Fig. 3. The generalized multilinear model for dimensionality reduction of neural populations.
A We hypothesized that the different stimulus directions and categories—including whether it is the sample or test stimulus—could be modeled as vectors as a function of time in a low-dimensional space where the dimensionality is the number of factors. Here, we constrain the direction tuning, but not category, to be the same over the sample and test stimuli. Thus, dimensionality reduction in our framework can take into account shared temporal dynamics and stimulus tuning information across the two stimulus presentations, possibly reflecting similar bottom-up input. Individual neurons’ stimulus tuning is a linear projection of the low-dimensional space. B Diagram of the GMLM. Incoming stimuli are factorized into temporal events and stimulus weights that encode direction and category information (left; Supplementary Fig. 3E–I). A set of temporal kernels and stimulus coefficients filter the linearized stimuli (left) into a low-dimensional stimulus response space. The touch-bar release event is similarly filtered using a low-dimensional set of temporal kernels. Each individual neuron’s firing rate at each time bin is a nonlinear function (here, ) of the sum of a linear weighting of the low-dimensional stimulus subspace, a linear weighting of the touch-bar subspace, and recent spike history. Spike trains (right) are modeled as a Poisson process given the instantaneous rate. Given the recorded spike trains, stimuli, and behavioral responses, the stimulus filter tensor, touch-bar filters, and spike history filters can be fit to the data.