  The ongoing exponential rise in recording capacity calls for new approaches
for analysing and interpreting neural data. Effective dimensionality has
emerged as an important property of neural activity across populations of
neurons, yet different studies rely on different definitions and
interpretations of this quantity. Here we focus on intrinsic and embedding
dimensionality, and discuss how they might reveal computational principles from
data. Reviewing recent works, we propose that the intrinsic dimensionality
reflects information about the latent variables encoded in collective activity,
while embedding dimensionality reveals the manner in which this information is
processed. We conclude by highlighting the role of network models as an ideal
substrate for testing more specifically various hypotheses on the computational
principles reflected through intrinsic and embedding dimensionality.
