English(EN) Group-Invariant Statistics Determine Embedding Geometry: Harmonic Analysis of Representations from Bach to the Night Sky

群对称性预测LLM嵌入几何，从音乐到星辰

作者 PulseAugur 编辑部 · [1 个来源] · 2026-10-03 04:00

研究人员证明，在语言模型嵌入中观察到的几何结构，例如月份的圆形和弦的鞍形流形，可以直接从训练数据中存在的统计对称性进行预测。通过应用谐波分析和群论，该研究表明，如果一个词族共现统计量在特定群G下不变，则学习到的嵌入将对应于G的不可约表示。该框架成功地解释并再现了月份的圆形几何、音乐和弦的统一几何以及大型语言模型中发现的天体球形表示。 AI

影响提供了一个理论框架，用于根据数据对称性来理解和预测LLM嵌入的几何结构。

排序理由学术论文发表在arXiv上，详细介绍了关于LLM嵌入的理论发现。[lever_c_demoted from research: ic=1 ai=1.0]

在 arXiv cs.LG 阅读 →

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报道来源 [1]

arXiv cs.LG TIER_1 English(EN) · Liam Storan, Andreas Tolias, Nina Miolane · 2026-10-03 04:00

群不变统计量决定嵌入几何：从巴赫到夜空的表示谐波分析

arXiv:2610.00647v1 Announce Type: new Abstract: The representations that language models learn for concepts such as months, weekdays, and places display consistent geometric structure: circles and saddle-shaped "Pringle" manifolds. Recent work traced these structures to $\textit{…

本文如何被排名

报道来源 [1]

群不变统计量决定嵌入几何：从巴赫到夜空的表示谐波分析

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