用隐藏状态几何偏差预测大模型能否答对，无需标注失败数据。
Geometric Deviation as an Unsupervised Pre-Generation Reliability Signal: Probing LLM Representations for Answerability
- 通过隐藏状态偏离可回答中心点的距离，判断问题是否可答。
- 数学题中未回答问题的偏差显著，AUC达0.78-0.84。
- 适合结构化任务如数学、代码，不适用于开放事实类问题。
可靠的语言模型应在生成前就识别出超出自身知识范围的问题。我们探究隐藏表示的几何结构是否可作为此类预生成信号，仅需测量隐藏状态与可回答参考集之间的偏差，无需标签化的失败数据，也无需访问模型输出。在三个指令微调模型（Llama 3.1-8B、Qwen 2.5-7B、Mistral-7B-Instruct）和三种提示形式（数学、事实、代码）上，发现几何结构主要编码任务形式。在数学提示中，不可回答输入始终显著偏离可回答中心，分离效果强（ROC-AUC 0.78–0.84）。该单次预生成信号优于简单拒绝基线，并媲美自一致性方法；还能捕捉模型未明确拒绝的情况。而在事实类提示中未发现可靠几何信号，表明该效应具有任务形式依赖性而非普遍适用。代码提示虽效果显著但方差较大，暗示其部分泛化能力超越数学形式。层分析显示该信号始于早期层，随生成过程逐渐减弱。结果表明，答案可回答性相关的几何结构在生成末期前已建立。综上，几何偏差可作为轻量级预生成信号，在具形式化答案约束的结构化领域中表现可靠，且其泛化边界清晰。
原文摘要 · Abstract (English)
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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