Dimensionality in recurrent spiking networks: Global trends in activity and local origins in connectivity

PLoS Comput Biol. 2019 Jul 12;15(7):e1006446. doi: 10.1371/journal.pcbi.1006446. eCollection 2019 Jul.


The dimensionality of a network's collective activity is of increasing interest in neuroscience. This is because dimensionality provides a compact measure of how coordinated network-wide activity is, in terms of the number of modes (or degrees of freedom) that it can independently explore. A low number of modes suggests a compressed low dimensional neural code and reveals interpretable dynamics [1], while findings of high dimension may suggest flexible computations [2, 3]. Here, we address the fundamental question of how dimensionality is related to connectivity, in both autonomous and stimulus-driven networks. Working with a simple spiking network model, we derive three main findings. First, the dimensionality of global activity patterns can be strongly, and systematically, regulated by local connectivity structures. Second, the dimensionality is a better indicator than average correlations in determining how constrained neural activity is. Third, stimulus evoked neural activity interacts systematically with neural connectivity patterns, leading to network responses of either greater or lesser dimensionality than the stimulus.

Publication types

  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Action Potentials / physiology*
  • Humans
  • Models, Neurological
  • Nerve Net / physiology*

Grant support

ES-B is supported by the NSF grant DMS-1514743. We gratefully acknowledge the support of the Swartz Foundation, through the Swartz Center for Theoretical Neuroscience at the University of Washington. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.