The Geometry of Tokens in Internal Representations of Large Language Models
This work provides incremental insights into the internal representations of large language models, potentially aiding researchers in understanding model behavior.
The study investigated the relationship between token embedding geometry and next token prediction performance in transformer models, finding that prompts with higher cross-entropy loss have tokens represented in higher-dimensional spaces.
We investigate the relationship between the geometry of token embeddings and their role in the next token prediction within transformer models. An important aspect of this connection uses the notion of empirical measure, which encodes the distribution of token point clouds across transformer layers and drives the evolution of token representations in the mean-field interacting picture. We use metrics such as intrinsic dimension, neighborhood overlap, and cosine similarity to observationally probe these empirical measures across layers. To validate our approach, we compare these metrics to a dataset where the tokens are shuffled, which disrupts the syntactic and semantic structure. Our findings reveal a correlation between the geometric properties of token embeddings and the cross-entropy loss of next token predictions, implying that prompts with higher loss values have tokens represented in higher-dimensional spaces.