The implications of categorical and category-free mixed selectivity on representational geometries

The firing rates of individual neurons displaying mixed selectivity are modulated by multiple task variables. When mixed selectivity is nonlinear, it confers an advantage by generating a high-dimensional neural representation that can be flexibly decoded by linear classifiers. Although the advantages of this coding scheme are well accepted, the means of designing an experiment and analyzing the data to test for and characterize mixed selectivity remain unclear. With the growing number of large datasets collected during complex tasks, the mixed selectivity is increasingly observed and is challenging to interpret correctly. We review recent approaches for analyzing and interpreting neural datasets and clarify the theoretical implications of mixed selectivity in the variety of forms that have been reported in the literature. We also aim to provide a practical guide for determining whether a neural population has linear or nonlinear mixed selectivity and whether this mixing leads to a categorical or category-free representation.