In this paper, we focus on the challenging task of reliably estimating factual knowledge that is embedded inside large language models (LLMs). To avoid reliability concerns with prior approaches, we propose to eliminate prompt engineering when probing LLMs for factual knowledge. Our approach, called Zero-Prompt Latent Knowledge Estimator (ZP-LKE), leverages the in-context learning ability of LLMs to communicate both the factual knowledge question as well as the expected answer format. Our knowledge estimator is both conceptually simpler (i.e., doesn't depend on meta-linguistic judgments of LLMs) and easier to apply (i.e., is not LLM-specific), and we demonstrate that it can surface more of the latent knowledge embedded in LLMs. We also investigate how different design choices affect the performance of ZP-LKE. Using the proposed estimator, we perform a large-scale evaluation of the factual knowledge of a variety of open-source LLMs, like OPT, Pythia, Llama(2), Mistral, Gemma, etc. over a large set of relations and facts from the Wikidata knowledge base. We observe differences in the factual knowledge between different model families and models of different sizes, that some relations are consistently better known than others but that models differ in the precise facts they know, and differences in the knowledge of base models and their finetuned counterparts. Code available at: https://github.com/QinyuanWu0710/ZeroPrompt_LKE

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