Correlation Dimension of Auto-Regressive Large Language Models

Large language models (LLMs) have achieved remarkable progress in natural language generation, yet they continue to display puzzling behaviors--such as repetition and incoherence--even when exhibiting low perplexity. This highlights a key limitation of conventional evaluation metrics, which emphasize local prediction accuracy while overlooking long-range structural complexity. We introduce correlation dimension, a fractal-geometric measure of self-similarity, to quantify the epistemological complexity of text as perceived by a language model.