LLMs encode, convey, and perpetuate stereotypes. Prior computational research focuses on a small set of semantic axes investigated in social psychology, and operates on word embeddings produced by language models, leaving open which other semantic axes carry stereotypical associations in LLMs and how LLMs internally represent such axes. We introduce STEREODISCO, a framework that adapts the semantic differential method (Osgood et al., 1957) to the systematic study of stereotypes in LLM internal representations. STEREODISCO constructs approx. 2,000 candidate semantic axes from WordNet antonym synsets, recovers each as a geometric axis in the LLM's activation space via probing, and identifies stereotypical axes via a statistical test over concept projections. As a case study, we apply STEREODISCO to social group stereotypes with LLAMA-3-8B-INSTRUCT and MISTRAL-7B-INSTRUCT. We find that the two LLMs agree with each other on social group ratings more than with humans, suggesting that LLM-encoded stereotype content diverges from that documented in social psychology. We also discover stereotypical axes not investigated in prior work -- including humble vs. proud, narrow-minded vs. broad-minded, and cowardly vs. brave, which human annotators independently confirm.

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