用于解释大语言模型的拉盖尔几何
Laguerre Geometry for Interpreting Large Language Models
- JMP Statistical Discovery（JMP统计发现公司）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
研究大语言模型中概念结构的形成，利用拉盖尔几何精确表征概念，通过分解Transformer层揭示隐藏轨迹控制机制，提出无需训练和超参数的几何透镜方法读出概念，开发可视化工具，还实现可操作的可解释性。
中文摘要 AI 辅助
现有假设将大语言模型中的概念表示为单个点、线性方向或高斯簇，但此类结构如何以及为何出现仍不清楚。本文表明，概念几何可通过拉盖尔几何精确表征，其中概念被定义为一个区域——拉盖尔 - 沃罗诺伊单元或单元的并集，这使我们能够严格定义、测量和区分概念。在此基础上，拉盖尔权重自然地揭示了更细粒度的概念结构，如包含关系和层次结构。然后将此几何应用于Transformer内部，通过将各层分解为分段线性算子，表明令牌的隐藏轨迹受两种耦合机制控制。这种分解产生了几何透镜，一种无需训练、无超参数的方法，用于读出隐藏向量在任何层编码的精确概念。还开发了拉盖尔自动编码器，一个二维可视化工具。最后，展示了几何透镜在模型受到上下文干扰提示时能恢复正确事实令牌，实现了可操作的可解释性。代码可在GitHub获取。
英文摘要
Existing hypotheses represent a concept in an LLM as a single point, a linear direction, or a Gaussian cluster, yet it remains unclear how and why such structures emerge. Here, we show that concept geometry can be precisely characterized via Laguerre Geometry, in which a concept is defined as a region--a Laguerre-Voronoi cell or a union of cells--allowing us to strictly define, measure, and separate concepts. Building on this formulation, we show that finer-grained concept structures, such as inclusion and hierarchy, are naturally revealed by the Laguerre weights. We then push this geometry inside the transformer. Decomposing each layer into piecewise-linear operators, we show that a token's hidden trajectory is governed by two coupled mechanisms: a static tree of self-contained piecewise-linear flow, and a dynamic transport that hops the trajectory across trees when cross-token attention fires. This decomposition yields Geometric Lens, a training-free, hyperparameter-free method for reading out the exact concept a hidden vector encodes at any layer. We also develop Laguerre Autoencoder, a 2D visualizer that renders both the decision geometry and a model's full reasoning trajectory in one view. Finally, we move beyond explanatory geometry toward actionable interpretability, showing that Geometric Lens recovers the correct factual token when a model is prompted with in-context interference. The code is available on GitHub.
