Andrew Lynn (@andrewclynn.bsky.social)

Rarely categorical, always high-dimensional: how the neural code changes along the cortical hierarchy The brain is highly structured both at anatomical and functional levels. However, within individual brain areas, neurons often exhibit very diverse and seemingly disorganized responses. A more careful analysis shows that these neurons can sometimes be grouped together into specialized subpopulations (categorical representations). Organization can also be found at the level of the representational geometry in the activity space, typically in the form of low-dimensional structures. It is still unclear how the geometry in the activity space and the structure of the response profiles of individual neurons are related. Here, we systematically analyzed the geometric and selectivity structure of the neural population from 40+ cortical regions in mice performing a decision-making task (IBL public Brainwide Map data set). We used a reduced-rank regression approach to quantify the selectivity profiles of single neurons and multiple measures of dimensionality to characterize the representational geometry of task variables. We then related these measures within single areas to the position of each area in the sensory-cognitive cortical hierarchy. Our findings reveal that only a few regions (in primary sensory areas) are categorical. When multiple brain areas are considered, we observe clustering that reflects the brain’s large-scale organization. The representational geometry of task variables also changed along the cortical hierarchy, with higher dimensionality in cognitive regions. These trends were explained by analytical computations linking the maximum dimensionality of representational geometry to the clustering of selectivity at the single neuron level. Finally, we computed the shattering dimensionality (SD), a measure of the linear separability of neural activity vectors; remarkably, the SD remained near maximal across all regions, suggesting that the observed variability in the selectivity profiles allows neural populations to maintain high computational flexibility. These results provide a new mathematical and empirical perspective on selectivity and representation geometry in the cortical neural code. ### Competing Interest Statement The authors have declared no competing interest. https://www.biorxiv.org/content/10.1101/2024.11.15.623878v1