Interpreting neural computations by examining intrinsic and embedding dimensionality of neural activity

Abstract

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.

Figure 1.

Non-linear organization of neural activity. a Population activity in the mouse primary visual cortex in response to gratings of different orientations indicated in color. Projection on the first three principal components of data from [9]. b Population activity in the macaque dorsomedial frontal cortex reflecting flexible motor planning in a context-dependent timing task [10]. The animal had to reproduce different time intervals in two contexts. In one context, the produced interval (t_p) had to match the sample, and in the other, t_p had to be 50% longer than the sample (gain=1 or 1.5, respectively). Different traces show DMFC population activity associated with the two contexts (gray and red) for different samples. Despite the fact that t_p distributions for the two contexts were part of a continuum, neural responses were separated in a highly nonlinear fashion along a “Gain axis” distinguishing between the two contexts. c Population activity in the rat head-direction system [11]. Colors represent a computationally-inferred angular latent variable that maps directly onto head orientation. Panel a courtesy of NeuroMatch Academy [12] Pod 001 (Daniela Buchwald, Agustina Frechou, Habiba Noamany, Antonio Ortega).