# The Truthfulness Spectrum Hypothesis

arXiv: https://arxiv.org/abs/2602.20273 · HTML: https://mlsanity.com/paper/2602.20273/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 45 references that are in the map.
- First posted on arXiv 23 Feb 2026.

## Builds on (most cited first, 30 of 41)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Language Models as Knowledge Bases?](https://mlsanity.com/paper/1909.01066/) (2019)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (2023)
- [Towards Understanding Sycophancy in Language Models](https://mlsanity.com/paper/2310.13548/) (2023)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [Discovering Language Model Behaviors with Model-Written Evaluations](https://mlsanity.com/paper/2212.09251/) (2022)
- [A Primer in BERTology: What we know about how BERT works](https://mlsanity.com/paper/2002.12327/) (2020)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [Discovering Latent Knowledge in Language Models Without Supervision](https://mlsanity.com/paper/2212.03827/) (2022)
- [Aligning AI With Shared Human Values](https://mlsanity.com/paper/2008.02275/) (2020)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [The Internal State of an LLM Knows When It's Lying](https://mlsanity.com/paper/2304.13734/) (2023)
- [Null It Out: Guarding Protected Attributes by Iterative Nullspace Projection](https://mlsanity.com/paper/2004.07667/) (2020)
- [LEACE: Perfect linear concept erasure in closed form](https://mlsanity.com/paper/2306.03819/) (2023)
- [LLMs Know More Than They Show: On the Intrinsic Representation of LLM Hallucinations](https://mlsanity.com/paper/2410.02707/) (2024)
- [LEEP: A New Measure to Evaluate Transferability of Learned Representations](https://mlsanity.com/paper/2002.12462/) (2020)
- [Simple synthetic data reduces sycophancy in large language models](https://mlsanity.com/paper/2308.03958/) (2023)
- [Do the Rewards Justify the Means? Measuring Trade-Offs Between Rewards and Ethical Behavior in the MACHIAVELLI Benchmark](https://mlsanity.com/paper/2304.03279/) (2023)
- [LogME: Practical Assessment of Pre-trained Models for Transfer Learning](https://mlsanity.com/paper/2102.11005/) (2021)
- [Large Language Models can Strategically Deceive their Users when Put Under Pressure](https://mlsanity.com/paper/2311.07590/) (2023)
- [The geometry of hidden representations of large transformer models](https://mlsanity.com/paper/2302.00294/) (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)

## Built on by (most cited first, 8 of 8)

- [LLMs Know They're Wrong and Agree Anyway: The Shared Sycophancy-Lying Circuit](https://mlsanity.com/paper/2604.19117/) (2026)
- [Testing the Limits of Truth Directions in LLMs](https://mlsanity.com/paper/2604.03754/) (2026)
- [Sycophantic Agreement Transfers with Neutral Data via Contrastive Preference Optimization](https://mlsanity.com/paper/2608.31079/) (2026)
- [Semantic Structure of Feature Space in Large Language Models](https://mlsanity.com/paper/2604.27169/) (2026)
- [Temporal Preference Concepts and their Functions in a Large Language Model](https://mlsanity.com/paper/2606.05194/) (2026)
- [Toward a Graded Measure of Belief Stability in Large Language Models](https://mlsanity.com/paper/2609.34158/) (2026)
- [Tracing mechanisms of sycophantic agreement in language models](https://mlsanity.com/paper/2609.35822/) (2026)
- [Evaluating Persistent Calibration under Evolving Model Knowledge](https://mlsanity.com/paper/2609.38797/) (2026)

## Abstract (arXiv)

Large language models (LLMs) have been reported to linearly encode truthfulness, yet recent work questions this finding's generality. We reconcile these views with the truthfulness spectrum hypothesis: the representational space contains directions ranging from broadly domain-general to narrowly domain-specific. To test this hypothesis, we systematically evaluate probe generalization across five truth types (definitional, empirical, logical, fictional, and ethical), sycophantic and expectation-inverted lying, and existing honesty benchmarks. Linear probes generalize well across most domains but fail on sycophantic and expectation-inverted lying. Yet training on all domains jointly recovers strong performance, confirming that domain-general directions exist despite poor pairwise transfer. The geometry of probe directions explains these patterns: Mahalanobis cosine similarity between probes near-perfectly predicts cross-domain generalization (R^2=0.98). Concept-erasure methods further isolate truth directions that are (1) domain-general, (2) domain-specific, or (3) shared only across particular domain subsets. Causal interventions reveal that domain-specific directions steer more effectively than domain-general ones. Finally, post-training reshapes truth geometry, pushing sycophantic lying further from other truth types, suggesting a representational basis for chat models' sycophantic tendencies. Together, our results support the truthfulness spectrum hypothesis: truth directions of varying generality coexist in representational space, with post-training reshaping their geometry. Code for all experiments is provided in https://github.com/zfying/truth_spec.