The geometric evolution of token representations in large language models (LLMs) presents a fundamental paradox: while human language inherently organizes semantic information in low-dimensional spaces ( dimensions), modern LLMs employ high-dimensional embeddings ( dimensions) processed through Transformer architectures. To resolve this paradox, this work bridges this conceptual gap by developing a geometric framework that tracks token dynamics across Transformers layers. Through layer-wise analysis of intrinsic dimensions across multiple architectures, we reveal an expansion-contraction pattern where tokens diffuse to a "working space" and then progressively project onto lower-dimensional submanifolds. Our finding implies a negative correlation between the working space dimension and parameter-sensitive performance of the LLMs, and indicates that effective models tend to compress tokens into approximately 10-dimensional submanifolds, closely resembling human semantic spaces. This work not only advances LLM interpretability by reframing Transformers layers as projectors that mediate between high-dimensional computation and low-dimensional semantics, but also provides practical tools for model diagnostics that do not rely on task-specific evaluations.
View on arXiv@article{song2025_2503.22547,
title={ Bridging the Dimensional Chasm: Uncover Layer-wise Dimensional Reduction in Transformers through Token Correlation },
author={ Zhuo-Yang Song and Zeyu Li and Qing-Hong Cao and Ming-xing Luo and Hua Xing Zhu },
journal={arXiv preprint arXiv:2503.22547},
year={ 2025 }
}