Culturally transmitted color categories in LLMs reflect a learning bias toward efficient compression

Converging evidence suggests that systems of semantic categories across human languages achieve near-optimal compression via the Information Bottleneck (IB) complexity-accuracy principle. Large language models (LLMs) are not trained for this objective, which raises the question: are LLMs capable of evolving efficient human-like semantic systems? To address this question, we focus on the domain of color as a key testbed of cognitive theories of categorization and replicate with LLMs (Gemini 2.0-flash and Llama 3.3-70B-Instruct) two influential human behavioral studies. First, we conduct an English color-naming study, showing that Gemini aligns well with the naming patterns of native English speakers and achieves a significantly high IB-efficiency score, while Llama exhibits an efficient but lower complexity system compared to English. Second, to test whether LLMs simply mimic patterns in their training data or actually exhibit a human-like inductive bias toward IB-efficiency, we simulate cultural evolution of pseudo color-naming systems in LLMs via iterated in-context language learning. We find that akin to humans, LLMs iteratively restructure initially random systems towards greater IB-efficiency and increased alignment with patterns observed across the world's languages. These findings demonstrate that LLMs are capable of evolving perceptually grounded, human-like semantic systems, driven by the same fundamental principle that governs semantic efficiency across human languages.