# The Confidence Manifold: Geometric Structure of Correctness Representations in Language Models

arXiv: https://arxiv.org/abs/2602.08159 · HTML: https://mlsanity.com/paper/2602.08159/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Probing deception, bias and beliefs, one of 13 directions in Mechanistic interpretability.
- Builds on 43 of its 56 references that are in the map.
- First posted on arXiv 8 Feb 2026.

## Placed in

- Mechanistic interpretability / [Probing deception, bias and beliefs](https://mlsanity.com/mechinterp/probing-deception-bias-and-beliefs/)

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

- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [FEVER: a large-scale dataset for Fact Extraction and VERification](https://mlsanity.com/paper/1803.05355/) (2018)
- [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)
- [FActScore: Fine-grained Atomic Evaluation of Factual Precision in Long Form Text Generation](https://mlsanity.com/paper/2305.14251/) (2023)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (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)
- [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)
- [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)
- [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)
- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2](https://mlsanity.com/paper/2408.05147/) (2024)
- [Finding Neurons in a Haystack: Case Studies with Sparse Probing](https://mlsanity.com/paper/2305.01610/) (2023)
- [Emergent Linear Representations in World Models of Self-Supervised Sequence Models](https://mlsanity.com/paper/2309.00941/) (2023)
- [Calibration of Pre-trained Transformers](https://mlsanity.com/paper/2003.07892/) (2020)
- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [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)
- [Not All Language Model Features Are One-Dimensionally Linear](https://mlsanity.com/paper/2405.14860/) (2024)
- [Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretability](https://mlsanity.com/paper/2301.04709/) (2023)
- [The Geometry of Categorical and Hierarchical Concepts in Large Language Models](https://mlsanity.com/paper/2406.01506/) (2024)
- [The Troubling Emergence of Hallucination in Large Language Models -- An Extensive Definition, Quantification, and Prescriptive Remediations](https://mlsanity.com/paper/2310.04988/) (2023)
- [Interpretability at Scale: Identifying Causal Mechanisms in Alpaca](https://mlsanity.com/paper/2305.08809/) (2023)

## Built on by (most cited first, 4 of 4)

- [A decodability criterion predicts when hidden-state selection beats majority voting in large language models](https://mlsanity.com/paper/2608.17124/) (2026)
- [The Geometry of Forgetting: Temporal Knowledge Drift as an Independent Axis in LLM Representations](https://mlsanity.com/paper/2605.09195/) (2026)
- [On the Robustness of LLMs' Internal Representation of Code Correctness](https://mlsanity.com/paper/2608.08266/) (2026)
- [Vision-Language Model Confidence Is Not a Property of the Answer](https://mlsanity.com/paper/2608.06571/) (2026)

## Abstract (arXiv)

When a language model asserts that "the capital of Australia is Sydney," does it know this is wrong? Models assert misconceptions with the same fluency as facts, so the question cannot be answered from output uncertainty. Truth-related signals are known to exist in the residual stream, but not their geometry: how many dimensions carry the signal, how simple a detector can be, and whether it transfers. We characterize this geometry across 11 models (124M-14B) and test it causally with activation steering, concept erasure, and distributed alignment search. The structure is simple: two class centroids in a 2-8 dimensional subspace match a trained linear probe, and 25 labeled examples recover 90% of full-data AUC on GPT-2. Steering shifts hallucination rates by 9.1 points on six models, erasure drops detection to chance, and distributed alignment search, the only method that bounds rank, localizes at most five causal dimensions. The internal advantage is regime-specific: probes far outperform P(True) and semantic entropy on adversarial misconceptions but tie on standard QA. Single-dataset probes transfer near-randomly until joint multi-dataset training restores 0.73-0.91 AUC. That centroid distance matches probe performance indicates class separation is a mean shift, making detection geometric rather than learned.