# The Geometries of Truth Are Orthogonal Across Tasks

arXiv: https://arxiv.org/abs/2506.08572 · HTML: https://mlsanity.com/paper/2506.08572/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 33 references that are in the map.
- First posted on arXiv 10 Jun 2025.

## Builds on (most cited first, 27 of 27)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Discovering Latent Knowledge in Language Models Without Supervision](https://mlsanity.com/paper/2212.03827/) (2022)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [The Internal State of an LLM Knows When It's Lying](https://mlsanity.com/paper/2304.13734/) (2023)
- [Measuring short-form factuality in large language models](https://mlsanity.com/paper/2411.04368/) (2024)
- [Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMs](https://mlsanity.com/paper/2406.15927/) (2024)
- [LLMs Know More Than They Show: On the Intrinsic Representation of LLM Hallucinations](https://mlsanity.com/paper/2410.02707/) (2024)
- [AI Deception: A Survey of Examples, Risks, and Potential Solutions](https://mlsanity.com/paper/2308.14752/) (2023)
- [Reasoning Models Know When They're Right: Probing Hidden States for Self-Verification](https://mlsanity.com/paper/2504.05419/) (2025)
- [Large Language Models Must Be Taught to Know What They Don't Know](https://mlsanity.com/paper/2406.08391/) (2024)
- [Still No Lie Detector for Language Models: Probing Empirical and Conceptual Roadblocks](https://mlsanity.com/paper/2307.00175/) (2023)
- [Adaptive Activation Steering: A Tuning-Free LLM Truthfulness Improvement Method for Diverse Hallucinations Categories](https://mlsanity.com/paper/2406.00034/) (2024)
- [Do Androids Know They're Only Dreaming of Electric Sheep?](https://mlsanity.com/paper/2312.17249/) (2023)
- [The Curious Case of Hallucinatory (Un)answerability: Finding Truths in the Hidden States of Over-Confident Large Language Models](https://mlsanity.com/paper/2310.11877/) (2023)
- [InternalInspector I2: Robust Confidence Estimation in LLMs through Internal States](https://mlsanity.com/paper/2406.12053/) (2024)
- [Revisiting Uncertainty Quantification Evaluation in Language Models: Spurious Interactions with Response Length Bias Results](https://mlsanity.com/paper/2504.13677/) (2025)
- [Overview of BioASQ 2023: The eleventh BioASQ challenge on Large-Scale Biomedical Semantic Indexing and Question Answering](https://mlsanity.com/paper/2307.05131/) (2023)
- [PAC Prediction Sets for Meta-Learning](https://mlsanity.com/paper/2207.02440/) (2022)

## Built on by (most cited first, 9 of 9)

- [LLM Knowledge is Brittle: Truthfulness Representations Rely on Superficial Resemblance](https://mlsanity.com/paper/2510.11905/) (2025)
- [The Truthfulness Spectrum Hypothesis](https://mlsanity.com/paper/2602.20273/) (2026)
- [Testing the Limits of Truth Directions in LLMs](https://mlsanity.com/paper/2604.03754/) (2026)
- [Simulated Adoption: Decoupling Magnitude and Direction in LLM In-Context Conflict Resolution](https://mlsanity.com/paper/2602.04918/) (2026)
- [Reading Calibrated Uncertainty from Language Model Trajectories](https://mlsanity.com/paper/2605.22864/) (2026)
- [Diagnosing Correctness Probes under Self-Judgement Confounding](https://mlsanity.com/paper/2607.16799/) (2026)
- [The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models](https://mlsanity.com/paper/2606.03645/) (2026)
- [GEMS: Geometric Constraints Enable Multi-Semantic Superposition in LLMs](https://mlsanity.com/paper/2606.19946/) (2026)
- [Toward a Gricean Retreat: Probing LLMs for Knowledge Boundaries and Referent Specificity](https://mlsanity.com/paper/2608.13484/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) have demonstrated impressive generalization capabilities across various tasks, but their claim to practical relevance is still mired by concerns on their reliability. Recent works have proposed examining the activations produced by an LLM at inference time to assess whether its answer to a question is correct. Some works claim that a "geometry of truth" can be learned from examples, in the sense that the activations that generate correct answers can be distinguished from those leading to mistakes with a linear classifier. In this work, we underline a limitation of these approaches: we observe that these "geometries of truth" are intrinsically task-dependent and fail to transfer across tasks. More precisely, we show that linear classifiers trained across distinct tasks share little similarity and, when trained with sparsity-enforcing regularizers, have almost disjoint supports. We show that more sophisticated approaches (e.g., using mixtures of probes and tasks) fail to overcome this limitation, likely because activation vectors commonly used to classify answers form clearly separated clusters when examined across tasks.