Tensor Analysis Reveals Distinct Population Structure that Parallels the Different Computational Roles of Areas M1 and V1

摘要

Cortical firing rates frequently display elaborate and heterogeneous temporal structure.One often wishes to compute quantitative summaries of such structure—a basic exampleis the frequency spectrum—and compare with model-based predictions. The advent oflarge-scale population recordings affords the opportunity to do so in new ways, with thehope of distinguishing between potential explanations for why responses vary with time.We introduce a method that assesses a basic but previously unexplored form of population-level structure: when data contain responses across multiple neurons, conditions, andtimes, they are naturally expressed as a third-order tensor. We examined tensor structurefor multiple datasets from primary visual cortex (V1) and primary motor cortex (M1). All V1datasets were ‘simplest’ (there were relatively few degrees of freedom) along the neuronmode, while all M1 datasets were simplest along the condition mode. These differencescould not be inferred from surface-level response features. Formal considerations suggestwhy tensor structure might differ across modes. For idealized linear models, structure issimplest across the neuron mode when responses reflect external variables, and simplestacross the condition mode when responses reflect population dynamics. This same patternwas present for existing models that seek to explain motor cortex responses. Critically, onlydynamical models displayed tensor structure that agreed with the empirical M1 data. Theseresults illustrate that tensor structure is a basic feature of the data. For M1 the tensor structure was compatible with only a subset of existing models.