Brain Dynamics and Connectivity

Murray Shanahan


An Overview of My Work

In the late 2000s and early 2010s, in tandem with thinking about consciousness from a philosophical and theoretical point of view, I became increasingly interested in the empirical question of how consciousness is realised in the biological brain. I was impressed with global workspace theory, which offers an appealing account of the distinction between conscious and unconscious information processing. Moreover, its foundation is a hypothesised cognitive architecture that supports the integration of information across the brain, allowing its full resources to be brought to bear on an ongoing situation when required (to deal with novelty, for example). Global workspace architecture, in other words, promised to account for both consciousness and sophisticated cognition.

But how does the messy wetware of a biological brain instantiate the proposed architecture? At the time, Stanislas Dehaene and his colleagues were building the empirical case for an answer based on the long-range white matter connections of the human brain, which they dubbed the global neuronal workspace. Their work was compelling, but largely confined to the human brain, whereas I wanted to understand consciousness in the space of possible minds. I wanted to know, for example, how consciousness might be realised in the brains of birds, which are very differently organised to mammalian brains. Moreover, birds have remarkably sophisticated cognitive capabilities, which I was learning all about as a visiting academic in Nicky Clayton's comparative cognition lab in Cambridge. The consciousness story I wanted to tell had to include other animals, including birds.

What I was looking for was a theoretical account at a level of description that transcended any individual species, but that could be mapped onto any species when it came to the empirical specifics. (I was thinking so much about AI at the time; I would return to my AI roots later.) The two essential ingredients I found for such a theory were network topology and neural dynamics, and I explained how they had to work together in Chapters 4 and 5 of my 2010 book "Embodiment and the Inner Life" and in my 2012 paper "The brain's connective core and its role in animal cognition".

Brain Connectivity

If we think of connections as conduits for information and influence, then we should expect certain patterns of connectivity in any brain that incorporates the sort of communications infrastructure hypothesised by global workspace theory to support both consciousness and sophisticated cognition. It should be possible for information to get from anywhere to anywhere in just a few hops (it should be a small-world network). We would expect to see dense local connections, supporting localised modular processing, complemented by sparser long-range, inter-modular connections. And we might expect to find hub nodes, regions that information would funnel into from all over the brain, and from where information would fan out again, broadcast back to the whole brain.

Drawing on the theory of complex networks, it was possible to give precise, mathematical definitions for each of those concepts. This is what researchers were doing for the human brain in the field of connectomics, using connectivity data obtained with diffusion tensor imaging techniques. In line with the theoretical stance of "Embodiment and the Inner Life", human brain connectivity indeed had all the expected features, including a connective core of cognitively important hub regions including the prefrontal cortex, the precuneus, and the hippocampal formation. But what about birds? According to my theory, the high-level network organisation of the avian brain should conform to the same pattern. Unfortunately, though, there was no whole brain connectome for the avian brain at the time, so it was impossible to verify this prediction.

But thanks to Nicky Clayton, I got to meet one of the world's top avian brain experts, Onur Güntürkün, who assured me the data was all there in scattered tracer studies; it just hadn't been collated into a single connectivity matrix for the whole avian brain. So we assembled a crack team of avian neuroanatomists, and together we carried out a meta-study from which we put together the whole-brain connectome of the pigeon. This we subjected to the same style of mathematical analysis others were carrying out on the human connectome. The results, published in our 2013 paper "Large-scale network organization in the avian forebrain", were striking. We found that the pigeon's brain too had a connective core of cognitively important hub nodes, including the nidopallium caudolaterale (NCL), which is the avian homologue of the preforntal coretx, and the hippocampal formation. In other words, the avian brain, despite being very different from the mammalian brain, had the sort of high-level organisation we would expect if it conformed to the global workspace archtectural blueprint.

Neurodynamics

Meanwhile, I was also working on the dynamics part of the story. Unlike almost all AI systems, the brain is never still, electrically speaking. An LLM-based conversational agent, for example, is completely dormant in the absence of user input. The brain, by contrast, is active not only during normal wakeful activity, but also while asleep, during meditation, and even under anaesthesia. It's activity can be detected with a variety of methods, such as EEG or MRI, and is markedly rhythmic. Like many neuroscientists, I suspected that this symphony of neural oscillations was intimately related to consciousness, and I wanted to understand how it might tie in with global workspace theory.

The most prominent feature of the brain's rhythmic neural activity is synchrony. The oscillations in one brain region are often synchronised with the oscillations in other brain regions. According to the communication through coherence hypothesis of Pascal Fries, there is a good reason for this; synchronising their neuronal activity allows two brain regions to exchange information, and thereby to co-operate, while simultaneously shutting out regions with which they are not synchronised. In other words, synchronisation might underpin both broadcast and competition, the essential ingredients of the global workspace architecture. To corroborate these ideas, we built a number of computer simulations in my lab based on mathematical models spiking neurons. For example, in a 2012 paper with my PhD student Mark Wildie, we showed how communication through coherence could indeed arise between populations of spiking neurons, and we showed that our model reproduced the statistical properties of the phenomenon of binocular rivalry.

But the phenomenon that fascinated me more than any other around that time was metastability. Most mathematical models of synchrony at the time were concerned with systems of coupled oscillators that converge on a stable, perfectly synchronised configuration, and remain that way indefinitely. But in the brain, synchrony between regions is a temporary phenomenon. What we see is not stability but metastability. A set of regions / processes will synchronise for a while, forming a temporary coalition, before going out of synchrony again while some different coalition of processes become synchronised. From the standpoint of global workspace theory, this procession of temporarily stable states would correspond to the unfolding content of consciousness, each global, brain-wide coalition lasting for a short while, exerting global influence on the brain, until succeeded by a rival coalition of processes.

My 2010 paper, "Metastable chimera states in community-structured oscillator networks" captures all of this in a simple mathematical model. Using a computer simulation, the paper shows that the model exhibits the dynamical signature of consciousness, according to my elaborated version of global workspace theory, namely a series of metastable states in which different coalitions of oscillators temporarily synchronise. Moreover, it does so thanks to the topology of the network of connections between the oscillators. Specifically, again as posited by my elaborated version of GWT, the oscillators form a modular, small-world network, just like the biological brain. Finally, the paper showed that the metastable dynamical regime lies in a critical region of parameter space, nestled between order and disorder.

The model in that 2010 paper, and the simple measure of metasbaility the paper introduced, have been pretty influential. One line of work connects the model directly with empirical findings on the human brain. Used in combination with methods pioneered by Joana Cabral in Gustavo Deco's lab in Barcelona, the model does a good job of predicting human fMRI data under various experimental conditions, but only when it is tuned to the metastable regime. With my Imperial College neuroscience collagues, I co-authored a number of papers exploring this application of the model, such as "The control of global brain dynamics: opposing actions of frontoparietal control and default mode networks on attention" in 2014.

Although I largely stopped working in this area when I joined DeepMind in 2017, I have retained a strong interest in it, and my (former) PhD student, Pedro Mediano, has pursued the topic with great success. In 2022, along with colleagues at the University of Sussex, we published a paper, "Integrated information as a common signature of dynamical and information-processing complexity", that (among other things) links my model to one of the other leading contenders for a theory of consciousness, namely Giulio Tononi's integrated information theory (IIT). In the paper, we show that a proxy for Φ (IIT's proposed quantitative measure of consciousness) is maximised in my model in the very same critical region of parameter space that maximises metastability.


A Selection of Papers

For a more complete list of my publications see my Google Scholar page