---
title: "The Geometry of Truth — Marks 2023"
description: "LLMs sometimes state things that are false even when they seem to \"know\" better."
authors: ["Samuel Marks", "Max Tegmark"]
year: 2023
venue: "arXiv:2310.06824"
source: "https://arxiv.org/abs/2310.06824"
doi: "10.48550/arxiv.2310.06824"
arxiv: "2310.06824"
licence: "CC BY 4.0 (arXiv)"
licence_url: "http://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/marks-2023-geometry-truth-emergent-linear-structure/"
---
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# The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets

**Authors:** Samuel Marks, Max Tegmark · **Year:** 2023 · **Venue:** arXiv:2310.06824 · **Licence:** [CC BY 4.0 (arXiv)](http://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://arxiv.org/abs/2310.06824) · [PDF](https://arxiv.org/pdf/2310.06824) · [DOI 10.48550/arxiv.2310.06824](https://doi.org/10.48550/arxiv.2310.06824) · [arXiv 2310.06824](https://arxiv.org/abs/2310.06824) · [OpenAlex](https://openalex.org/W4387561538)

**Citations:** 20 citations (openalex-snapshot · 2026-10-14) · [139](#cited-by) in our library, of the 140673 papers whose bibliographies we read

## Summary
LLMs sometimes state things that are false even when they seem to "know" better. Earlier attempts to detect truthfulness by probing internal activations generalized poorly, which raised doubts about whether those probes found truth or only features that correlate with it. Marks and Tegmark study this question in LLaMA-2 models. They use curated sets of short, unambiguous factual statements (city locations, Spanish–English word translations, number comparisons), along with negated, conjunctive and disjunctive versions of them. They add noisier uncurated sets from earlier work and a likely control set, which separates truth from how probable the text is. Patching experiments first show which hidden states matter most: those over the statement's last token and its closing punctuation. In PCA projections of these states, true and false statements separate along a clear linear axis. Probes trained on one dataset carry over to others, and shifting activations along a probe direction flips the model's TRUE/FALSE judgments. The authors conclude that sufficiently large models encode factual truth linearly. They propose mass-mean (difference-in-means) probing, a simple method that finds the most causally relevant directions.

## Key points
- **Datasets:** the curated sets include cities (1,496 statements), sp_en_trans (354), larger_than and smaller_than (1,980 each), and neg_*, conj and disj variants. The uncurated sets are companies_true_false (1,200), common_claim_true_false (4,450) and counterfact_true_false (31,960). The likely control set has 10,000 nonfactual texts whose final token is either LLaMA-13B's top completion or its 100th most likely one.
- **Truth is not the same as probability:** in LLaMA-2-70B, a statement's truth and its log-probability are negatively correlated for neg_cities (r = −.63) and neg_sp_en_trans (r = −.89). For the non-negated sets the correlation is positive (.85 and .95). Because of this split, the linear structure cannot simply be a "likely text" signal.
- **Where truth is stored:** patching on LLaMA-2-13B finds three groups of causally important states: the subject entity, the summary over the end of the statement, and the final prediction. The truth representation sits in the middle group.
- **Causal tests:** interventions were scored on sp_en_trans with normalized indirect effects (NIE). Mass-mean directions beat logistic regression (LR) and CCS in 7 of 8 settings. For LLaMA-2-70B they reach NIE ≈ 1, meaning the swap was essentially complete.
- **Resources and limits:** the code, datasets and an interactive data explorer are at github.com/saprmarks/geometry-of-truth. Only LLaMA-2 models were tested, and simple statements cannot separate "true" from related ideas such as "commonly believed".

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

Fields: [AI & machine learning](https://md.research.elamur.ai/free/en/shelves/ai/)

## Cited by

Cited by

139 papers of our library cite it (of the 140673 whose bibliographies we read); 5 of them have a page here, 134 not yet.

- [Refusal in Language Models Is Mediated by a Single Direction](https://md.research.elamur.ai/free/en/papers/arditi-2024-refusal-language-models-mediated-single/)
- [In-Distribution Steering: Balancing Control and Coherence in Language Model Generation](https://md.research.elamur.ai/free/en/papers/vogels-2026-distribution-steering-balancing-control-coherence/)
- [Do Llamas Work in English? On the Latent Language of Multilingual Transformers](https://md.research.elamur.ai/free/en/papers/wendler-2024-do-llamas-work-english-latent/)
- [Rhetorical Questions in LLM Representations: A Linear Probing Study](https://md.research.elamur.ai/free/en/papers/yao-2026-rhetorical-questions-llm-representations-linear/)
- [Explainability for Large Language Models: A Survey](https://md.research.elamur.ai/free/en/papers/zhao-2023-explainability-large-language-models-survey/)

## Cite

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@misc{marks2023geometry,
  title = {{The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets}},
  author = {Marks, Samuel and Tegmark, Max},
  year = {2023},
  doi = {10.48550/arxiv.2310.06824},
  eprint = {2310.06824},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2310.06824}
}
```

- [← previous The Flan Collection: Designing Data and Methods for Effective Instruction Tuning](https://md.research.elamur.ai/free/en/papers/longpre-2023-flan-collection-designing-data-methods/)
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- [↑ back to papers of 2023](https://md.research.elamur.ai/free/en/papers/2023/page/7/)

## References

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40. Andy Zou, Long Phan, Sarah Chen, James Campbell, Phillip Guo, Richard Ren, Alexander Pan, Xuwang Yin, Mantas Mazeika, Ann-Kathrin Dombrowski, Shashwat Goel, Nathaniel Li, Michael J. Byun, Zifan Wang, Alex Mallen, Steven Basart, Sanmi Koyejo, Dawn Song, Matt Fredrikson, J. Zico Kolter, and Dan Hendry… [find](https://scholar.google.com/scholar?q=Andy+Zou%2C+Long+Phan%2C+Sarah+Chen%2C+James+Campbell%2C+Phillip+Guo%2C+Richard+Ren%2C+Alexander+Pan%2C+Xuwang+Yin%2C+Mantas+Mazeika%2C+Ann%2DKathrin+Dombrowski%2C+Shashwat+Goel%2C+Nathaniel+Li%2C+Michael+J%2E+Byun%2C+Zifan+Wang%2C+) [our card](https://md.research.elamur.ai/free/en/papers/zou-2023-representation-engineering-top-down-approach/)