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Models of neural circuits as optimally driven dynamical systems


Type

Thesis

Change log

Authors

Schimel, Marine 

Abstract

Animal brains are composed of large numbers of neurons, whose time-varying activity is shaped by their recurrent connections. %neurons are connected. Recent advances in experimental techniques now make it possible to record the activity of up to thousands of neurons simultaneously, providing a unique opportunity to characterise their dynamics, as a window into the underlying connectivity patterns. Thus, recent years have seen increased interest from the neuroscience community in modelling neuronal populations through the lens of dynamical systems. However, most recordings are performed in one or a small subset of brain areas, such that the underlying dynamics do not come from an isolated system, but are instead being driven by signals from the rest of the brain, and external world. Unfortunately, the presence of these unobserved inputs makes it very challenging to characterise the system's dynamics, as there exists a degeneracy between unobserved inputs and unknown dynamics. The work presented in this thesis attempts to tackle this problem. We do so by introducing statistical priors over inputs, which can be understood as a way of softly constraining the set of values they can take. When combined with neural or behavioural observations, these constraints allow to formulate unobserved inputs driving a neural population as the solution to an optimal control problem -- which here we solve using the iLQR algorithm. We first use this framework to understand under what settings it is optimal for motor cortical circuits to rely on preparatory inputs to drive their dynamics -- in this case defining performance in a delayed reaching task as the objective of optimisation. Next, we propose a novel method to learn input-driven dynamical systems directly from data, this time optimising the inputs to yield the best possible description of the observations given a setting of the dynamics, and using a bilevel optimisation approach to learn the system's parameters. We apply it to sets of behavioural recordings, using it to gain insights into the dynamics underlying zebrafish swimming behaviour, and to dissect the mechanisms underlying visual information processing in mice. Overall, our work highlights a set of computational and theoretical tools highly relevant to the systems neuroscience community, that can be used to model neural circuits as input-driven dynamics systems, and dissect the resulting models.

Description

Date

2024-02-01

Advisors

Hennequin, Guillaume

Keywords

behaviour, dynamical systems, neural activity, neural circuits, neuroscience, optimal control, time series modeling

Qualification

Doctor of Philosophy (PhD)

Awarding Institution

University of Cambridge
Sponsorship
Engineering and Physical Sciences Research Council (2275430)