Convex Conceptual Regions in Neural Representations

Thesis Supervision, University of Freiburg, July 2026.

• Deuerlein's Bachelor thesis

• Code

A geometric view of conceptual representation holds that concepts are represented as regions in an internal similarity space, and natural concepts as convex regions of that space. Building on this idea, recent work has shown that the decision regions of trained artificial neural networks become increasingly convex across processing layers. Whether biological neural populations exhibit comparable convex organization, however, has not yet been directly tested. We adapt the graph-based convexity framework of Tětková et al. to neural spiking data and apply it to the IBL Brainwide Map dataset, in which mice perform a perceptual decision-making task. We measure convexity of population activity with respect to the animal's choice, using time within the decision interval as a substitute for the layer depth available in artificial networks. We find that brainwide convexity of recorded population activity rises from near baseline at stimulus onset to substantially elevated values as the decision is expressed. It emerges across all regions examined but differs in timing and magnitude, and convex representation is positively associated with decision accuracy. These results indicate that convex organization of choice-related representations is a feature of biological neural populations, not only of artificial ones.