On convexity and efficiency in semantic systems

2026-02-09

AI Summary

This study investigates the relationship between convexity and communicative efficiency in semantic categorization systems, clarifying whether they are causally linked or conceptually independent. Within the information bottleneck (IB) framework, and integrating conceptual space modeling, computational simulations, and cross-linguistic color naming data, the work provides the first rigorous demonstration that convexity and efficiency are conceptually distinct. It further shows that communicative efficiency serves as a superior explanatory principle: while IB-optimal systems often exhibit convexity, efficiency robustly discriminates between real and hypothetical semantic systems, whereas convexity alone offers negligible additional predictive power. These findings indicate that efficiency accounts for a broader range of empirical phenomena beyond the scope of convexity, offering a unified theoretical foundation for the evolution of semantic systems.

Technology Category

• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Natural Language Processing: Lexical Semantics and Morphology
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• convexity
• efficiency
• semantic systems
• color naming
• Information Bottleneck

Innovation

• convexity
• efficiency
• Information Bottleneck
• semantic typology
• color naming