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New Quadratic Model Refines Heaps' Law for Word Type-Token Relations

By PulseAugur Editorial · [1 sources] ·

Researchers have proposed a quadratic term correction to Heaps' Law, which traditionally describes the relationship between word types and tokens using a power-law function. While Heaps' Law is linear on a log-log scale, empirical observations show a slight concavity. The new quadratic model, tested on English novels, fits the type-token data more accurately with a linear coefficient slightly above 1 and a quadratic coefficient around -0.02. This formalism also offers a way to estimate curvature using a 'pseudo-variance' concept, though it may face numerical instability with large token counts. AI

RANK_REASON The cluster contains an academic paper detailing a new mathematical model for linguistic analysis. [lever_c_demoted from research: ic=1 ai=0.4]

Read on arXiv cs.CL →

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New Quadratic Model Refines Heaps' Law for Word Type-Token Relations

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The cluster contains an academic paper detailing a new mathematical model for linguistic analysis. [lever_c_demoted from research: ic=1 ai=0.4]
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COVERAGE [1]

  1. arXiv cs.CL TIER_1 English(EN) · Oscar Fontanelli, Wentian Li ·

    Quadratic Term Correction on Heaps' Law

    arXiv:2511.14683v2 Announce Type: replace Abstract: Heaps' or Herdan's law characterizes the word-type vs. word-token relation by a power-law function, which is concave in linear-linear scale but a straight line in log-log scale. However, it has been observed that even in log-log…

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