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

arXiv: https://arxiv.org/abs/2610.02902 · HTML: https://mlsanity.com/paper/2610.02902/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 43 of its 50 references that are in the map.
- First posted on arXiv 2 Oct 2026.

## Builds on (most cited first, 30 of 43)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Language Models as Knowledge Bases?](https://mlsanity.com/paper/1909.01066/) (2019)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [BERT Rediscovers the Classical NLP Pipeline](https://mlsanity.com/paper/1905.05950/) (2019)
- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Discovering Latent Knowledge in Language Models Without Supervision](https://mlsanity.com/paper/2212.03827/) (2022)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [The Internal State of an LLM Knows When It's Lying](https://mlsanity.com/paper/2304.13734/) (2023)
- [Knowledge Neurons in Pretrained Transformers](https://mlsanity.com/paper/2104.08696/) (2021)
- [Towards Faithfully Interpretable NLP Systems: How should we define and evaluate faithfulness?](https://mlsanity.com/paper/2004.03685/) (2020)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [How Can We Know When Language Models Know? On the Calibration of Language Models for Question Answering](https://mlsanity.com/paper/2012.00955/) (2020)
- [The Reversal Curse: LLMs trained on "A is B" fail to learn "B is A"](https://mlsanity.com/paper/2309.12288/) (2023)
- [DataComp-LM: In search of the next generation of training sets for language models](https://mlsanity.com/paper/2406.11794/) (2024)
- [Studying Large Language Model Generalization with Influence Functions](https://mlsanity.com/paper/2308.03296/) (2023)
- [The Alignment Problem from a Deep Learning Perspective](https://mlsanity.com/paper/2209.00626/) (2022)
- [RealTime QA: What's the Answer Right Now?](https://mlsanity.com/paper/2207.13332/) (2022)
- [LLMs Know More Than They Show: On the Intrinsic Representation of LLM Hallucinations](https://mlsanity.com/paper/2410.02707/) (2024)
- [Linearity of Relation Decoding in Transformer Language Models](https://mlsanity.com/paper/2308.09124/) (2023)
- [Causal Mediation Analysis for Interpreting Neural NLP: The Case of Gender Bias](https://mlsanity.com/paper/2004.12265/) (2020)
- [A Careful Examination of Large Language Model Performance on Grade School Arithmetic](https://mlsanity.com/paper/2405.00332/) (2024)

## Abstract (arXiv)

Current analyses of LLMs' parametric knowledge are largely output-centric, drawing conclusions about what a model knows without verifying what it was actually trained on. This leaves fundamental questions, such as whether a correct response reflects genuine generalization or rote memorization, grounded in speculation rather than evidence. To resolve these ambiguities, we introduce LUMOS, a diagnostic framework that traces knowledge along the causal chain from training-data exposure to behavioral output, leveraging OLMo 2 with its fully transparent training corpus. By grounding analysis in verified exposure, we reveal that models internally encode rare facts with high separability (84%) yet fail to express them behaviorally (54%), though this retrieval gap narrows with scale. Furthermore, when models are asked to self-reflect on their own answers, they perform reliably on trained content (83%) but drop to random-baseline levels (49%) on unseen content. This collapse persists even under chain-of-thought prompting, which inflates confidence signals rather than improving calibration. Collectively, these findings demonstrate that incorporating the training-data axis into LLM evaluation transforms speculative diagnoses into verifiable claims, and we advocate that this axis should be a standard component of knowledge assessment in LLMs.