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What does the synthetic frog's heart tell it's Bayesian brain? Read our new pre-print "In the Body's Eye: The Computational Anatomy of Interoceptive Active Inference" to find out! biorxiv.org/content/10.110… - explainer thread below: 
"Interoceptive inference" theories are increasingly popular. See e.g, work by @anilkseth, @LFeldmanBarrett, @manos_tsakiris et al. These are great, but so far, mostly conceptual. Here, we wanted to offer the community a formal model, to guide more concerte hypothesis testing.
How can we best understand the influence of visceral states on hierarchical Bayesian inference? Our idea in this paper was to treat the body as a cylic osscilator which periodically attenutates sensory precision.
Our motivation here was twofold; first, the increased evidence linking visceral rythms (breath, heart, gut, etc) to fluctuations in cortical noise (e.g., 1/precision), and second, nearly a century of research which suggests that exteroception is linked to the cardiac cycle.
In our generative model, implemented as a markov-decision-process, the agent must infer which exteroceptive stimulus is present (a 'spider' or a 'flower'), and also what it's cardiac state is. Cardiac states osscilate from from early diastole->late dia -> systole.
Crucially, the linkage of visceral and exteroceptive states is operationalized entirely as attenuation of exteroceptive precision on each heartbeat (systole). Depending on what it infers (spider vs flower), the agent can either select an 'aroused' or 'unaroused' policy.
These policies correspond to either selecting a transition matrix which skips directly from early diastole to systole (heart-rate acceleration) or orbits the entire cycle (deceleration).
As in all MDP schemes, the agents has prior preferences - it prefers to be aroused in the presence of spiders, and relaxed in the presence of flowers. These preferences evolve over the course of each simulated experiment, as the agent attempts to minimize free energy.
This means that our agent must balance between getting accurate information about it's cardiac and exteroceptive states, versus the sensory attenutation that is caused by correctly inferring that an arousing stimulus is present. An affective explore-exploit dilemma if you will.
So what can we learn about perceptual inference from our agent? To find out, we first tried to simulate some basic psychophysiological phenomenon, such as the defensive startle reflex. [image from: researchgate.net/figure/Top-lef…]
To do so, we created a little experiment: 14 blissful trials of a relaxed heart-rate and only flowers, followed by the presentation of an 'oddball' spider stimulus. We then observe how the agent performs before and after the suprising threat.
We then simulate these conditions for 60 randomized virtual agents, half of which had a 'lesion' ablating their visceral precision. This revealed some really interesting results:
First, the healthy agents: 1) the agent exhibits a 'startle-like' reflex, accelerating heart-rate and rapidly updating it's fear expecatons at the first spider-trial. 2) Fascinatingly, in the baseline spider-expectations increase at each heart beat.
We think this could explain findings by @DrSFink et al who report potentiation of fear-perception by baroceptor output. What about the 'lesioned' agent? Here we see that 1) the cardiac response & belief update are both blunted & 2) the baseline 'spider hallucination' is higher!
For me, this set of simulations really illuminated the model. It's such a simple implementation (in Karl's words: "the simplest possible model") of the cardiac cycle, yet these plausible effects already emerge! What about metacognition - i.e., the uncertainty of beliefs?
Recent evidence from our lab and others suggests that cardiac arousal may increase metacognitive biases. This suggests that metacognition may integrate interoceptive and exteroceptive precision. Do we see this in our agent? elifesciences.org/articles/18103
To test this hypothesis, we calculated the negative entropy of the agent's exteroceptive and interoceptive beliefs. Because these emerge from active inference, you can think of them as the posterior uncertainty in an inferred belief (e.g., 'spider', 'systole').
Here, we plot entropy (H) for each belief state under a full range of intero vs extero precision, from lesion (0.5) to hyper-precise (1.0), shown in the left panels. We also split these by each phase of the cardiac cycle (right panels).
What does this reveal? Well, the first thing is pretty obvious: when summing across cardiac states, it's mostly within-modality precision driving belief uncertainty. However, there are still some interactions; the lowest uncertainty state has maximal intero+extero precision.
Next - individual cardiac states. Uncertainty is strongly increased on each heartbeat - that is hard-wired into the model. But we can also see that while exteroceptive 'lesions' increase average uncertainty, intero lesions seem to alter the relative difference between cycles.
This is an interesting finding; it suggests that while our agents 'metacognition' is largely 'unimodal', there is also some direct linkage through interoception. It's subtle, but we can see it best in the extreme lesion cases and for individual cardiac states.
Next, we performed synthetic HRV analyses. We simulated heart-rate variability under different, potentially clinically relevant settings: healthy (left), hyper precise visceral prediction errors, and a hyper-precise arousal prior sciencedirect.com/science/articl…
This analysis is really just a demo of a simple concept: low and high-frequency HRV are complex observed phenomena which are likely over-determined by priors, likelihoods, and policies. Individual differences in these factors are likely to produce idiosyncratic responses.
And they do! As you can see, slight variations in these parameters cause fairly substantial and idiosyncratic patterns in our toy-model of the heart. Our hope is that in the future, we can expand our model to be more biophysically realistic.
This would [potentially] enable the recovery of individual interoceptive inference phenotypes from HRV data collected during tasks or at rest. That would mean we could one day perform 'embodied' computational phenotyping! onlinelibrary.wiley.com/doi/full/10.10… /thread
That's about it for now! We underscore in the paper that this just one particular operational definition. There are many others - & many other visceral systems - to consider. We do think however that this provides an excellent starting point for hypothesis testing in this space
E.g., a strength of the MDP scheme used here is that it can be flexibly adapted to model just about any task in discrete state space. Is has already been applied to reward, navigation, memory, ballistic saccades, and more!
This means that you can use our model to explore cardiac cycle effects in all of these domains and more! The underlying cardiac active inference scheme will be in the next public release of SPM12, and all our code is available on github: github.com/embodied-compu…
That is all for now! Thanks very much to my awesome collaborators - Andrew Levy for the HRV analysis code, Thomas Parr for being generally brilliant and tolerating my zillion questions about the MDP scheme, and of course Karl for his excellent mentorship of this project!
Almost forgot - thank you @lundbeckfonden @AIAS_dk @wellcometrust and @psychiatry_ucam for supporting this research!
Hey @AdamLinson - heard you were using our model to simulated PTSD! Sounds like a cool project - check out our paper and let me know if you want any help!
I apologize for the many errors and typos in this thread. I was overly aroused by the excitement of sharing this project. Leaving the thread up for posterity :) :P
Just noticed there is a glaring error in the introduction. This section is meant to read 'At still slower timescales, respiratory and even gastric fluctuations are coupled to neural oscillations and behavior'. I think the gastric citations missing here too. Will fix!
