Stimuli Reduce the Dimensionality of Cortical Activity

Abstract

The activity of ensembles of simultaneously recorded neurons can be represented as a set of points in the space of firing rates. Even though the dimension of this space is equal to the ensemble size, neural activity can be effectively localized on smaller subspaces. The dimensionality of the neural space is an important determinant of the computational tasks supported by the neural activity. Here, we investigate the dimensionality of neural ensembles from the sensory cortex of alert rats during periods of ongoing (inter-trial) and stimulus-evoked activity. We find that dimensionality grows linearly with ensemble size, and grows significantly faster during ongoing activity compared to evoked activity. We explain these results using a spiking network model based on a clustered architecture. The model captures the difference in growth rate between ongoing and evoked activity and predicts a characteristic scaling with ensemble size that could be tested in high-density multi-electrode recordings. Moreover, we present a simple theory that predicts the existence of an upper bound on dimensionality. This upper bound is inversely proportional to the amount of pair-wise correlations and, compared to a homogeneous network without clusters, it is larger by a factor equal to the number of clusters. The empirical estimation of such bounds depends on the number and duration of trials and is well predicted by the theory. Together, these results provide a framework to analyze neural dimensionality in alert animals, its behavior under stimulus presentation, and its theoretical dependence on ensemble size, number of clusters, and correlations in spiking network models.

Scaling Properties of Dimensionality Reduction for Neural Populations and Network Models

“…By contrast, principal components analysis (PCA), a standard dimensionality reduction method, applied to spike counts measures dimensionality of the raw covariability. Recently, Mazzucato et al used PCA to examine the dimensionality of 3 to 9 neurons recorded simultaneously in rat gustatory cortex [19]. Despite the difference in methods used to compute dimensionality, they also found that dimensionality increases with neuron and trial count in in vivo recordings and spiking network models.…”

“…Our study could be extended to scaling trends in evoked activity, in which visual stimuli are presented during the V1 recordings and non-zero inputs are used in the spiking network models. Previous studies have found that shared variance tends to decrease after stimulus presentation [20, 35, 38–40] and that the scaling properties of PCA dimensionality change after stimulus presentation [19]. However, under certain conditions, the population activity patterns expressed in spontaneous activity can resemble those expressed in evoked activity [9, 41].…”

“…At one end is the classic balanced network with homogeneous connectivity which has been studied for decades (i.e., the non-clustered network) [14, 15]. At the other end is a balanced network in which each excitatory neuron belongs to a particular cluster and there is high within-cluster connectivity (i.e., the clustered network) [17–19]. Although neither of these model networks is a perfect match with cortical networks, both model networks have been shown to mimic some single-neuron and pairwise spiking statistics measured in cortical neurons [14, 15, 17, 19].…”

“…Recent studies have introduced clustering structure and found that the single-neuron and pairwise statistics of these networks better capture the slow fluctuations in firing rate observed during in vivo recordings [17–19]. In this work, we focus on two types of spiking network models: clustered networks and classic balanced (non-clustered) networks.…”

A gustocentric perspective to understanding primary sensory cortices

“…Such a model features balanced excitation/inhibition and a clustered architecture and generates an attractor landscape that spontaneous activity explores (Figure 1e). The model built to explain spontaneous activity could reproduce fundamental features of stimulus-evoked activity [27,28], indicating that the elusive relationship between spontaneous and evoked cortical activity [33] is grounded in the dynamics internally generated by a network with clustered architecture [34]. …”