Recognition-Refusal Misalignment in LLMs: Why Models Answer Structurally Unanswerable Questions
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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.
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References · 24
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- 2018Know What You Don't Know: Unanswerable Questions for SQuADcited by 1,554
- 2023Inference-Time Intervention: Eliciting Truthful Answers from a Language Modelcited by 1,302
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- 2022Discovering Latent Knowledge in Language Models Without Supervisioncited by 767
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- 2024LLMs Know More Than They Show: On the Intrinsic Representation of LLM Hallucinationscited by 244
- 2020Selective Question Answering under Domain Shiftcited by 238
12 more
- 2024Programming Refusal with Conditional Activation Steeringcited by 206
- 2020Probing the Probing Paradigm: Does Probing Accuracy Entail Task Relevance?cited by 151
- 2025AbstentionBench: Reasoning LLMs Fail on Unanswerable Questionscited by 145
- 2025The Geometry of Refusal in Large Language Models: Concept Cones and Representational Independencecited by 115
- 2023Still No Lie Detector for Language Models: Probing Empirical and Conceptual Roadblockscited by 78
- 2023Won't Get Fooled Again: Answering Questions with False Premisescited by 48
- 2021Which Linguist Invented the Lightbulb? Presupposition Verification for Question-Answeringcited by 41
- 2025SafeSwitch: Steering Unsafe LLM Behavior via Internal Activation Signalscited by 29
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- 2026The Geometry of Harmful Intent: Training-Free Anomaly Detection via Angular Deviation in LLM Residual Streamscited by 3
- 2026Geometric Deviation as an Unsupervised Pre-Generation Reliability Signal: Probing LLM Representations for Answerabilitycited by 1
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