# The Changing Geometry of Grammar: Dimensionality and Neighborhood Reorganization across Transformer Layers

arXiv: https://arxiv.org/abs/2608.25166 · HTML: https://mlsanity.com/paper/2608.25166/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 17 references that are in the map.
- First posted on arXiv 25 Aug 2026.

## Builds on (most cited first, 8 of 8)

- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [Universal Dependencies v2: An Evergrowing Multilingual Treebank Collection](https://mlsanity.com/paper/2004.10643/) (2020)
- [Scikit-dimension: a Python package for intrinsic dimension estimation](https://mlsanity.com/paper/2109.02596/) (2021)
- [Emergence of a High-Dimensional Abstraction Phase in Language Transformers](https://mlsanity.com/paper/2405.15471/) (2024)
- [Bridging Information-Theoretic and Geometric Compression in Language Models](https://mlsanity.com/paper/2310.13620/) (2023)
- [Ranking the information content of distance measures](https://mlsanity.com/paper/2104.15079/) (2021)
- [Prediction hubs are context-informed frequent tokens in LLMs](https://mlsanity.com/paper/2502.10201/) (2025)

## Abstract (arXiv)

Transformer representations describe trajectories through high-dimensional vector spaces, which are shaped dynamically as tokens incorporate relational context across layers. Such data tend to concentrate on lower-dimensional sub-manifolds, a form of compression quantified by the Intrinsic Dimensionality (ID), the minimum number of independent variables needed to represent them without significant information loss. In this work, we ask whether the grammatical role of tokens, as marked by their part-of-speech (PoS) tag, shapes the local geometry of this manifold. To this end: (1) We investigate the layer-wise evolution of ID, finding that closed-class items expand earlier and collapse sooner than open-class ones; (2) We show its expansion and contraction to be explained by changes in the neighborhood structure, and hence in the relations between words within a sentence; (3) We compare encoders (ModernBERT, bigbird-roberta-large) and decoders (gemma-2-2B, Llama-3.2-3B), finding that the two families evolve differently across layers, consistently with how each integrates context;(4) We show that geometric features alone recover a token's grammatical role, and use them to interpret how the semantic content of each PoS evolves across layers in a downstream classification task.