Found first: a primary source the press has not covered yet.
A paper accepted to EMNLP 2026 finds that language models already encode structural impossibility before generation begins, but that encoding is nearly orthogonal to the internal direction that drives safety-trained refusal. The gap between recognizing an unanswerable question and refusing it is a routing problem, not a knowledge problem. The paper is at arXiv:2608.29109.
What the source says
Yucheng Du and Xiyang Hu tested instruction-tuned models from 1.7B to 70B parameters on structurally impossible math and code prompts, such as computing cot(−540°) or evaluating (1).startswith('1'). Across all model sizes, a single linear direction in the hidden states reliably separates these impossible inputs from answerable ones. Steering the model along this recognition direction at generation time shifts abstention behavior bidirectionally and dose-responsively; steering along random directions produces no such effect. The recognition direction and the canonical safety-refusal direction, which mediates harmful-content refusal, are nearly orthogonal.
Why it matters
Models already carry the signal needed to abstain on unanswerable questions. The failure is in routing that signal to a refusal response. Safety training reinforces a direction that is nearly orthogonal to the one encoding structural impossibility, so more harmful-content fine-tuning does nothing to fix abstention on impossible prompts. Improving that behavior likely requires targeted intervention on the recognition-to-abstention pathway, which sits in a different part of the model's representation space than current safety training reaches.