Understanding Mechanism of Functional Dynamics Through An Explainable Neural Network Landscape with Geometric Control

Project Summary/Abstract One of the fundamental scientific problems in neuroscience is to have a good understanding of how cognition and behavior emerge from brain function. Tremendous strides have been made over the past decade to elucidate the biological mechanism that creates remarkable oscillatory patterns of functional fluctuations. From a data science perspective,

functional neural activities manifest geometric patterns, as evidenced by the evolving network topology of functional connectivities (FC) even in the resting state. Since the co-activation of spontaneous functional fluctuations is often encoded in a symmetric and positive-definite (SPD) matrix, it is more reasonable to put the spotlight on the geometric

patterns of evolving functional connectomes on the Riemannian manifold of SPD matrices, instead of using Euclidean operations. In this regard, we will develop a novel computational model to understand the control mechanism underlying functional dynamics through the lens of cutting-edge manifold, control theory, and machine learning technologies. The

overarching goal of our project is to establish a new underpinning of the relationship between analytic measurement of control mechanisms and cognitive functions, which allows us to understand the mechanism of how the human brain works and discover new imaging biomarkers with great mathematics guarantee. To do so, we define a trajectory of the complex

neural system to be the temporal path on the Riemannian manifold that steers the human brain traverses through diverse

cognitive states. In this regard, we will first develop a deep end-to-end model to uncover the characteristic equation of dynamical systems from the time series of FC matrices in Aim 1. The backbone of our deep model is a data-driven linearization process that projects high-dimensional manifold instances to a subspace such that the nonlinear dynamic

mechanism of evolving SPD matrices on the manifold can be dissected using a well-studied linear model on the latent

vector space. Furthermore, we integrate the notion of optimal control into the deep model, which allows us to (i) uncover

the multi-frequency oscillatory functional network modes for brain state transitions and (ii) measure the controllability for

not only the whole brain but also each brain region. We will address the following scientific questions in Aim 2 using the existing unprecedented amount of human connectomes: (i) What is the relationship between brain controllability and visual working memory? (ii) In what control mechanism does each brain region contribute to the altered functional

dynamics associated with auditory verbal hallucinations (AVH)? (iii) What is the statistical power associated with the identification of disease-specific connectomes using the newly established system-level understanding of functional dynamics? Successfully executing this project will shed new light on elucidating the working mechanism that links brain

function and cognition, which is instrumental in understanding cognitive control in the neuroscience field. We will release the software to facilitate other human connectome studies.