# Recognition-Refusal Misalignment in LLMs: Why Models Answer Structurally Unanswerable Questions

arXiv: https://arxiv.org/abs/2608.29109 · HTML: https://mlsanity.com/paper/2608.29109/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 37 references that are in the map.
- First posted on arXiv 29 Aug 2026.

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

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Know What You Don't Know: Unanswerable Questions for SQuAD](https://mlsanity.com/paper/1806.03822/) (2018)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [Refusal in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2406.11717/) (2024)
- [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 Latent Knowledge in Language Models Without Supervision](https://mlsanity.com/paper/2212.03827/) (2022)
- [Phi-4-Mini Technical Report: Compact yet Powerful Multimodal Language Models via Mixture-of-LoRAs](https://mlsanity.com/paper/2503.01743/) (2025)
- [LLMs Know More Than They Show: On the Intrinsic Representation of LLM Hallucinations](https://mlsanity.com/paper/2410.02707/) (2024)
- [Selective Question Answering under Domain Shift](https://mlsanity.com/paper/2006.09462/) (2020)
- [Programming Refusal with Conditional Activation Steering](https://mlsanity.com/paper/2409.05907/) (2024)
- [Probing the Probing Paradigm: Does Probing Accuracy Entail Task Relevance?](https://mlsanity.com/paper/2005.00719/) (2020)
- [AbstentionBench: Reasoning LLMs Fail on Unanswerable Questions](https://mlsanity.com/paper/2506.09038/) (2025)
- [The Geometry of Refusal in Large Language Models: Concept Cones and Representational Independence](https://mlsanity.com/paper/2502.17420/) (2025)
- [Still No Lie Detector for Language Models: Probing Empirical and Conceptual Roadblocks](https://mlsanity.com/paper/2307.00175/) (2023)
- [Won't Get Fooled Again: Answering Questions with False Premises](https://mlsanity.com/paper/2307.02394/) (2023)
- [Which Linguist Invented the Lightbulb? Presupposition Verification for Question-Answering](https://mlsanity.com/paper/2101.00391/) (2021)
- [SafeSwitch: Steering Unsafe LLM Behavior via Internal Activation Signals](https://mlsanity.com/paper/2502.01042/) (2025)
- [Large Language Models Struggle with Unreasonability in Math Problems](https://mlsanity.com/paper/2403.19346/) (2024)
- [Identifying and Transferring Reasoning-Critical Neurons: Improving LLM Inference Reliability via Activation Steering](https://mlsanity.com/paper/2601.19847/) (2026)
- [The Geometry of Harmful Intent: Training-Free Anomaly Detection via Angular Deviation in LLM Residual Streams](https://mlsanity.com/paper/2603.27412/) (2026)
- [Geometric Deviation as an Unsupervised Pre-Generation Reliability Signal: Probing LLM Representations for Answerability](https://mlsanity.com/paper/2605.03196/) (2026)

## Abstract (arXiv)

Large language models often answer structurally unanswerable questions, such as computing cot(-540deg) or evaluating (1).startswith("1"), instead of abstaining. We ask whether this failure reflects missing recognition or failed routing from recognition to abstention. Across instruction-tuned models from 1.7B to 70B parameters, a single linear direction in the hidden state separates answerable from structurally impossible math and code prompts, showing that models represent impossibility before generation. Yet this recognition direction is nearly orthogonal to the canonical safety-refusal direction that mediates trained harmful-content refusal. An in-domain behavior-defined invalidity-aware direction is closer to recognition, but only partially aligned with it, and remains near-orthogonal to safety refusal. Generation-time steering along the recognition direction changes invalidity-aware behavior bidirectionally and dose-responsively on structural math and code cells, while random directions do not. Base/instruct comparisons further show that the low-cosine geometry is already present at the pretraining endpoint. The confident-on-impossible failure is therefore better explained as a routing failure than as an encoding failure: the model has a usable "no admissible answer" signal, but the safety-refusal pathway is not aligned to use it.