understanding selective recruitment in brain networks via systems theory
Name: Erfan Nozari
Grad Year: 2019
At any given moment, the human brain must process the diverse flux of information from the senses while suppressing the effects of distractions and integrating relevant information with memory to take current actions. This results in the premise that network dimensionality, as measured by the number of neurons that are active any any given time, is a tightly controlled resource on a moment-to-moment basis. Extensive experimental research in neuroscience suggests that inhibition and oscillatory coherence play key roles in performing these functions. The hypothesis is that while targeted inhibition of task-irrelevant sub-networks prevents them from firing, coherent oscillations between task-relevant sub-networks mediates information transfer between them. Taking a systems and controls perspective, we present in this work a mathematical theory of the first phenomena, i.e., selective inhibitory control, in neuronal networks with rate dynamics and its interplay with network structure. To study the network mechanisms for selective inhibitory control, we suggest dynamical stability as a key constraint. Recent advances in machine learning suggest that expressivity of a neural network is maximized when it operates at the edge between stability and instability (a.k.a. edge of chaos). This observation motivates our analysis of the stability of neuronal networks with rate dynamics as a function of its external input current. Focusing on a biologically-motivated class networks with piecewise-affine activation functions, we first derived several necessary and sufficient conditions for fundamental dynamical properties such as existence and uniqueness of equilibria and asymptotic stability. We then analyzed the implications of these results for selective inhibitory control through stabilization. In both feedforward and feedback control schemes, interestingly, our main conclusion is that network stabilizability is solely determined by the latent sub-network of nodes that do not directly receive external stabilizing controls. This result allows us to quantify the proportion of nodes that need to be directly controlled for efficient inhibitory control, as well as a computational theory for achieving such feedback and feedforward stabilization. Finally, motivated by the multiple-time scale structure of the brain, we study a layered structure in which selective inhibitory control of faster subnetworks is realized by higher-level slower ones, considering the collective dynamics of both networks into account. We show through an illustrative example how this theory can be utilized to achieve different functionalities over different time intervals simply by switching between appropriately sized subnetworks of the same neuronal network.
Industry Application Area(s)
Control Systems | Life Sciences/Medical Devices & Instruments