Abstract
There are two widely held characterizations of human semantic category systems: (1) they form convex partitions of conceptual spaces, and (2) they are efficient for communication. While prior work observed that convexity and efficiency co-occur in color naming, the analytical relation between them and why they co-occur have not been well understood. We address this gap by combining analytical and empirical analyses that build on the Information Bottleneck (IB) framework for semantic efficiency. First, we show that convexity and efficiency are distinct in the sense that neither entails the other: there are convex systems which are inefficient, and optimally-efficient systems that are non-convex. Crucially, however, the IB-optimal systems are mostly convex in the domain of color naming, explaining the main empirical basis for the convexity approach. Second, we show that efficiency is a stronger predictor for discriminating attested color naming systems from hypothetical variants, with convexity adding negligible improvement on top of that. Finally, we discuss a range of empirical phenomena that convexity cannot account for but efficiency can. Taken together, our work suggests that while convexity and efficiency can yield similar structural observations, they are fundamentally distinct, with efficiency providing a more comprehensive account of semantic typology.
Figure 3 from the paper. (a) IB trade-off for human color naming systems (blue circles) from the World Color Survey and a large sample of artificial convex systems (gray circles). Black circles indicate costly convex systems, visualized in (e-g). (b) Same systems in (a), with 𝑘 (number of major terms) vs. communicative cost. (c,d) Example human color naming system (Buglere, Panama) and its fitted IB system. (e-g) Three example convex, inefficient category systems as partitions in the 2D WCS grid (top row) and convex hulls in the 3D CIELAB color space (bottom row). Interactive versions of these figures and additional systems can be viewed in our SM interactive app.
Interactive Demo
Visit our interactive web application below, where you can explore convex color naming systems in 3D visualizations.
BibTeX
@inproceedings{
imel2026convexity,
title = {On Convexity and Efficiency in Semantic Systems},
author = {Nathaniel Imel and Noga Zaslavsky},
year = {2026},
booktitle = {Proceedings of the 47th Annual Meeting of the Cognitive Science Society},
url = {https://arxiv.org/abs/2602.08238},
}