发现语言模型输出的逻辑向量具有低秩结构，可用无关提示生成新内容。
Sequences of Logits Reveal the Low Rank Structure of Language Models
- 通过分析模型对不同提示的输出逻辑向量，揭示其低秩特性。
- 用无关提示的输出线性组合，成功生成目标提示的合理回复。
- 提出通用抽象模型并证明其学习能力，适用于多种语言任务。
大型语言模型内在的低维结构是研究中的关键难题。本文提出一种模型无关的方法，将语言模型视为序列概率模型来研究其低维结构。我们通过实验证明，多种现代语言模型的输出逻辑向量矩阵具有低秩近似特征。进一步表明，该低秩结构可用于生成：仅需线性组合模型对无关甚至无意义提示的输出，即可生成目标提示的合理响应。理论上，我们观察到该方法对应的近似秩分析可导出一个简单的通用抽象模型，其理论预测与实验结果高度一致。随后，我们分析了该抽象模型的表征能力，并给出了可证明的学习保证。
原文摘要 · Abstract (English)
A major problem in the study of large language models is to understand their inherent low-dimensional structure. We introduce an approach to study the low-dimensional structure of language models at a model-agnostic level: as sequential probabilistic models. We first empirically demonstrate that a wide range of modern language models exhibit low-rank structure: in particular, matrices built from the model's logits for varying sets of prompts and responses have low approximate rank. We then show that this low-rank structure can be leveraged for generation -- in particular, we can generate a response to a target prompt using a linear combination of the model's outputs on unrelated, or even nonsensical prompts. On the theoretical front, we observe that studying the approximate rank of language models in the sense discussed above yields a simple universal abstraction whose theoretical predictions parallel our experiments. We then analyze the representation power of the abstraction and give provable learning guarantees.
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