Sajid, Noor; (2024) A Bayesian account of how neural structures shape function. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

Considering the enormous complexity of the brain, advancing our understanding necessitates computational abstraction to analyse its intricate components. This thesis provides a comprehensive examination of the Bayesian computations theorised to underpin neural function, examining the dynamics interplay between neural structures and function. For this, it investigates models that enable environmental interactions, the impact of internal system disturbances on these functions, and the models' adaptability in response to neural damage. The goal is to distill the Bayesian principles that inform brain function and to showcase how underlying latent structures support adaptive behaviour post-damage, positing that the brain's engagement with its environment is fundamentally Bayesian and shaped by its intrinsic structural and functional characteristics. Given this, the first part examines i) the capacity of particular neural structures to sustain meaningful interactions with our environment and ii) the effects of disruptions within these structures on functionality. We assess how transitioning from single-level latent structures to more complex model specifications, encompassing deep temporal encoding or hyper-priors, can support suitable functional outcomes. First, in deterministic situations we demonstrate the sufficiency of simple neural structures approximated by a partially observable Markov decision process underpinning active (Bayesian) inference. Our attention then shifts to understanding the neural structures that facilitate adaptive functional processing despite perturbations. To this end, we formalise functional degeneracy in the context of belief updating under active inference and illustrate how degenerate model parameterisations can alter functional processing without impeding functional outcomes. Building upon this, we complexify the model architecture to include a deep temporal formulation and simulate functional recovery after various lesion types, demonstrating the model's resilience to damage. Subsequently, we introduce a (deep) model structure that promotes adaptive exchanges with the environment without external reward signals. Through simulations in varied environments, we validate the effectiveness of our formulation, demonstrating how a change in environment dynamics leads to adaptive behaviour changes. The final part of the thesis ventures into the realm of functional manipulation; exploring how functional loss alterations can induce behavioural variations within the confines of an identical model structure. We propose a novel framework that employs Rényi divergences to explain behavioural variability. Variations in the α parameter within the Rényi bounds result in different posterior estimates, thus leading to variations in behaviour. In sum, we provide a novel exploration of how neural structures shape function that has significant implications not only for neuroscience but also for artificial intelligence, fostering new opportunities for developing adaptive systems that echo the complexity and resilience of the human brain.

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