Modeling the Law of Abbreviation in Classical, Modern, and C hat GPT -Generated C hinese: A Power-Law Analysis of Structural Economy (2025)

Abstract: This study investigates the Law of Abbreviation—the inverse relationship between word length and frequency—across Classical, Modern, and ChatGPT-generated Chinese. Using a tri-partite parallel corpus and a power-law model y = a*x^(-b), we analyze the relationship between word length and the average usage frequency of words within a given word length category to assess structural economy. Results confirm consistent Zipfian distribution across all text types, with high R2 values indicating strong model fit. However, the parameter b varies significantly: Classical Chinese shows the steepest decline, suggesting strong pressure for brevity; Modern Chinese exhibits a moderated pattern; ChatGPT-generated texts display the weakest pressure, prioritizing fluency over compression. These differences reflect evolving communicative priorities and reveal that while AI models can mimic statistical distributions, they underrepresent deeper structural pressures found in natural language evolution. This study offers new insights into lexical optimization and the parameter b offers a useful metric for comparing structural efficiency across modalities. Implications are discussed in relation to language modeling, cognitive economy, and the evolution of linguistic structure.

## introduction one of the most enduring empirical patterns in quantitative linguistics is the inverse relationship between word length and word frequency, commonly known as the law of abbreviation. @xcite famously hypothesized that "the magnitude of words tends, on the whole, to stand in an inverse (not necessarily proportionate) relationship to the number of occurrences," and also asserted that "the larger a word is in length, the less likely it is to be used" @xcite . this observation has given rise to a long-standing discussion regarding the appropriate directionality of modeling: should word length be treated as a function of frequency, or should frequency be modeled as a function of word length @xcite ? researchers who model word length as a function of frequency often draw on @xcite "principle of least effort," which suggests that frequently used linguistic forms tend to be shorter for communicative efficiency (e.g., @xcite . for instance, @xcite found that higherfrequency words tend to be shorter based on frequency dictionaries. @xcite used corpus data and confirmed a negative correlation between frequency and length in chinese, consistent with a power-law distribution. moreover, @xcite , in a large-scale crosslinguistic study covering 1,262 texts in 986 languages, found robust negative correlations between frequency and word length, attributing the universal pattern to fundamental principles of information processing: "words that are used more frequently tend to be shorter" (p. 1). in contrast, other scholars have argued for the reverse modeling direction, treating word frequency as a function of word length. this approach aligns with @xcite assertion that longer words are inherently less frequent, reflecting structural constraints on usage. it has been adopted by @xcite , @xcite , and li and lei (2025), etc. for example, @xcite demonstrated that the law of abbreviation holds in natural spoken dialogues, extending prior findings based on written corpora. @xcite validated the law in chinese texts across four genres, revealing that while the inverse relationship persists, genre-specific factors and character polysemy may modulate the strength of the effect. while both approaches may be mathematically equivalent under parameter transformation @xcite , they embody distinct theoretical assumptions, and entail different perspectives on how form and usage interact. modeling word length as a function of frequency suggests that linguistic structure is shaped by language use-frequent forms tend to become shorter over time. conversely, modeling frequency as a function of word length assumes that structural features of language constrain how often a form is used, with shorter or simpler forms being more cognitively efficient and therefore more likely to recur. notably, most prior studies have focused on languages using alphabetic writing systems, particularly those using latin scripts such as english, dutch, or german. research on chinese remains limited, with only a handful of studies examining the length-frequency relationship (e.g., @xcite @xcite . moreover, few studies utilize parallel corpora or consider how emerging forms of language generation-such as ai-generated textmay reflect or deviate from natural linguistic patterns. this study addresses both gaps by focusing on chinese and incorporating aigenerated texts as a comparison. in this study, we adopt the modeling perspective that treats frequency as a function of word length, based on three key considerations. first, this direction emphasizes the structural constraints that word form imposes on usage, aligning with the linguistic principle that shorter forms are more cognitively efficient and thus more likely to recur. second, in diachronic and cross-system comparisons, word length is more stable than 1 https://github.com/niutrans/classica l-modern frequency, making it a more reliable independent variable; and treating frequency as a response variable enables us to assess whether different language production systems-including large language models-adhere to the same efficiency principles observed in human language. finally, this approach is empirically grounded in @xcite , who modeled the length-frequency relationship in chinese using the power-law function and demonstrated that the parameter b captures the rate at which average usage frequency decreases with increasing word length, reflecting the evolutionary dynamics of the chinese lexicon: a larger value of b indicates a steeper decline in frequency as length increases, signaling a stronger pressure for efficiency and simplification. specifically, we apply the power-law function to the corpus comprises three parallel versions: (1) classical chinese texts, (2) their modern chinese equivalents, and (3) their modern chinese translations generated by chatgpt from the same classical chinese input. this study aims to address three research questions: question 1: does the inverse relationship between word length and word frequency hold consistently across classical chinese, modern chinese, and chatgpt-generated chinese? question 2: how do the fitted power-law parameters, namely the parameter b, differ across these text types, and what do they reveal about structural pressures toward lexical economy? question 3: to what extent does chatgptgenerated language replicate or diverge from the natural patterns of lexical economy observed in natural languages? this diachronic and cross-modal design allows us to examine how structural features such as word length influence language usage across ancient, modern, and ai-generated language. ## conclusion this study examined whether the inverse relationship between word length and frequencycommonly known as the law of abbreviationholds across three language modalities: classical chinese, modern chinese, and chatgpt-generated chinese. using a power-law model, we analyzed the relationship between word length and average usage frequency measured by mwr across three text types. all texts showed strong zipfian patterns, with high r² values indicating good model fit. however, significant differences emerged in the fitted b parameter, which reflects lexical economy. classical chinese exhibited the largest b-values, indicating the strongest preference for short, frequent words. modern chinese showed moderate brevity pressure, while chatgpt-generated texts had the smallest b-values, suggesting weaker structural constraints. a kruskal-wallis h test confirmed significant group differences, and post hoc analysis found a significant contrast between classical chinese and chatgpt, while differences involving modern chinese were not significant. these findings suggest that while large language models like chatgpt can replicate surface-level zipfian distributions, they do not fully reproduce the deeper efficiency pressures observed in humanauthored language, particularly in highly compressed systems like classical chinese. the b parameter thus serves as a useful indicator of structural economy across production modalities. there are some limitations for this study. first, the corpus was limited to 2,000 sentences per text type. although balanced and systematically sampled, the dataset may not capture the full lexical variability of each modality. second, chinese segmentations relied on the nlp tools which, despite manual check, may overlook certain morphological subtleties. third, chatgpt outputs were generated using a fixed prompt under a single condition, which may have limited stylistic variation. repeating the generation process under varied prompts and conditions may offer greater lexical and stylistic diversity. future research could extend the corpus to include larger and more genre-diverse datasets, compare across different llms (e.g., deepseek, claude, gemini, etc.), and incorporate additional complexity metrics such as syntactic depth, semantic density, or information-theoretic entropy. longitudinal tracking of ai-generated texts across training iterations may also reveal whether structural economy emerges or erodes as model architectures evolve.