Linking the statistics of network activity and network connectivity

Abstract: There is an avalanche of new data on the brain’s activity, revealing the collective dynamics of vast numbers of neurons. In principle, these collective dynamics can be of almost arbitrarily high dimension, with many independent degrees of freedom — and this may reflect powerful capacities for general computing or information. In practice, datasets reveal a range of outcomes, including collective dynamics of much lower dimension — and this may reflect the structure of tasks or latent variables. For what networks does each case occur? Our contribution to the answer is a new framework that links tractable statistical properties of network connectivity with the dimension of the activity that they produce. I’ll describe where we have succeeded, where we have failed, and the many avenues that remain.