Data from: Tensor analysis reveals distinct population structure that parallels the different computational roles of areas M1 and V1

Cortical firing rates frequently display elaborate and heterogeneous
temporal structure. One often wishes to compute quantitative summaries of
such structure—a basic example is the frequency spectrum—and compare with
model-based predictions. The advent of large-scale population recordings
affords the opportunity to do so in new ways, with the hope 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, and times, they are naturally
expressed as a third-order tensor. We examined tensor structure for
multiple datasets from primary visual cortex (V1) and primary motor cortex
(M1). All V1 datasets were ‘simplest’ (there were relatively few degrees
of freedom) along the neuron mode, while all M1 datasets were simplest
along the condition mode. These differences could not be inferred from
surface-level response features. Formal considerations suggest why tensor
structure might differ across modes. For idealized linear models,
structure is simplest across the neuron mode when responses reflect
external variables, and simplest across the condition mode when responses
reflect population dynamics. This same pattern was present for existing
models that seek to explain motor cortex responses. Critically, only
dynamical models displayed tensor structure that agreed with the empirical
M1 data. These results 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.