# Probing the Geometry of Truth: Consistency and Generalization of Truth Directions in LLMs Across Logical Transformations and Question Answering Tasks

arXiv: https://arxiv.org/abs/2506.00823 · HTML: https://mlsanity.com/paper/2506.00823/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 41 references that are in the map.
- First posted on arXiv 1 Jun 2025.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Don't Give Me the Details, Just the Summary! Topic-Aware Convolutional Neural Networks for Extreme Summarization](https://mlsanity.com/paper/1808.08745/) (2018)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [Discovering Latent Knowledge in Language Models Without Supervision](https://mlsanity.com/paper/2212.03827/) (2022)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Truthful AI: Developing and governing AI that does not lie](https://mlsanity.com/paper/2110.06674/) (2021)
- [How Alignment and Jailbreak Work: Explain LLM Safety through Intermediate Hidden States](https://mlsanity.com/paper/2406.05644/) (2024)
- [How to Catch an AI Liar: Lie Detection in Black-Box LLMs by Asking Unrelated Questions](https://mlsanity.com/paper/2309.15840/) (2023)
- [Overthinking the Truth: Understanding how Language Models Process False Demonstrations](https://mlsanity.com/paper/2307.09476/) (2023)
- [Truth is Universal: Robust Detection of Lies in LLMs](https://mlsanity.com/paper/2407.12831/) (2024)
- [Still No Lie Detector for Language Models: Probing Empirical and Conceptual Roadblocks](https://mlsanity.com/paper/2307.00175/) (2023)
- [Do Androids Know They're Only Dreaming of Electric Sheep?](https://mlsanity.com/paper/2312.17249/) (2023)
- [Eliciting Latent Knowledge from Quirky Language Models](https://mlsanity.com/paper/2312.01037/) (2023)
- [Cognitive Dissonance: Why Do Language Model Outputs Disagree with Internal Representations of Truthfulness?](https://mlsanity.com/paper/2312.03729/) (2023)
- [Factual Confidence of LLMs: on Reliability and Robustness of Current Estimators](https://mlsanity.com/paper/2406.13415/) (2024)
- [Personas as a Way to Model Truthfulness in Language Models](https://mlsanity.com/paper/2310.18168/) (2023)
- [Probing Classifiers are Unreliable for Concept Removal and Detection](https://mlsanity.com/paper/2207.04153/) (2022)
- [Linguistic Properties of Truthful Response](https://mlsanity.com/paper/2305.15875/) (2023)

## Built on by (most cited first, 18 of 18)

- [No Answer Needed: Predicting LLM Answer Accuracy from Question-Only Linear Probes](https://mlsanity.com/paper/2509.10625/) (2025)
- [The Truthfulness Spectrum Hypothesis](https://mlsanity.com/paper/2602.20273/) (2026)
- [Bridging the Knowledge-Prediction Gap in LLMs on Multiple-Choice Questions](https://mlsanity.com/paper/2509.23782/) (2025)
- [Streaming Hallucination Detection in Long Chain-of-Thought Reasoning](https://mlsanity.com/paper/2601.02170/) (2026)
- [Testing the Limits of Truth Directions in LLMs](https://mlsanity.com/paper/2604.03754/) (2026)
- [SCOPE: Sequential Conformal Probing for Reliable OOD Rejection in LLM Services](https://mlsanity.com/paper/2606.21255/) (2026)
- [Language Models Encode the Contextual Truth of Propositions](https://mlsanity.com/paper/2608.03035/) (2026)
- [A decodability criterion predicts when hidden-state selection beats majority voting in large language models](https://mlsanity.com/paper/2608.17124/) (2026)
- [How Context Shapes Truth: Geometric Transformations of Statement-level Truth Representations in LLMs](https://mlsanity.com/paper/2601.06599/) (2026)
- [Shared Doubt: Zero-Shot Cross-Lingual Confidence Estimation for Language Models](https://mlsanity.com/paper/2605.31220/) (2026)
- [Diagnosing Correctness Probes under Self-Judgement Confounding](https://mlsanity.com/paper/2607.16799/) (2026)
- [STEREODISCO: Discovering Stereotypicality in LLMs](https://mlsanity.com/paper/2607.27824/) (2026)
- [On the Robustness of LLMs' Internal Representation of Code Correctness](https://mlsanity.com/paper/2608.08266/) (2026)
- [The Hallucination Signal Is a Mean Shift: Why Simple Probes Suffice](https://mlsanity.com/paper/2608.28930/) (2026)
- [The Right to Be Remembered: Preserving Maximally Truthful Digital Memory in the Age of AI](https://mlsanity.com/paper/2510.16206/) (2025)
- [Three Concrete Challenges and Two Hopes for the Safety of Unsupervised Elicitation](https://mlsanity.com/paper/2602.20400/) (2026)
- [CAST: Mitigating Object Hallucination in Large Vision-Language Models via Caption-Guided Visual Attention Steering](https://mlsanity.com/paper/2605.04641/) (2026)
- [Wrong Prediction, Right Answer: Recovering Evidence from Collapsed LLM Sequence Scores](https://mlsanity.com/paper/2608.31068/) (2026)

## Abstract (arXiv)

Large language models (LLMs) are trained on extensive datasets that encapsulate substantial world knowledge. However, their outputs often include confidently stated inaccuracies. Earlier works suggest that LLMs encode truthfulness as a distinct linear feature, termed the "truth direction", which can classify truthfulness reliably. We address several open questions about the truth direction: (i) whether LLMs universally exhibit consistent truth directions; (ii) whether sophisticated probing techniques are necessary to identify truth directions; and (iii) how the truth direction generalizes across diverse contexts. Our findings reveal that not all LLMs exhibit consistent truth directions, with stronger representations observed in more capable models, particularly in the context of logical negation. Additionally, we demonstrate that truthfulness probes trained on declarative atomic statements can generalize effectively to logical transformations, question-answering tasks, in-context learning, and external knowledge sources. Finally, we explore the practical application of truthfulness probes in selective question-answering, illustrating their potential to improve user trust in LLM outputs. These results advance our understanding of truth directions and provide new insights into the internal representations of LLM beliefs. Our code is public at https://github.com/colored-dye/truthfulness_probe_generalization