based on a generative model of the world.” Neither of these definitions even mentions Bayesian computations, which, one may expect, should be central to the idea of a Bayesian brain. So, what then, is exactly meant by the “Bayesian brain?”
Any model of Bayesian computation contains at a minimum a set S of known stimuli, a set r of internal responses, and a known generative model P(r|S) of the response generated by each stimulus. Bayes’ theorem is used to invert the generative model to compute a likelihood function that is then combined with a prior P(S) to obtain a posterior distribution. The result can be used to inform a forthcoming action or simply the percept of the observer.
A Bayesian brain must be implementing such Bayesian computations on some level. One can distinguish between two possible views here (Block Reference Block2018). The “as if” view holds that the brain does not necessarily literally have a generative model and does not literally use Bayes’ theorem to derive a likelihood function. Instead, the computations performed by the brain can be seen “as if” it performs these operations. The “realist” view, on the other hand, holds that a generative model, a likelihood function, and a prior are actually represented in the brain and that the computations performed are literally the computations required by Bayes’ theorem. Unfortunately, most authors do not necessarily commit to one or the other interpretation and, in some cases, appear to make different theoretical commitments in different papers.
Importantly, the “as if” view is typically expressed at Marr's “computational level” with no commitment to brain implementation (Griffiths et al. Reference Griffiths, Chater, Norris and Pouget2012). Consequently, using the term “Bayesian brain” in an “as if” sense appears almost contradictory because this usage is explicitly not about what happens in the brain. Thus, if the “Bayesian brain” is really a claim about the brain, then it has to be reserved for the realist view that the brain literally implements the components of Bayesian computation.
Is there evidence for the claim that humans have a Bayesian brain in the realist sense? No direct evidence has been presented to date. Instead, what is usually offered is an indirect argument from behavior. For example, Knill and Pouget (Reference Knill and Pouget2004) motivated the view that brains are Bayesian by “the myriad ways in which human observers behave as optimal Bayesian observers” (p. 712). The problem is that this argument ignores the fact that findings of suboptimality are at least as common as findings of optimality (Rahnev and Denison Reference Rahnev and Denison2018). Even more importantly, Bayesian optimality can be achieved by non-Bayesian algorithms (Ma Reference Ma2012), and thus. such findings do not imply that brain computations are literally Bayesian.
In fact, as Brette eloquently explains, there are many reasons to doubt that brains are literally implementing Bayesian computations. Here, I formalize some of the issues examined by Brette and discuss some additional problems.
First, as pointed out by Brette, the internal response depends on more than just the stimulus of interest. Instead, the internal response to, for example, a tilted bar is better described not as P(r|S) but as P(r|S, Θ), where Θ is a set of variables that affect neural firing, including the color of the bar, the color of the background, the size of the bar, the level of illumination, contrast, attention, arousal, metabolic state, and so forth. Dozens of such “confounding” variables can easily be present in any real-world situation. Inverting this generative model necessitates the integration (i.e., marginalization) over all possible values of all of these variables. For many forms of the assumed internal response, this computation is infeasible in real brains.
Second, as also discussed by Brette, Bayesian computations depend on the existence of a well-defined response r. However, brain activity is a dynamic, recurrent, never-ending string of action potentials. It is unclear how the Bayesian brain isolates “the response” to any given stimulus to perform the necessary Bayesian computations.
Third, an even more insidious problem that Brette did not examine in the context of the Bayesian brain is that a realist Bayesian brain must already know the set S of possible stimuli and the generative model P(r|S) for each stimulus. However, the brain has to first learn both the stimuli in the world and their associated generative models. A truly Bayesian brain would thus form a probability distribution over the stimuli and generative models, which goes against current models that assume the existence of a predefined set S of stimuli.
Finally, a central tenet of the Bayesian brain – that the brain represents and computes with full probability distributions – has only been supported by theoretical proposals of how this could be achieved. Recent empirical research has, however, challenged this tenet (Yeon and Rahnev Reference Yeon and Rahnev2019).
The idea of the “Bayesian brain” has gained popularity perhaps not despite but because of the fact that it has never been clearly defined. This ambiguity shields it from criticism but it also robs it from any chance of contributing to scientific progress. To be useful, the term should be defined according to its plain meaning of a realist view where the brain literally represents the different components of Bayesian computations and researchers should present evidence for it that goes beyond “some behavior is close to optimal.” Until then, the “Bayesian brain” should be seen for what it is: a theoretical possibility fully divorced and shielded from the empirical reality.