1. Introduction
It is a pleasure to comment upon Andy Clark's exposition of the Bayesian brain, predictive coding, and the free-energy principle. Clark describes modern thinking about the brain as a constructive and predictive machine in a compelling and accessible way. Furthermore, he develops the fundaments of this approach from basic questions about the nature of life and consciousness – remarkably, without recourse to mathematical equations.
Clark's synthesis is impressive – it highlights the consistency (and convergence) of the underlying ideas from many perspectives, ranging from the psychophysics of perceptual inference through to motor control and embodiment. The key thing that emerges from his treatment is that minimising surprise or surprisal (Tribus Reference Tribus1961) accommodates many intuitions and theories about brain function that have emerged over the past century or so. Had space allowed, other ideas could have been celebrated (developed) within this framework; for example, the principle of efficient coding (Barlow Reference Barlow and Rosenblith1961); the notion of perception as hypothesis testing (Gregory Reference Gregory1980), and the action-perception cycle (Fuster Reference Fuster2001) – all rest on the premise that we build parsimonious models to explain our world (Dayan et al. Reference Dayan, Hinton and Neal1995).
In what follows, I revisit three challenges – highlighted by Clark – to the free-energy principle, and its incarnations like predictive coding and the Bayesian brain. Specifically, these are: (1) the relationship between free-energy minimisation and predictive coding, (2) the dark room problem, and (3) explanatory power.
2. Free-energy and predictive coding
Clark frames surprise minimisation in terms of predictive coding in the Bayesian brain (Mumford Reference Mumford1992; Rao & Ballard Reference Rao and Ballard1999; Yuille & Kersten Reference Yuille and Kersten2006). This works extremely well and is a useful way to introduce the ideas. However, it may detract from a simple but important point: Predictive coding is a consequence of surprise minimisation, not its cause. Free-energy is a mathematical bound on surprise, where prediction error is a measure of free-energy that is easy to compute (neurobiologically). Free-energy minimisation is an instance of the celebrated principle of least action – because the average energy over time is also called action. Furthermore, it entails the maximum entropy principle (Jaynes Reference Jaynes1957) – because free-energy is expected energy minus the entropy of predictions. These principles will be familiar to anyone in physics or statistics because they govern the behaviour of known physical systems. The important thing – for self-organising systems – is that the long-term average of surprise is (almost surely) equal to the entropy of sensations. This means that minimising free-energy minimises sensory entropy. As articulated nicely by Clarke, we can minimise free-energy (prediction errors) by either changing our predictions (perception) or changing the things that we predict (action). The key thing that the free-energy principle brings to the table is that both perception and action minimise prediction error but only action minimises surprise (because surprise is an attribute of sensations actively sampled). This is active inference (Friston Reference Friston2010). The imperative to minimise surprise rests on the need to resist a natural tendency to disorder – to minimise sensory entropy (Ashby Reference Ashby1947). The Bayesian brain and predictive coding are then seen as a consequence of, or requirement for, this fundamental imperative – not as a causal explanation for how our brains work. This is important, because any evidence that suggests we are Bayes-optimal can be taken as evidence for active inference.
3. The dark room problem
Clark introduces and then (almost) dismisses the dark room problem by appeal to itinerant (exploratory) behaviours that minimise surprise over long periods of time (that is, minimise sensory entropy). I think that his discussion is exactly right; however, the “grain of truth” in the dark room problem can be dismissed in an even simpler way – by noting that predication errors are only defined in relation to predictions. For example, when we enter a dark room, the first thing we do is switch on a light. This is because we expect the room to be brightly lit (or more exactly, we expect our bodily movements to bring this about). In other words, the state of a room being dark is surprising because we do not expect to occupy dark rooms. This surprise depends upon (prior) expectations, but where do these prior beliefs come from? They come from evolution and experience, in the sense that if we did not have these prior beliefs, we would be drawn to dark rooms and die there. In short, a dynamic world can only support a generative model of that world (prior beliefs) that predicts the dynamics it encounters – predictions that action fulfils.
4. Evidence and explanatory power
Clark questions the evidence for surprise minimisation and its explanatory power. I am more complacent about this issue, because the free-energy formulation explains so much already. Potent examples rest on appreciating that an agent does not have a model of its world – it is a model. In other words, the form, structure, and states of our embodied brains do not contain a model of the sensorium – they are that model. This allows one to equate the long-term minimisation of surprise with the entropy of our physical (sensory) states – and explains our curious (biological) ability to resist the second law of thermodynamics (Ashby Reference Ashby1947). But what does this mean practically? It means that every aspect of our brain can be predicted from our environment. This seems a powerful explanation for neuroanatomy and neurophysiology. A nice example is the anatomical division into what and where pathways in visual cortex (Ungerleider & Mishkin Reference Ungerleider, Mishkin, Ingle, Goodale and Mansfield1982). Could this have been predicted from the free-energy principle? Yes – if anatomical structure in the brain recapitulates causal structure in the environment, then one would expect independent causes to be encoded in functionally segregated neuronal structures. Given that objects can be in different places, they possess separable attributes of “what” and “where.” This translates into separate neuronal representations in segregated visual pathways. In summary, the evidence for the free-energy principle may not necessarily be in next month's scientific journals but may lie in the accumulated wealth of empirical neurobiological knowledge that Andy Clark has unpacked for us.
1. Introduction
It is a pleasure to comment upon Andy Clark's exposition of the Bayesian brain, predictive coding, and the free-energy principle. Clark describes modern thinking about the brain as a constructive and predictive machine in a compelling and accessible way. Furthermore, he develops the fundaments of this approach from basic questions about the nature of life and consciousness – remarkably, without recourse to mathematical equations.
Clark's synthesis is impressive – it highlights the consistency (and convergence) of the underlying ideas from many perspectives, ranging from the psychophysics of perceptual inference through to motor control and embodiment. The key thing that emerges from his treatment is that minimising surprise or surprisal (Tribus Reference Tribus1961) accommodates many intuitions and theories about brain function that have emerged over the past century or so. Had space allowed, other ideas could have been celebrated (developed) within this framework; for example, the principle of efficient coding (Barlow Reference Barlow and Rosenblith1961); the notion of perception as hypothesis testing (Gregory Reference Gregory1980), and the action-perception cycle (Fuster Reference Fuster2001) – all rest on the premise that we build parsimonious models to explain our world (Dayan et al. Reference Dayan, Hinton and Neal1995).
In what follows, I revisit three challenges – highlighted by Clark – to the free-energy principle, and its incarnations like predictive coding and the Bayesian brain. Specifically, these are: (1) the relationship between free-energy minimisation and predictive coding, (2) the dark room problem, and (3) explanatory power.
2. Free-energy and predictive coding
Clark frames surprise minimisation in terms of predictive coding in the Bayesian brain (Mumford Reference Mumford1992; Rao & Ballard Reference Rao and Ballard1999; Yuille & Kersten Reference Yuille and Kersten2006). This works extremely well and is a useful way to introduce the ideas. However, it may detract from a simple but important point: Predictive coding is a consequence of surprise minimisation, not its cause. Free-energy is a mathematical bound on surprise, where prediction error is a measure of free-energy that is easy to compute (neurobiologically). Free-energy minimisation is an instance of the celebrated principle of least action – because the average energy over time is also called action. Furthermore, it entails the maximum entropy principle (Jaynes Reference Jaynes1957) – because free-energy is expected energy minus the entropy of predictions. These principles will be familiar to anyone in physics or statistics because they govern the behaviour of known physical systems. The important thing – for self-organising systems – is that the long-term average of surprise is (almost surely) equal to the entropy of sensations. This means that minimising free-energy minimises sensory entropy. As articulated nicely by Clarke, we can minimise free-energy (prediction errors) by either changing our predictions (perception) or changing the things that we predict (action). The key thing that the free-energy principle brings to the table is that both perception and action minimise prediction error but only action minimises surprise (because surprise is an attribute of sensations actively sampled). This is active inference (Friston Reference Friston2010). The imperative to minimise surprise rests on the need to resist a natural tendency to disorder – to minimise sensory entropy (Ashby Reference Ashby1947). The Bayesian brain and predictive coding are then seen as a consequence of, or requirement for, this fundamental imperative – not as a causal explanation for how our brains work. This is important, because any evidence that suggests we are Bayes-optimal can be taken as evidence for active inference.
3. The dark room problem
Clark introduces and then (almost) dismisses the dark room problem by appeal to itinerant (exploratory) behaviours that minimise surprise over long periods of time (that is, minimise sensory entropy). I think that his discussion is exactly right; however, the “grain of truth” in the dark room problem can be dismissed in an even simpler way – by noting that predication errors are only defined in relation to predictions. For example, when we enter a dark room, the first thing we do is switch on a light. This is because we expect the room to be brightly lit (or more exactly, we expect our bodily movements to bring this about). In other words, the state of a room being dark is surprising because we do not expect to occupy dark rooms. This surprise depends upon (prior) expectations, but where do these prior beliefs come from? They come from evolution and experience, in the sense that if we did not have these prior beliefs, we would be drawn to dark rooms and die there. In short, a dynamic world can only support a generative model of that world (prior beliefs) that predicts the dynamics it encounters – predictions that action fulfils.
4. Evidence and explanatory power
Clark questions the evidence for surprise minimisation and its explanatory power. I am more complacent about this issue, because the free-energy formulation explains so much already. Potent examples rest on appreciating that an agent does not have a model of its world – it is a model. In other words, the form, structure, and states of our embodied brains do not contain a model of the sensorium – they are that model. This allows one to equate the long-term minimisation of surprise with the entropy of our physical (sensory) states – and explains our curious (biological) ability to resist the second law of thermodynamics (Ashby Reference Ashby1947). But what does this mean practically? It means that every aspect of our brain can be predicted from our environment. This seems a powerful explanation for neuroanatomy and neurophysiology. A nice example is the anatomical division into what and where pathways in visual cortex (Ungerleider & Mishkin Reference Ungerleider, Mishkin, Ingle, Goodale and Mansfield1982). Could this have been predicted from the free-energy principle? Yes – if anatomical structure in the brain recapitulates causal structure in the environment, then one would expect independent causes to be encoded in functionally segregated neuronal structures. Given that objects can be in different places, they possess separable attributes of “what” and “where.” This translates into separate neuronal representations in segregated visual pathways. In summary, the evidence for the free-energy principle may not necessarily be in next month's scientific journals but may lie in the accumulated wealth of empirical neurobiological knowledge that Andy Clark has unpacked for us.