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Fractal Patterns May Unravel the Intelligence in Next-Token Prediction

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We study the fractal structure of language, aiming to provide a precise formalism for quantifying several properties that may have been previously suspected but not formally shown. We establish that language is: (1) self-similar, exhibiting complexities at all levels of granularity, with no particular characteristic granularity level or context length, and (2) long-range dependent (LRD), with tokens at any instant typically correlated with all subsequent tokens. Based on these findings, we argue that short-term patterns in language, such as in paragraphs, mirror the patterns seen in larger scopes, like entire documents. This may shed some light on how next-token prediction can lead to a comprehension of the structure of text at multiple levels of granularity, from words and clauses to broader contexts and intents. In addition, we demonstrate a connection between fractal parameters, such as the Hurst exponent, and scaling laws when varying the context length at inference time. We hope that these findings offer a fresh perspective on the nature of language and the mechanisms underlying the success of LLMs.


Ibrahim Alabdulmohsin, Vinh Q. Tran, Mostafa Dehghani