大语言模型的晶格表示假说
The Lattice Representation Hypothesis of Large Language Models
AI总结：
本文提出大语言模型的晶格表示假说，通过嵌入几何将概念层次和逻辑运算统一到线性表示中，实验表明LLM嵌入编码概念晶格及其逻辑结构。
摘要：
我们提出大语言模型的晶格表示假说：一种符号骨架，将概念层次和逻辑运算根植于嵌入几何中。我们的框架将线性表示假说与形式概念分析（FCA）统一起来，显示线性属性方向带有分离阈值诱导概念晶格通过半空间交集。这种几何使通过几何meet（交集）和join（并集）操作实现符号推理，并且当属性方向线性无关时具有标准形式。在WordNet子层次上的实验提供了经验证据，表明LLM嵌入编码概念晶格及其逻辑结构，揭示了连续几何与符号抽象之间有原则的桥梁。
英文摘要：
We propose the Lattice Representation Hypothesis of large language models: a symbolic backbone that grounds conceptual hierarchies and logical operations in embedding geometry. Our framework unifies the Linear Representation Hypothesis with Formal Concept Analysis (FCA), showing that linear attribute directions with separating thresholds induce a concept lattice via half-space intersections. This geometry enables symbolic reasoning through geometric meet (intersection) and join (union) operations, and admits a canonical form when attribute directions are linearly independent. Experiments on WordNet sub-hierarchies provide empirical evidence that LLM embeddings encode concept lattices and their logical structure, revealing a principled bridge between continuous geometry and symbolic abstraction. Datasets and code are open available at https://github.com/xiongbo010/lattice-representation-hypothesis.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
