Surprisal correlates closely with reading time and is widely used in the cognitive science of reading as a measure of processing difficulty. Classical readability formulae such as the Flesch-Kincaid Grade Level, which scores a text by the US school grade expected to read it, are the most widely used practical measures of text difficulty, but their coefficients are unitless regression constants and have never been related to surprisal. We theoretically show that these coefficients can be interpreted as surprisal: every formula of the classical additive shape is a sum of per-word and per-sentence cross-entropies under a memoryless model, and once that model is tied to the language through Zipf's law and the formula is read as its linearisation at a reference text, each coefficient factorises into a scale in grades per nat, a Zipf slope and a reference sentence length. A grade thereby becomes a quantity in surprisal. Because the formula outputs grades and children's vocabulary has been measured by grade, the interpretation recovers the vocabulary growth the formula implicitly assumes and lets it be checked against development: holding sentence length fixed, the word coefficient of the Flesch-Kincaid formula converts to 0.18 nat of unigram surprisal per word per grade (0.15 to 0.19 across the regression-derived formulae), and normative root-word vocabulary growth (Biemiller and Slonim, 2001), converted through Zipf's law, gives 0.16 nat per year at the frontier of the known vocabulary. The word coefficient is one year of vocabulary growth, and the grade is a vocabulary scale. The identification also yields a diagnostic (the sentence-length terms are not those of a memoryless surprisal) and extends to a Japanese formula.
Measuring the breadth of a word’s meaning, or its spread across contexts, has become feasible with contextualized token embeddings. A word type can be represented as a cloud of token vectors, with dispersion-based statistics serving as proxies for contextual diversity (Nagata and Tanaka-Ishii, ACL2025). These measurements are useful for deciding appropriate sense distinctions when constructing thesauri and domain-specific dictionaries. However, when comparing the breadth of two word types, naive hypothesis testing on dispersion can be misleading: differences in semantic direction can masquerade as dispersion differences, inflating Type-I error and yielding “statistically significant” outcomes even when there is no true breadth difference. This is problematic because significance testing should distinguish genuine effects from incidental fluctuations in small-difference regimes. We propose a Householder-aligned permutation test to isolate dispersion differences from directional differences. Our method applies a single Householder reflection to align the mean directions of the two word types and then performs a permutation test on the aligned token clouds, yielding calibrated, non-parametric p-values. For practicality, we introduce a GPU-oriented implementation that batches permutations and linear algebra operations. Empirically, our alignment reduced Type-I error by 32.5% while preserving sensitivity to genuine breadth differences, and achieved a 23\times speedup over the CPU baseline.
cs.CL
Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表