Geometric Deviation as an Unsupervised Pre-Generation Reliability Signal: Probing LLM Representations for Answerability

• URL: http://arxiv.org/abs/2605.03196v1
• Date: Mon, 04 May 2026 22:24:34 GMT
• Title: Geometric Deviation as an Unsupervised Pre-Generation Reliability Signal: Probing LLM Representations for Answerability
• Abstract summary: A reliable language model should be able to signal, prior to generation, when a query falls outside its knowledge.<n>We investigate whether representation geometry can provide such a pre-generation signal by measuring the deviation of hidden states from an answerable reference set.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A reliable language model should be able to signal, prior to generation, when a query falls outside its knowledge. We investigate whether representation geometry can provide such a pre-generation signal by measuring the deviation of hidden states from an answerable reference set, requiring no labeled failure data and no access to model outputs. Across three instruction-tuned models (Llama 3.1-8B, Qwen 2.5-7B, and Mistral-7B-Instruct) and three prompt forms (Math, Fact, Code), we find that geometry primarily encodes task form. Within mathematical prompts, unanswerable inputs consistently deviate from the answerable centroid, yielding strong separation (ROC-AUC 0.78-0.84). This single-pass pre-generation signal outperforms a simple refusal baseline and compares favorably to self-consistency. It also captures cases where models do not explicitly refuse. In contrast, no reliable geometric signal emerges for factual prompts, indicating that the effect is form-conditional rather than universal. Code prompts show large effect sizes with higher variance, suggesting partial generalization beyond mathematical form. A layer-wise analysis reveals that the signal arises in early layers and gradually attenuates toward the output. These results suggest that answerability-related geometry is established before the final stages of generation. Together, these findings indicate that geometric deviation can serve as a lightweight pre-generation signal that is reliable in structured domains with formal answerability constraints, with clear boundaries on where it generalizes.

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