The structure of the token space for large language models
This work addresses the foundational understanding of LLM behavior for researchers, though it is incremental as it builds on existing geometric analysis methods.
The authors tackled the problem of understanding the topological and geometric structure of token subspaces in large language models, finding that these subspaces are stratified manifolds with significantly negative Ricci curvature across three models (GPT2, LLEMMA7B, MISTRAL7B), and that dimension and curvature correlate with generative fluency.
Large language models encode the correlational structure present in natural language by fitting segments of utterances (tokens) into a high dimensional ambient latent space upon which the models then operate. We assert that in order to develop a foundational, first-principles understanding of the behavior and limitations of large language models, it is crucial to understand the topological and geometric structure of this token subspace. In this article, we present estimators for the dimension and Ricci scalar curvature of the token subspace, and apply it to three open source large language models of moderate size: GPT2, LLEMMA7B, and MISTRAL7B. In all three models, using these measurements, we find that the token subspace is not a manifold, but is instead a stratified manifold, where on each of the individual strata, the Ricci curvature is significantly negative. We additionally find that the dimension and curvature correlate with generative fluency of the models, which suggest that these findings have implications for model behavior.