# Detecting (Un)answerability in Large Language Models with Linear Directions

arXiv: https://arxiv.org/abs/2509.22449 · HTML: https://mlsanity.com/paper/2509.22449/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 39 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Builds on (most cited first, 25 of 25)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [ALBERT: A Lite BERT for Self-supervised Learning of Language Representations](https://mlsanity.com/paper/1909.11942/) (2019)
- [Know What You Don't Know: Unanswerable Questions for SQuAD](https://mlsanity.com/paper/1806.03822/) (2018)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [Man is to Computer Programmer as Woman is to Homemaker? Debiasing Word Embeddings](https://mlsanity.com/paper/1607.06520/) (2016)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (2023)
- [BERT Rediscovers the Classical NLP Pipeline](https://mlsanity.com/paper/1905.05950/) (2019)
- [Refusal in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2406.11717/) (2024)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Do Large Language Models Know What They Don't Know?](https://mlsanity.com/paper/2305.18153/) (2023)
- [Don't Hallucinate, Abstain: Identifying LLM Knowledge Gaps via Multi-LLM Collaboration](https://mlsanity.com/paper/2402.00367/) (2024)
- [Probing Pretrained Language Models for Lexical Semantics](https://mlsanity.com/paper/2010.05731/) (2020)
- [Can Large Language Models Faithfully Express Their Intrinsic Uncertainty in Words?](https://mlsanity.com/paper/2405.16908/) (2024)
- [Retrospective Reader for Machine Reading Comprehension](https://mlsanity.com/paper/2001.09694/) (2020)
- [CREPE: Open-Domain Question Answering with False Presuppositions](https://mlsanity.com/paper/2211.17257/) (2022)
- [Knowledge of Knowledge: Exploring Known-Unknowns Uncertainty with Large Language Models](https://mlsanity.com/paper/2305.13712/) (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)
- [Uncertainty-Based Abstention in LLMs Improves Safety and Reduces Hallucinations](https://mlsanity.com/paper/2404.10960/) (2024)
- [RepLiQA: A Question-Answering Dataset for Benchmarking LLMs on Unseen Reference Content](https://mlsanity.com/paper/2406.11811/) (2024)
- [The Reasoning-Memorization Interplay in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2503.23084/) (2025)
- [Do Sparse Autoencoders Generalize? A Case Study of Answerability](https://mlsanity.com/paper/2502.19964/) (2025)
- [Line of Duty: Evaluating LLM Self-Knowledge via Consistency in Feasibility Boundaries](https://mlsanity.com/paper/2503.11256/) (2025)
- [Pretrained LLMs Learn Multiple Types of Uncertainty](https://mlsanity.com/paper/2505.21218/) (2025)

## Built on by (most cited first, 13 of 13)

- [I-CALM: Incentivizing Confidence-Aware Abstention for LLM Selective Answering](https://mlsanity.com/paper/2604.03904/) (2026)
- [Two Axes of LLM Abstention: Answer Correctness and Question Answerability](https://mlsanity.com/paper/2607.08456/) (2026)
- [Hyperparameter Transfer in Graph Neural Networks](https://mlsanity.com/paper/2607.05017/) (2026)
- [STEREODISCO: Discovering Stereotypicality in LLMs](https://mlsanity.com/paper/2607.27824/) (2026)
- [Bounding Hallucinations: Merlin-Arthur Protocols for Mutual-Information Bounds in Language Models](https://mlsanity.com/paper/2512.11614/) (2025)
- [CORE: Comprehensive Ontological Relation Evaluation for Large Language Models](https://mlsanity.com/paper/2602.06446/) (2026)
- [Bridging the Know-Act Gap via Task-Level Autoregressive Reasoning](https://mlsanity.com/paper/2603.22619/) (2026)
- [TIPS: Topological Ill-Posedness Probing and Steering in Large Language Models](https://mlsanity.com/paper/2606.23590/) (2026)
- [You Only Pass Once: Answering and Abstaining Together in a Single Forward Pass of a Frozen Language Model](https://mlsanity.com/paper/2608.14465/) (2026)
- [Who Do Language Models Think Is Competent? A Mechanistic Analysis of Occupational Bias](https://mlsanity.com/paper/2608.20347/) (2026)
- [From Reweighting to Rewriting: Unlocking the Intervention Effects of Influential Samples in Training Data Attribution](https://mlsanity.com/paper/2609.02771/) (2026)
- [Before Answering: Evidence Sufficiency under Size-Matched Memory Construction](https://mlsanity.com/paper/2609.32269/) (2026)
- [The Commit-Abstain Circuit: Why Language Models Hallucinate Instead of Abstaining](https://mlsanity.com/paper/2609.32964/) (2026)

## Abstract (arXiv)

Large language models (LLMs) often respond confidently to questions even when they lack the necessary information, leading to hallucinated answers. In this work, we study the problem of (un)answerability detection, focusing on extractive question answering (QA) where the model should determine if a passage contains sufficient information to answer a given question. We propose a simple approach for identifying a direction in the model's activation space that captures unanswerability and uses it for classification. This direction is selected by applying activation additions during inference and measuring their impact on the model's abstention behavior. We show that projecting hidden activations onto this direction yields a reliable score for (un)answerability classification. Experiments on two open-weight LLMs and four extractive QA benchmarks show that our method effectively detects unanswerable questions and generalizes better across datasets than existing prompt-based and classifier-based approaches. Moreover, the obtained directions extend beyond extractive QA to unanswerability that stems from factors, such as lack of scientific consensus and subjectivity. Last, causal interventions show that adding or ablating the directions effectively controls the abstention behavior of the model.