[Submitted on 28 Jul 2026]
Title:A scaling law of contextual persistence in human language
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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 ($P(d) \propto d^{-\alpha}$, mean $\alpha = 1.04$; 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.
Comments: 21 pages, 5 figures (plus 1 supplementary figure); Supplementary Information included
Subjects:
Computation and Language (cs.CL)
Cite as: arXiv:2607.25184 [cs.CL]
(or arXiv:2607.25184v1 [cs.CL] for this version)
https://doi.org/10.48550/arXiv.2607.25184
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Elan Barenholtz [view email] [v1] Tue, 28 Jul 2026 01:28:19 UTC (146 KB)
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