A scaling law of contextual persistence in human language

• URL: http://arxiv.org/abs/2607.25184v1
• Date: Tue, 28 Jul 2026 01:28:19 GMT
• Title: A scaling law of contextual persistence in human language
• Abstract summary: We show that the arrangement of words in sequence obeys a comparable law.<n>We measured the reduction in target perplexity conferred by prior context at distance d beyond that of the same words scrambled.<n>The results establish a scaling law of contextual persistence in human language.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Human language exhibits lawful structure at the level of words (frequency, vocabulary growth) and word pairs (co-occurrence across distance). Here we show that the arrangement of words in sequence -- a central determinant of meaning -- obeys a comparable law. Using large language models as probabilistic probes, we measured the reduction in target perplexity conferred by prior context at distance d beyond that of the same words scrambled; this difference, the contextual persistence function P(d), isolates the influence of arrangement. Across ten corpora spanning six language families and written and spoken modalities, P(d) decayed approximately as 1/d ($P(d) \propto d^{-α}$, mean $α= 1.04$; median $r^2 = 0.96$). The effect vanished in scrambled and synthetic controls, replicated across independent probes, and did not appear in genomic or protein sequences under domain-native models. An exponent near 1 distributes contextual influence approximately uniformly across logarithmic timescales. The results establish a scaling law of contextual persistence in human language.

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