Publications

In this chapter, we identify fundamental geometric structures that underlie the problems of sampling, optimisation, inference and adaptive decision-making. Based on this identification, we derive algorithms that exploit these geometric structures to solve these problems efficiently. We show that a wide range of geometric theories emerge naturally in these fields, ranging from measure-preserving processes, information divergences, Poisson geometry, and geometric integration. Specifically, we explain how \emph{(i)} leveraging the symplectic geometry of Hamiltonian systems enable us to construct (accelerated) sampling and optimisation methods, \emph{(ii)} the theory of Hilbertian subspaces and Stein operators provides a general methodology to obtain robust estimators, \emph{(iii)} preserving the information geometry of decision-making yields adaptive agents that perform active inference. Throughout, we emphasise the rich connections between these fields; e.g., inference draws on sampling and optimisation, and adaptive decision-making assesses decisions by inferring their counterfactual consequences. Our exposition provides a conceptual overview of underlying ideas, rather than a technical discussion, which can be found in the references herein.

Biological agents have meaningful interactions with their environment despite the absence of immediate reward signals. In such instances, the agent can learn preferred modes of behaviour that lead to predictable states -- necessary for survival. In this paper, we pursue the notion that this learnt behaviour can be a consequence of reward-free preference learning that ensures an appropriate trade-off between exploration and preference satisfaction. For this, we introduce a model-based Bayesian agent equipped with a preference learning mechanism (pepper) using conjugate priors. These conjugate priors are used to augment the expected free energy planner for learning preferences over states (or outcomes) across time. Importantly, our approach enables the agent to learn preferences that encourage adaptive behaviour at test time. We illustrate this in the OpenAI Gym FrozenLake and the 3D mini-world environments -- with and without volatility. Given a constant environment, these agents learn confident (i.e., precise) preferences and act to satisfy them. Conversely, in a volatile setting, perpetual preference uncertainty maintains exploratory behaviour. Our experiments suggest that learnable (reward-free) preferences entail a trade-off between exploration and preference satisfaction. Pepper offers a straightforward framework suitable for designing adaptive agents when reward functions cannot be predefined as in real environments.

Analyses of brain structure in genetic speech and language disorders provide an opportunity to identify neurobiological phenotypes and further elucidate the neural bases of language and its development. Here we report such investigations in a large family, known as the KE family, half the members of which are affected by a severe disorder of speech and language, which is transmitted as an autosomal-dominant monogenic trait. The structural brain abnormalities associated with this disorder were investigated using two morphometric methods of MRI analysis. A voxel-based morphometric method was used to compare the amounts of grey matter in the brains of three groups of subjects: the affected members of the KE family, the unaffected members and a group of age-matched controls. This method revealed a number of mainly motor- and speech-related brain regions in which the affected family members had significantly different amounts of grey matter compared with the unaffected and control groups, who did not differ from each other. Several of these regions were abnormal bilaterally, including the caudate nucleus, which was of particular interest because this structure was also found to show functional abnormality in a related PET study. We performed a more detailed volumetric analysis of this structure. The results confirmed that the volume of this nucleus was reduced bilaterally in the affected family members compared with both the unaffected members and the group of age-matched controls. This reduction in volume was most evident in the superior portion of the nucleus. The volume of the caudate nucleus was significantly correlated with the performance of affected family members on a test of oral praxis, a test of non-word repetition and the coding subtest of the Wechsler Intelligence Scale. These results thus provide further evidence of a relationship between the abnormal development of this nucleus and the impairments in oromotor control and articulation reported in the KE family.

Repetitive transcranial magnetic stimulation (rTMS) of human primary motor cortex (M1) changes cortical excitability at the site of stimulation and at distant sites without affecting simple motor performance. The aim of this study was to explore how rTMS changes regional excitability and how the motor system compensates for these changes. Using functional brain imaging, activation was mapped at rest and during freely selected finger movements after 30 min of 1 Hz rTMS. rTMS increased synaptic activity in the stimulated left M1 and induced widespread changes in activity throughout areas engaged by the task. In particular, movement-related activity in the premotor cortex of the nonstimulated hemisphere increased after 1 Hz rTMS. Analyses of effective connectivity confirmed that the stimulated part of M1 became less responsive to input from premotor and mesial motor areas. Conversely, after rTMS our results were consistent with increased coupling between an inferomedial portion of left M1 and anterior motor areas. These results are important for three reasons. First, they show changes in motor excitability to central inputs from other cortical areas (as opposed to peripheral or exogenous inputs used in previous studies). Second, they suggest that maintenance of task performance may involve activation of premotor areas contralateral to the site of rTMS, similar to that seen in stroke patients. Third, changes in motor activations at the site of rTMS suggest an rTMS-induced remodeling of motor representations during movement. This remapping may provide a neural substrate for acute compensatory plasticity of the motor system in response to focal lesions such as stroke.

Persistent Postural Perceptual Dizziness (PPPD) is a common and disabling chronic disorder, comprising core symptom clusters involving perceived (i.e., subjective) unsteadiness during upright posture and intolerance for self- and visual motion. There are diagnostic criteria, conceptual models and therapeutic approaches to managing specific components of PPPD, such as physiotherapy, cognitive behavioural therapy and anti-depressant medication. However, no diagnostic tests or unifying neurobiological basis for the condition exists. PPPD has been viewed as a subtype of functional neurological disorder (FND), sharing some similarities in altered brain function and behaviour, but lacks other hallmarks of FND. Here, using the framework of Active Inference - in which both action and perception are based on internal predictions about the state of the body and the world and their precision (estimated reliability) - we define a singular neurobiological process responsible for core PPPD symptoms: namely, a failure to attenuate precision-weighted prediction error (PWPE) during self-motion, leading to subjective postural instability. Specifically, self-motion prediction errors per se are not increased, but their precision weighting is, thereby reducing the relative precision of self-motion predictions. More simply, this reflects a shift of operating mode from top-down, efficient ‘autopilot’ to a ‘feedback’ mode, dominated by bottom-up sensory processing errors. Ordinarily, experience-dependent learning naturally produces a drift to the autopilot mode, but we present four processes - each potentially present in any individual and characterised by a positive feedback loop - that keep the system stuck in a feedback mode, resulting in PPPD: elevated attention/vigilance; perceptual inferences of imbalance; preventative or corrective movement behaviours; and over-reliance on visual inputs. This model can form the basis of tools for clinical assessment and management. Finally, the foundation of our model – on defined and measurable neurobiological processes – affords testable hypotheses for investigative work and lends itself to computational modelling. A modified version of the model can also explain other forms of chronic dizziness without structural causes, like Mal de débarquement syndrome (MdDS), or ‘unexplained dizziness’ in later life.