LUMOS: Tracing Parametric Knowledge from Training Data to Behavioral Outputs in LLMs

We study self-modeling: an LLM's ability to answer questions about its own behavior. We focus on verifiable behavioral questions, such as whether a prompt edit would change the model's final answer. To measure this capability, we introduce a benchmark that tests diverse types of self-modeling questions. Current models show non-trivial but limited self-modeling skill, and make systematic mistakes on simple counterfactual questions about their own behavior. To improve self-modeling skill, we develop a scalable synthetic-data pipeline that produces self-modeling training data, and show that reinforcement-learning can improve aggregate self-modeling skill across three open-source model families with some transfer to held-out tasks. These gains, however, do not seem to constitute introspection consistently: improved self-modeling may not arise from privileged access to the model's internal decision process.

How do large language models (LLMs) know what they know? Answering this question has been difficult because pre-training data is often a "black box" - unknown or inaccessible. The recent release of nanochat - a family of small LLMs with fully open pre-training data - addresses this as it provides a transparent view into where a model's parametric knowledge comes from. Towards the goal of understanding how knowledge is encoded by LLMs, we release NanoKnow, a benchmark dataset that partitions questions from Natural Questions and SQuAD into splits based on whether their answers are present in nanochat's pre-training corpus. Using these splits, we can now properly disentangle the sources of knowledge that LLMs rely on when producing an output. To demonstrate NanoKnow's utility, we conduct experiments using eight nanochat checkpoints. Our findings show: (1) closed-book accuracy is strongly influenced by answer frequency in the pre-training data, (2) providing external evidence can mitigate this frequency dependence, (3) even with external evidence, models are more accurate when answers were seen during pre-training, demonstrating that parametric and external knowledge are complementary, and (4) non-relevant information is harmful, with accuracy decreasing based on both the position and the number of non-relevant contexts. We release all NanoKnow artifacts at https://github.com/castorini/NanoKnow.

Parametric knowledge in large language models (LLMs) is a cornerstone of their success, yet remains poorly understood. Existing knowledge benchmarks typically rely on predefined questions (e.g., "What is the birth date of M.L. King?"), evaluating only knowledge that benchmark designers explicitly choose to query, a problematic availability bias. In this paper, we introduce open knowledge evaluation, a new paradigm for benchmarking the stated knowledge of LLMs. Instead of asking narrow questions, it evaluates models on the knowledge they choose to surface in response to open-ended elicitation prompts (e.g., "Tell me everything you know about M.L. King"). This shifts the focus from predefined answer retrieval toward characterizing the knowledge models naturally express. We instantiate this paradigm with BeQu (Beyond Questions), a benchmark of 10,000 entities paired with reference corpora for statement verification. Using BeQu, we evaluate a broad range of language models and analyze the effects of reasoning effort, model scale, prompt format, and knowledge domain. Data and leaderboard are available on this work's GitHub repository and at ANONYMIZED.