Large Language Models (LLMs) have shown impressive capabilities in natural language understanding and reasoning; however, their internal conceptual organization remains largely opaque. This study introduces a novel prompt engineering approach to explore the latent conceptual spaces of LLMs by identifying maximally divergent conceptual regions. It draws on the conceptual spaces framework, in which knowledge is represented as geometric regions defined by quality dimensions. Within this framework, a proxy metric referred to as the conceptual divergence count is proposed. This metric represents the number of maximally divergent conceptual regions identified through structured prompts. Although the metric does not measure dimensionality in the geometric or architectural sense, it serves as an indicator of a model’s conceptual diversity. The method is applied to a range of LLMs, including models from the Gemini, GPT, and Claude families, as well as additional models such as Llama-3.3-70B-Instruct, Mistral-7B-Instruct-v0.3, Gemma-3-12B-IT, and Grok-3. The results show substantial variation in diversity, with gemini-2.5-flash-preview-05-20 achieving the highest value of 91 and claude-3-7-sonnet-20250219 recording the lowest value of 7. These findings suggest that diversity, as measured by this method, may provide insights into the internal organization of conceptual representations. While the metric is to be an indicator of a model’s factual knowledge structure, providing complementary insight into its internal organization, it does not directly measure knowledge accuracy. The proposed approach contributes a geometric perspective to the evaluation of LLM knowledge, complementing existing benchmarks and supporting interpretability.

conceptual spaces, prompt engineering, knowledge representation, interpretability, conceptual regions, maximally divergent, factual knowledge capacity