Scaling Properties of Dimensionality Reduction for Neural Populations and Network Models

Abstract

Recent studies have applied dimensionality reduction methods to understand how the multi-dimensional structure of neural population activity gives rise to brain function. It is unclear, however, how the results obtained from dimensionality reduction generalize to recordings with larger numbers of neurons and trials or how these results relate to the underlying network structure. We address these questions by applying factor analysis to recordings in the visual cortex of non-human primates and to spiking network models that self-generate irregular activity through a balance of excitation and inhibition. We compared the scaling trends of two key outputs of dimensionality reduction—shared dimensionality and percent shared variance—with neuron and trial count. We found that the scaling properties of networks with non-clustered and clustered connectivity differed, and that the in vivo recordings were more consistent with the clustered network. Furthermore, recordings from tens of neurons were sufficient to identify the dominant modes of shared variability that generalize to larger portions of the network. These findings can help guide the interpretation of dimensionality reduction outputs in regimes of limited neuron and trial sampling and help relate these outputs to the underlying network structure.

Author Summary

We seek to understand how billions of neurons in the brain work together to give rise to everyday brain function. In most current experimental settings, we can only record from tens of neurons for a few hours at a time. A major question in systems neuroscience is whether our interpretation of how neurons interact would change if we monitor orders of magnitude more neurons and for substantially more time. In this study, we use realistic networks of model neurons, which allow us to analyze the activity from as many model neurons as we want for as long as we want. For these models, we found that we can identify the salient interactions among neurons and interpret their activity meaningfully within the range of neurons and recording time available in current experiments. Furthermore, we studied how the neural activity from the models reflects how the neurons are connected. These results help to guide the interpretation of analyses using populations of neurons in the context of the larger network to understand brain function.