The paper shows that the geometric patterns seen in language model embeddings—such as circles for months and saddle-shaped manifolds—arise from group-invariant statistics in word co‑occurrence data. By extending previous work on translation symmetry to arbitrary finite, compact, and homogeneous groups, the authors prove that embeddings correspond to matrix elements of the irreducible representations of the symmetry group. They validate this theory experimentally with the cyclic group <Z_{12}> for months, a dihedral group for musical chords, and a spherical‑harmonic embedding for celestial objects.
By Liam Storan, Andreas Tolias, Nina Miolane
How concepts are represented in neural networks is a fundamental question in machine learning. The dominant view treats concept representations as stationary geometric objects.
arXiv:2607. 04525v1 Announce Type: cross Abstract: How concepts are represented in neural networks is a fundamental question in machine learning.
By Zhimin Hu, Lanhao Niu, Sashank Varma
arXiv:2609.05721v1 Announce Type: new
Abstract: Understanding whether language-model embeddings encode structured real-world information is important for both representation analysis and information...
By Esteban Feuerstein, Victoria Klimkowski, Juan Manuel Ortiz de Zarate, Federico Hern\'an Suaiter
arXiv:2607. 07047v1 Announce Type: cross Abstract: Understanding the geometric structure of pre-trained language model embeddings matters for interpretability and safety.
By Szczepan Konior, Alexandre Quemy, Przemys{\l}aw Klocek, Gr\'egoire Cattan, Bart{\l}omiej Sobieski
arXiv:2608.30315v1 Announce Type: new
Abstract: Token embeddings are the basic representational units that connect discrete tokens with continuous computation in language models. Although modern lang...
By Junjie Yao, Liangkai Hang, Zhi-Qin John Xu