Correlation Dimension of Auto-Regressive Large Language Models
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908609760198656 |
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| author | Du, Xin Tanaka-Ishii, Kumiko |
| author_facet | Du, Xin Tanaka-Ishii, Kumiko |
| contents | 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. This measure captures the hierarchical recurrence structure of language, bridging local and global properties in a unified framework. Through extensive experiments, we show that correlation dimension (1) reveals three distinct phases during pretraining, (2) reflects context-dependent complexity, (3) indicates a model's tendency toward hallucination, and (4) reliably detects multiple forms of degeneration in generated text. The method is computationally efficient, robust to model quantization (down to 4-bit precision), broadly applicable across autoregressive architectures (e.g., Transformer and Mamba), and provides fresh insight into the generative dynamics of LLMs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21258 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Correlation Dimension of Auto-Regressive Large Language Models Du, Xin Tanaka-Ishii, Kumiko Computation and Language Artificial Intelligence Chaotic Dynamics 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. This measure captures the hierarchical recurrence structure of language, bridging local and global properties in a unified framework. Through extensive experiments, we show that correlation dimension (1) reveals three distinct phases during pretraining, (2) reflects context-dependent complexity, (3) indicates a model's tendency toward hallucination, and (4) reliably detects multiple forms of degeneration in generated text. The method is computationally efficient, robust to model quantization (down to 4-bit precision), broadly applicable across autoregressive architectures (e.g., Transformer and Mamba), and provides fresh insight into the generative dynamics of LLMs. |
| title | Correlation Dimension of Auto-Regressive Large Language Models |
| topic | Computation and Language Artificial Intelligence Chaotic Dynamics |
| url | https://arxiv.org/abs/2510.21258 |