Some thoughts on writing ‘Bayes Glaze’ theoretical papers.

[This was a twitter navel-gazing thread someone ‘unrolled’. I was really surprised that it read basically like a blog post, so I thought why not post it here directly! I’ve made a few edits for readability. So consider this an experiment in micro-blogging ….]

In the past few years, I’ve started and stopped a paper on metacognition, self-inference, and expected precision about a dozen times. I just feel conflicted about the nature of these papers and want to make a very circumspect argument without too much hype. As many of you frequently note, we have way too many ‘Bayes glaze’ review papers in glam mags making a bunch of claims for which there is no clear relationship to data or actual computational mechanisms.

It has gotten so bad, I sometimes see papers or talks where it feels like they took totally unrelated concepts and plastered “prediction” or “prediction error” in random places. This is unfortunate, and it’s largely driven by the fact that these shallow reviews generate a bonkers amount of citations. It is a land rush to publish the same story over and over again just changing the topic labels, planting a flag in an area and then publishing some quasi-related empirical stuff. I know people are excited about predictive processing, and I totally share that. And there is really excellent theoretical work being done, and I guess flag planting in some cases is not totally indefensible for early career researchers. But there is also a lot of cynical stuff, and I worry that this speaks so much more loudly than the good, careful stuff. The danger here is that we’re going to cause a blowback and be ultimately seen as ‘cargo cult computationalists’, which will drag all of our research down both good and otherwise.

In the past my theoretical papers in this area have been super dense and frankly a bit confusing in some aspects. I just wanted to try and really, really do due-diligence and not overstate my case. But I do have some very specific theoretical proposals that I think are unique. I’m not sure why i’m sharing all this, but I think because it is always useful to remind people that we feel imposter syndrome and conflict at all career levels. And I want to try and be more transparent in my own thinking – I feel that the earlier I get feedback the better. And these papers have been living in my head like demons, simultaneously too ashamed to be written and jealous at everyone else getting on with their sexy high impact review papers.

Specifically, I have some fairly straightforward ideas about how interoception and neural gain (precision) inter-relate, and also have a model i’ve been working on for years about how metacognition relates to expected precision. If you’ve seen any of my recent talks, you get the gist of these ideas.

Now, I’m *really* going to force myself to finally write these. I don’t really care where they are published, it doesn’t need to be a glamour review journal (as many have suggested I should aim for). Although at my career stage, I guess that is the thing to do. I think I will probably preprint them on my blog, or at least muse openly about them here, although i’m not sure if this is a great idea for theoretical work.

Further, I will try and hold to three key promises:

  1. Keep it simple. One key hypothesis/proposal per paper. Nothing grandiose.
  2. Specific, falsifiable predictions about behavioral & neurophysiological phenomenon, with no (minimal?) hand-waving
  3. Consider alternative models/views – it really gets my goat when someone slaps ‘prediction error’ on their otherwise straightforward story and then acts like it’s the only game in town. ‘Predictive processing’ tells you almost *nothing* about specific computational architectures, neurobiological mechanisms, or general process theories. I’ve said this until i’m blue in the face: there can be many, many competing models of any phenomenon, all of which utilize prediction errors.

These papers *won’t* be explicitly computational – although we have that work under preparation as well – but will just try to make a single key point that I want to build on. If I achieve my other three aims, it should be reasonably straight-forward to build computational models from these papers.

That is the idea. Now I need to go lock myself in a cabin-in-the-woods for a few weeks and finally get these papers off my plate. Otherwise these Bayesian demons are just gonna keep screaming.

So, where to submit? Don’t say Frontiers…

Predictive coding and how the dynamical Bayesian brain achieves specialization and integration

Authors note: this marks the first in a new series of journal-entry style posts in which I write freely about things I like to think about. The style is meant to be informal and off the cuff, building towards a sort of socratic dialogue. Please feel free to argue or debate any point you like. These are meant to serve as exercises in writing and thinking,  to improve the quality of both and lay groundwork for future papers. 

My wife Francesca and I are spending the winter holidays vacationing in the north Italian countryside with her family. Today in our free time our discussions turned to how predictive coding and generative models can accomplish the multimodal perception that characterizes the brain. To this end Francesca asked a question we found particularly thought provoking: if the brain at all levels is only communicating forward what is not predicted (prediction error), how can you explain the functional specialization that characterizes the different senses? For example, if each sensory hierarchy is only communicating prediction errors, what explains their unique specialization in terms of e.g. the frequency, intensity, or quality of sensory inputs? Put another way, how can the different sensations be represented, if the entire brain is only communicating in one format?

We found this quite interesting, as it seems straightforward and yet the answer lies at the very basis of predictive coding schemes. To arrive at an answer we first had to lay a little groundwork in terms of information theory and basic neurobiology. What follows is a grossly oversimplified account of the basic neurobiology of perception, which serves only as a kind of philosopher’s toy example to consider the question. Please feel free to correct any gross misunderstandings.

To begin, it is clear at least according to Shannon’s theory of information, that any sensory property can be encoded in a simple system of ones and zeros (or nerve impulses). Frequency, time, intensity, and so on can all be re-described in terms of a simplistic encoding scheme. If this were not the case then modern television wouldn’t work. Second, each sensory hierarchy presumably  begins with a sensory effector, which directly transduces physical fluctuations into a neuronal code. For example, in the auditory hierarchy the cochlea contains small hairs that vibrate only to a particular frequency of sound wave. This vibration, through a complex neuro-mechanic relay, results in a tonitopic depolarization of first order neurons in the spiral ganglion.

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The human cochlea, a fascinating neural-mechanic apparatus to directly transduce air vibrations into neural representations.

It is here at the first-order neuron where the hierarchy presumably begins, and also where functional specialization becomes possible. It seems to us that predictive coding should say that the first neuron is simply predicting a particular pattern of inputs, which correspond directly to an expected external physical property. To try and give a toy example, say we present the brain with a series of tones, which reliably increase in frequency at 1 Hz intervals. At the lowest level the neuron will fire at a constant rate if the frequency at interval n is 1 greater than the previous interval, and will fire more or less if the frequency is greater or less than this basic expectation, creating a positive or negative prediction error (remember that the neuron should only alter its firing pattern if something unexpected happens). Since frequency here is being signaled directly by the mechanical vibration of the cochlear hairs; the first order neuron is simply predicting which frequency will be signaled. More realistically, each sensory neuron is probably only predicting whether or not a particular frequency will be signaled – we know from neurobiology that low-level neurons are basically tuned to a particular sensory feature, whereas higher level neurons encode receptive fields across multiple neurons or features. All this is to say that the first-order neuron is specialized for frequency because all it can predict is frequency; the only afferent input is the direct result of sensory transduction. The point here is that specialization in each sensory system arises in virtue of the fact that the inputs correspond directly to a physical property.

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Presumably, first order neurons predict the presence or absence of a particular, specialized sensory feature owing to their input. Credit: wikipedia.

Now, as one ascends higher in the hierarchy, each subsequent level is predicting the activity of the previous. The first-order neuron predicts whether a given frequency is presented, the second perhaps predicts if a receptive field is activated across several similarly tuned neurons, the third predicts a particular temporal pattern across multiple receptive fields, and so on. Each subsequent level is predicting a “hyperprior” encoding a higher order feature of the previous level. Eventually we get to a level where the prediction is no longer bound to a single sensory domain, but instead has to do with complex, non-linear interactions between multiple features. A parietal neuron thus might predict that an object in the world is a bird if it sings at a particular frequency and has a particular bodily shape.

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The motif of hierarchical message passing which encompasses the nervous system, according the the Free Energy principle.

If this general scheme is correct, then according to hierarchical predictive coding functional specialization primarily arises in virtue of the fact that at the lowest level each hierarchy is receiving inputs that strictly correspond to a particular feature. The cochlea is picking up fluctuations in air vibration (sound), the retina is picking up fluctuations in light frequency (light), and the skin is picking up changes in thermal amplitude and tactile frequency (touch). The specialization of each system is due to the fact that each is attempting to predict higher and higher order properties of those low-level inputs, which are by definition particular to a given sensory domain. Any further specialization in the hierarchy must then arise from the fact that higher levels of the brain predict inputs from multiple sensory systems – we might find multimodal object-related areas simply because the best hyper-prior governing nonlinear relationships between frequency and shape is an amodal or cross-model object. The actual etiology of higher-level modules is a bit more complicate than this, and requires an appeal to evolution to explain in detail, but we felt this was a generally sufficient explanation of specialization.

Nonlinearity of the world and perception: prediction as integration

At this point, we felt like we had some insight into how predictive coding can explain functional specialization without needing to appeal to special classes of cortical neurons for each sensation. Beyond the sensory effectors, the function of each system can be realized simply by means of a canonical, hierarchical prediction of each layered input, right down to the point of neurons which predict which frequency will be signaled. However, something still was missing, prompting Francesca to ask – how can this scheme explain the coherent, multi-modal, integrated perception, which characterizes conscious experience?

Indeed, we certainly do not experience perception as a series of nested predictions. All of the aforementioned machinery functions seamlessly beyond the point of awareness. In phenomenology a way to describe such influences is as being prenoetic (before knowing; see also prereflective); i.e. things that influence conscious experience without themselves appearing in experience. How then can predictive coding explain the transition from segregated, feature specific predictions to the unified percept we experience?

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When we arrange sensory hierarchies laterally, we see the “markov blanket” structure of the brain emerge. Each level predicts the control parameters of subsequent levels. In this way integration arises naturally from the predictive brain.

As you might guess, we already hinted at part of the answer. Imagine if instead of picturing each sensory hierarchy as an isolated pyramid, we instead arrange them such that each level is parallel to its equivalent in the ‘neighboring’ hierarchy. On this view, we can see that relatively early in each hierarchy you arrive at multi-sensory neurons that are predicting conjoint expectations over multiple sensory inputs. Conveniently, this observation matches what we actually know about the brain; audition, touch, and vision all converge in tempo-parietal association areas.

Perceptual integration is thus achieved as easily as specialization; it arises from the fact that each level predicts a hyperprior on the previous level. As one moves upwards through the hierarchy, this means that each level predicts more integrated, abstract, amodal entities. Association areas don’t predict just that a certain sight or sound will appear, but instead encode a joint expectation across both (or all) modalities. Just like the fusiform face area predicts complex, nonlinear conjunctions of lower-level visual features, multimodal areas predict nonlinear interactions between the senses.

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A half-cat half post, or a cat behind a post? The deep convolutional nature of the brain helps us solve this and similar nonlinear problems.

It is this nonlinearity that makes predictive schemes so powerful and attractive. To understand why, consider the task the brain must solve to be useful. Sensory impressions are not generated by simple linear inputs; certainly for perception to be useful to an organism it must process the world at a level that is relevant for that organism. This is the world of objects, persons, and things, not disjointed, individual sensory properties. When I watch a cat walk behind a fence, I don’t perceive it as two halves of a cat and a fence post, but rather as a cat hidden behind a fence. These kinds of nonlinear interactions between objects and properties of the world are ubiquitous in perception; the brain must solve not for the immediately available sensory inputs but rather the complex hidden causes underlying them. This is achieved in a similar manner to a deep convolutional network; each level performs the same canonical prediction, yet together the hierarchy will extract the best-hidden features to explain the complex interactions that produce physical sensations. In this way the predictive brain summersaults the binding problem of perception; perception is integrated precisely because conjoint hypothesis are better, more useful explanations than discrete ones. As long as the network has sufficient hierarchical depth, it will always arrive at these complex representations. It’s worth noting we can observe the flip-side of this process in common visual illusions, where the higher-order percept or prior “fills in” our actual sensory experience (e.g. when we perceive a convex circle as being lit from above).

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Our higher-level, integrative priors “fill in” our perception.

Beating the homunculus: the dynamic, enactive Bayesian brain

Feeling satisfied with this, Francesca and I concluded our fun holiday discussion by thinking about some common misunderstandings this scheme might lead one into. For example, the notion of hierarchical prediction explored above might lead one to expect that there has to be a “top” level, a kind of super-homunculus who sits in the prefrontal cortex, predicting the entire sensorium. This would be an impossible solution; how could any subsystem of the brain possibly predict the entire activity of the rest? And wouldn’t that level itself need to be predicted, to be realised in perception, leading to infinite regress? Luckily the intuition that these myriad hypotheses must “come together” fundamentally misunderstands the Bayesian brain.

Remember that each level is only predicting the activity of that before it. The integrative parietal neuron is not predicting the exact sensory input at the retina; rather it is only predicting what pattern of inputs it should receive if the sensory input is an apple, or a bat, or whatever. The entire scheme is linked up this way; the individual units are just stupid predictors of immediate input. It is only when you link them all up together in a deep network, that the brain can recapitulate the complex web of causal interactions that make up the world.

This point cannot be stressed enough: predictive coding is not a localizationist enterprise. Perception does not come about because a magical brain area inverts an entire world model. It comes about in virtue of the distributed, dynamic activity of the entire brain as it constantly attempts to minimize prediction error across all levels. Ultimately the “model” is not contained “anywhere” in the brain; the entire brain itself, and the full network of connection weights, is itself the model of the world. The power to predict complex nonlinear sensory causes arises because the best overall pattern of interactions will be that which most accurately (or usefully) explains sensory inputs and the complex web of interactions which causes them. You might rephrase the famous saying as “the brain is it’s own best model of the world”.

As a final consideration, it is worth noting some misconceptions may arise from the way we ourselves perform Bayesian statistics. As an experimenter, I formalize a discrete hypothesis (or set of hypotheses) about something and then invert that model to explain data in a single step. In the brain however the “inversion” is just the constant interplay of input and feedback across the nervous system at all levels. In fact, under this distributed view (at least according to the Free Energy Principle), neural computation is deeply embodied, as actions themselves complete the inferential flow to minimize error. Thus just like neural feedback, actions function as  ‘predictions’, generated by the inferential mechanism to render the world more sensible to our predictions. This ultimately minimises prediction error just as internal model updates do, albeit in a different ‘direction of fit’ (world to model, instead of model to world). In this way the ‘model’ is distributed across the brain and body; actions themselves are as much a part of the computation as the brain itself and constitute a form of “active inference”. In fact, if one extends their view to evolution, the morphological shape of the organism is itself a kind of prior, predicting the kinds of sensations, environments, and actions the agent is likely to inhabit. This intriguing idea will be the subject of a future blog post.

Conclusion

We feel this is an extremely exciting view of the brain. The idea that an organism can achieve complex intelligence simply by embedding a simple repetitive motif within a dynamical body seems to us to be a fundamentally novel approach to the mind. In future posts and papers, we hope to further explore the notions introduced here, considering questions about “where” these embodied priors come from and what they mean for the brain, as well as the role of precision in integration.

Questions? Comments? Feel like i’m an idiot? Sound off in the comments!

Further Reading:

Brown, H., Adams, R. A., Parees, I., Edwards, M., & Friston, K. (2013). Active inference, sensory attenuation and illusions. Cognitive Processing, 14(4), 411–427. http://doi.org/10.1007/s10339-013-0571-3
Feldman, H., & Friston, K. J. (2010). Attention, Uncertainty, and Free-Energy. Frontiers in Human Neuroscience, 4. http://doi.org/10.3389/fnhum.2010.00215
Friston, K., Adams, R. A., Perrinet, L., & Breakspear, M. (2012). Perceptions as Hypotheses: Saccades as Experiments. Frontiers in Psychology, 3. http://doi.org/10.3389/fpsyg.2012.00151
Friston, K., & Kiebel, S. (2009). Predictive coding under the free-energy principle. Philosophical Transactions of the Royal Society of London B: Biological Sciences, 364(1521), 1211–1221. http://doi.org/10.1098/rstb.2008.0300
Friston, K., Thornton, C., & Clark, A. (2012). Free-Energy Minimization and the Dark-Room Problem. Frontiers in Psychology, 3. http://doi.org/10.3389/fpsyg.2012.00130
Moran, R. J., Campo, P., Symmonds, M., Stephan, K. E., Dolan, R. J., & Friston, K. J. (2013). Free Energy, Precision and Learning: The Role of Cholinergic Neuromodulation. The Journal of Neuroscience, 33(19), 8227–8236. http://doi.org/10.1523/JNEUROSCI.4255-12.2013