Recognition-Refusal Misalignment in LLMs: Why Models Answer Structurally Unanswerable Questions
A linear hidden-state direction encodes question impossibility in 1.7B-70B LLMs, but misalignment with the safety-refusal pathway explains why models answer unanswerable questions.
The study examines why instruction-tuned LLMs from 1.7B to 70B parameters answer structurally unanswerable math and code questions instead of abstaining. A single linear direction in the hidden state separates answerable from impossible prompts, showing models represent impossibility before generation, but this direction is nearly orthogonal to the canonical safety-refusal direction. Generation-time steering along the recognition direction changes invalidity-aware behavior dose-responsively, and the geometry is present even at the pretraining endpoint, indicating a routing failure rather than an encoding failure.