形式化潛在思維：大型語言模型中思維表徵的四條公理

摘要

我們提出一個針對大語言模型中潛在思維表徵的公理化評估框架，包含獨立於下游基準分數的指標，能夠揭示基準準確率所掩蓋的表徵失敗。現有評估方式將表徵品質與模型能力混為一談，因此無法將失敗歸因於表徵本身，而非處理該表徵的模型。我們形式化定義了四個功能公理（因果性、最小性、可分離性與穩定性），並為每個公理訂定量化衡量指標，這些指標直接在表徵上計算，獨立於下游準確率。我們針對23個推理任務（例如空間推理、事實問答）審查了開放權重的大語言模型。結果發現，沒有任何候選表徵能同時滿足所有四個公理；這些表徵能可靠地區分任務類型，但無法區分同一任務內的兩個問題；且表徵編碼的資訊幾乎未超越輸入嵌入中已有的內容。此失敗在密集模型、推理蒸餾模型及強化學習訓練模型系列中一致存在，顯示這是結構性差距，而非模型規模或訓練過程的屬性。

English

We introduce an axiomatic evaluation framework for latent thought representations in LLMs, comprising metrics that are independent of downstream benchmark scores and reveal representational failures that benchmark accuracy masks. Existing evaluations conflate representation quality with model capacity. Therefore, failures cannot be attributed to the representation rather than to the model that processes it. We formalize four functional axioms (Causality, Minimality, Separability, and Stability) and define a quantitative measure for each, computed directly on the representation independently of downstream accuracy. We audit open-weight LLMs across 23 reasoning tasks (e.g., Spatial Reasoning, Factual QA). We find that no candidate satisfies all four axioms simultaneously, that the representations distinguish task type reliably but cannot distinguish between two questions within the same task, and that the representations encode little information beyond what is already present in the input embedding. The failure is consistent across dense, reasoning-distilled, and RL-trained model families, indicating that the gap is structural rather than a property of model size or training procedure.