Sensory and motor computations require tens of thousands of highly stochastic neurons in a cortical circuit to meaningfully coordinate their firing activity for a common goal. The trial- to-trial variability structure of neuronal population activity characterizes the coordinated neural dynamics underlying computation. Unsurprisingly, the dimension of the variability shared across neurons in one cortical population is generally orders of magnitude smaller than the number of neurons involved in a task. But how does this shared neuronal variability map across multiple cortical areas involved in the same computation?

In this thesis, I study the propagation of low dimensional shared variance across cortical regions as a means to understand the dynamics of multi-area brain computation. I first present a statistical model of movement encoding in human primary motor cortex that uncovers a one- dimensional trajectory of latent activity differentially modulated during movements in which the subject received somatosensory feedback. I then present new evidence that the dimension of shared variability increases from V4 to PFC during distributed processing of visual stimuli. I develop a multi-layer spiking network model with tuning-structured connectivity that, through non-linear recurrent dynamics, replicates the dimensionality expansion observed in vivo. Finally, I show evidence that my model’s non-linear recurrent dynamics can be interpreted as time- sharing between multiple states of low-dimension, linear dynamics inherited from the upstream brain area. Together, these results aid our understanding of the subspaces of neuronal activity that are relevant across multiple brain areas during sensory and motor behaviors.