# Correctness Is a Direction: Geometric Answer Selection in Language Models

arXiv: https://arxiv.org/abs/2610.04512 · HTML: https://mlsanity.com/paper/2610.04512/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 27 references that are in the map.
- First posted on arXiv 3 Oct 2026.

## Builds on (most cited first, 24 of 24)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [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)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [BERT Rediscovers the Classical NLP Pipeline](https://mlsanity.com/paper/1905.05950/) (2019)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [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)
- [SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models](https://mlsanity.com/paper/2303.08896/) (2023)
- [Discovering Latent Knowledge in Language Models Without Supervision](https://mlsanity.com/paper/2212.03827/) (2022)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [DoLa: Decoding by Contrasting Layers Improves Factuality in Large Language Models](https://mlsanity.com/paper/2309.03883/) (2023)
- [INSIDE: LLMs' Internal States Retain the Power of Hallucination Detection](https://mlsanity.com/paper/2402.03744/) (2024)
- [LLMs Know More Than They Show: On the Intrinsic Representation of LLM Hallucinations](https://mlsanity.com/paper/2410.02707/) (2024)
- [Is MAP Decoding All You Need? The Inadequacy of the Mode in Neural Machine Translation](https://mlsanity.com/paper/2005.10283/) (2020)

## Abstract (arXiv)

Answer correctness is encoded as a recoverable geometric direction in the hidden states of language models. We show that the mean displacement from incorrect to correct answer representations, computed at approximately 70% of model depth from fifty labeled examples with no parameter updates, yields a scoring direction that outperforms zero-shot log-probability scoring by up to +32.0 percentage points on factual benchmarks (ARC-Challenge and MMLU) and by +38.1 to +51.8 percentage points on TruthfulQA, across five models spanning 1B to 8B parameters in three architecture families (Llama, Qwen, Gemma). The method requires one forward pass and one dot product per candidate; no generation is performed at inference. Applied as a hallucination detector on individual (question, answer) pairs, the recovered direction achieves 0.693~AUROC versus 0.578 for log-probability scoring. We additionally find that correctness directions for factual reasoning, domain knowledge, and calibrated truthfulness are near-orthogonal in representation space, revealing that language models allocate geometrically independent subspaces to qualitatively distinct notions of correct answer, with architecture-dependent variation in the degree of separation. This structure explains the observed transfer pattern---the direction calibrated on factual questions transfers within task type but not across it---and suggests that LLM calibration failures may reflect a routing problem: the model's internal representation contains more correctness signal than its output behaviour exploits.