大型語言模型中的辨識－拒答錯位：為何模型會回答結構性不可回答的問題

摘要

大型語言模型常會回答結構上無法回答的問題，例如計算 cot(-540°) 或評估 (1).startswith("1")，而非棄答。我們探問此失敗反映的是缺少辨識，還是從辨識到棄答的路由失敗。在從 1.7B 到 70B 參數的指令微調模型中，隱藏狀態中的單一線性方向可區分可回答與結構上不可能的數學及程式碼提示，顯示模型在生成前即表徵了不可能性。然而，此辨識方向與中介經訓練習得的有害內容拒絕之典型安全拒絕方向幾乎正交。一個領域內、以行為定義的無效性感知方向更接近辨識，但僅與其部分對齊，且仍與安全拒絕近乎正交。在生成時沿著辨識方向進行引導，會在結構性數學與程式碼單元上雙向且呈劑量反應地改變無效性感知行為，而隨機方向則不會。基礎/指令模型比較進一步顯示，低餘弦幾何早已存在於預訓練終點。因此，對不可能問題表現自信的失敗，更適合解釋為路由失敗而非編碼失敗：模型具有可用的「無可接受答案」訊號，但安全拒絕路徑並未對齊以使用它。

English

Large language models often answer structurally unanswerable questions, such as computing cot(-540°) 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.