More frequent verbs are associated with more diverse valency frames: Efficient principles at the lexicon-grammar interface (2024)

Abstract: A substantial body of work has provided evidence that the lexicons of natural languages are organized to support efficient communication. However, existing work has largely focused on word-internal properties, such as Zipf’s observation that more frequent words are optimized in form to minimize communicative cost. Here, we investigate the hypothesis that efficient lexicon organization is also reflected in valency, or the combinations and orders of additional words and phrases a verb selects for in a sentence. We consider two measures of valency diversity for verbs: valency frame count (VFC), the number of distinct frames associated with a verb, and valency frame entropy (VFE), the average information content of frame selection associated with a verb. Using data from 79 languages, we provide evidence that more frequent verbs are associated with a greater diversity of valency frames, suggesting that the organization of valency is consistent with communicative efficiency principles. We discuss our findings in relation to classical findings such as Zipf’s meaning-frequency law and the principle of least effort, as well as implications for theories of valency and communicative efficiency principles.

## introduction the idea that functional pressures shape the organization of natural language lexicons has a long tradition, a prominent early example being zipf's law of abbreviation: the length of the word is inversely related to the frequency of its use, motivated by the "principle of least effort" @xcite . further evidence has been provided by a functionalist line of research studying the emergence of the lexicon from the frequency of use (e.g. @xcite as well as more recent work that formalizes such ideas using information theory (e.g. @xcite @xcite . common across this literature is the idea that the lexicon reflects a pressure for efficient language use under the constraints posed by human cognition. evidence has been adduced from domains such as word lengths @xcite , morphological complexity @xcite , orthographic forms @xcite , and the partitioning of semantic space into word meanings (e.g. @xcite @xcite . however, a key aspect of the lexicon has gone unaddressed in this literature: words are not used in isolation but systematically integrated within the broader structure of a sentence. verbs in particular play a key role in determining the syntactic and semantic structure of a sentence, and the study of valency features prominently in theoretical linguistics (e.g. @xcite . in broad strokes, the valency of a verb indicates the type and number of dependents it takes. certain features of valency are shared across many but not all languages, e.g., a majority of verbs in many languages minimally requires a subject @xcite ; and a transitive category of verbs may take on one or more objects in addition @xcite . typological literature has documented the many ways in which valency differs across verbs within a language, and across languages (e.g. @xcite . fig. 1 shows how the sentences equivalent to english the teacher helped the children with the homework are rendered differently in several languages, with dependency relations of verb annotated according to universal dependencies (ud, v.2 @xcite guidelines. we observe both cross-lingual similarities and differences: for example, there is a subject (ud relation nsubj), an ob-ject (obj) and an oblique dependent (obl) in both english and finnish, but all three dependents are marked for case in finnish (nominative, partitive and inessive, respectively). other languages use other combinations of relation types to express the same meaning; for instance, the verb has only two dependents in japanese and chinese: in japanese the verb takes homework as obj and in chinese the sentence must be formulated with another verb as a clausal complement (ccomp). within a language, different verbs allow different valency frames: specific configurations of morphosyntactic features they appear with. for example, fig. 2 shows some other valency frames observed with the english verb help (also known as its diathesis alternations). there is general consensus that the syntactic frames can at least in part be predicted by semantics (e.g. @xcite , but divergent explanations of the findings have been offered @xcite . a substantial body of work has also classified verbs within a language based on their diathesis alternations (e.g. @xcite . here, we investigate whether valency properties of verbs show signatures of efficient organization and test the hypothesis that verbs will systematically differ in the diversity of valency frames they are associated with, so that high-frequency verbs will be associated with a greater diversity of frames. a range of theoretical considerations converge on this prediction. our hypothesis is related to zipf's meaning-frequency law, which states that more frequent words tend to have more meanings and can be derived assuming two other zipfian laws, the law for word frequencies and the law of meaning distribution @xcite . it has been empirically verified in corpus-based studies for various languages, among others dutch, english @xcite and turkish @xcite . psycholinguistic evidence has similarly suggested a correlation between semantic ambiguity and verb frequency -more frequent verbs tend to be more ambiguous semantically @xcite . as the syntactic frames of a verb correlate with its semantics, a corollary of the meaning-frequency law is that the more frequency verbs will have more diverse valency frames, i.e., our hypothesis. like other zipfian observations of statistical regularities in languages, our hypothesis follows from the principle of least effort. the greater semantic ambiguity associated with the verbs requires more freedom with respect to the syntactic frames to allow speakers to convey nuanced meanings or contextual information more efficiently. from a comprehension perspective, this kind of pattern also ensures frames are predictable when verbs are not, reducing spikes in information density. we argue that similar considerations apply from the perspective of language production and learning. we operationalize valency at a lexeme-level, and use two information-theoretic metrics of the diversity of valency frames: (i) valency frame count (vfc) that measures the number of distinct frames associated with a verb; and (ii) valency frame entropy (vfe) that measures the average surprisal of valency frames as conditioned by the verb, determined by the diversity of frames associated with that verb. this allows us to quantitative test our hypothesis regarding the correlation between these metrics and the diversity of valency frames in experiments and show that effects predicted by learnability and efficiency considerations shape valency systems of languages cross-linguistically. ## background and motivation the notion of valency the notion of valency, and closely related notions such as argument structure, subcategorization and diathesis alternation, have received a variety of formalizations across formal linguistic theories (e.g. @xcite @xcite @xcite . while many theories make a formal distinction between arguments and adjuncts @xcite , others treat them in a similar fashion @xcite . for this study, we abstract away from such theoretical questions, and adopt a broad definition of verb valency within ud, a dependency grammar framework. in doing so, we aim for a broad descriptive basis for cross-linguistic comparison, as ud classifies dependency relations into cross-linguistically meaningful types (cf. figures 1 2 ); pragmatically, this also allows applicable operationalization on large-scale cross-linguistic usage data available as ud treebanks. we formalize as valency the set of such relation types of dependents a verb co-occurs with, and a valency frame as a set of ud relations corresponding to dependents of a verb (see § 4.1). computational studies of valency a key line of computational research on valency has cre-老師 幫助 孩子們 完成 了 作業 teacher help child-pl complete perf homework ccomp nsubj nsubj aux obj (a) chinese the teacher helped the children with the homework nsubj obj obl case (b) english opettaja auttoi lapsia läksyissä teacher help.past child.pl.part homework.pl.inessive @xmath0.pl child.pl prep det.pl homework.pl help.ptcp @xmath1.pl.dat homework.pl.3poss.dat helper become-past @xmath2: further examples of the verb "help" in english, showing its diathesis alternations. theories of communicative and processing efficiency one justification for efficient organization of the lexicon comes from learnability considerations. for instance, it has been suggested that infrequent irregular verbs are poorly acquired, leading to morphological irregularity being focused on high-frequency words (e.g. @xcite . similar considerations apply to valency: when learning from a finite sample, a learner should be able to acquire a larger variety of frames for frequent verbs, as more data is available for them. thus, if learnability affects the organization of valency, one expects that infrequent verbs should be associated with smaller diversity of frames. another key justification for efficient organization of the lexicon (and language in general) comes from online processing, in both language production and comprehension. on the production side, accessibility, i.e. the ease of retrieval, has been shown to play a key role in shaping language form and structure @xcite . to the extent that verbs may be planned in advance of their arguments in sentence production (e.g. @xcite , reducing the diversity of frames associated with a verb should increase the accessibility of any of these frames. such a pressure should be stronger for the long tail of low-frequency verbs, as producers will be less attuned to their production. conversely, being compatible with a larger number of frames could make a verb more versatile and therefore encourage its use. on the comprehension side, we expect consequences for sentence interpretation as well as the distribution of information density. psycholinguistic evidence shows that argument structure information is used in online comprehension to eliminate implausible interpretations @xcite . the more frequent verbs, being more ambiguous or vague @xcite , would require additional information to disambiguate or narrow down the meaning. additionally, the uniform information density (uid) hypothesis @xcite posits that language speakers prefer a more even distribution of surprisal values across utterances in order to maximize but not overload the capacity of the communication channel. less frequent verbs will, on average, have high surprisal; high entropy in the valency frames associated with it would lead to an undesirable spike in overall surprisal. ## results we report primarily results with both subsampling and cross-entropy estimation, as these choices lead to the most conservative estimates for testing our hypothesis. the effect of subsampling is examined below. we quantify the hypothesized relationships using spearman's rank correlation coefficient @xcite . the results show robust correlation between frequency and our valency metrics: when using vfe, we observe at least moderate correlations (ρ ≥ .40, following @xcite in 66 out of 75 languages and strong to very strong correlations (defined as ρ ≥ .70) in 18. the remaining 9 languages show only weak correlations 3 . the mean spearman's ρ is .59, with a standard 2 manx (10), mbya guarani (5), upper sorbian (10), welsh (9) we note that our correlation hypothesis takes the form of an overall trend rather than a strict rule. a more frequent verb is not guaranteed nor expected to always have higher diversity of frames. outliers to this trend among high-frequency verbs illustrate this: in english, verbs like arrive (@xmath3, @xmath4, @xmath5.94) have significantly lower vfc and vfe values than others with similar frequency, e.g. call (@xmath6, @xmath7, @xmath8.22) and work (@xmath9, @xmath10, @xmath11.23). fig. 3a shows how the correlation coefficients vary across the languages and in relation to the sample sizes, using vfe. larger sample sizes, either measured by the number of verb lexemes or by the overall ud corpora size, reduce cross-lingual variance by allowing for better estimations of the entropy and count foot_2 measures. effects of subsampling our subsampling procedure as described in §3.2 eliminates the circularity confound by fixing the sample size, albeit at the expense of statistical power. results without subsampling validate our cautious approach, especially for vfc: the mean ρ between vfc and frequency rank is a staggering 0.996 (sd=.004), i.e., almost perfect correlations for all languages. performing subsampling but then including verbs below the cutoff results in similar numbers (mean ρ =.996, 3 ; entropies are estimated as cross-entropies. see appendix, fig. 8 for results for all languages, fig. 9 for results without subsampling. @xmath12.073 for vfc). these results are arguably a reflection of the circularity confound, eliminated using subsampling. a visual confirmation of this effect is possible when we plot individual verb lexemes by their frequency ranks on the x-axis and vfe and vfc on y-axes. as seen in fig. 4 , subsampling introduces a flattening effect to the vfe and vfc metrics of verbs with frequency above the subsampling threshold ∆ (i.e., verbs to the left of the dotted lines), such that the plot density makes the correlations less visually clear (which can nevertheless be statistically confirmed); in contrast, the clean correlations for the excluded verbs with frequency below ∆ (i.e., verbs to the right) reflect how circularity confound would have clouded our analysis without subsampling. for the vfe measure, cross-entropy estimation alone reverses the circularity confound, even without subsampling ( § 3.2). the stronger correlation (mean ρ =.849, @xmath13.073) we observe without subsampling helps to confirm that our hypothesis apply to less frequent verbs that were elsewhere excluded. fig 3b shows cross-linguistic variation in the correlation coefficient (vfe) without subsampling. compared to the subsampled version (fig 3a ), we also observe a greater correlation between the sample size and correlation strength, as the larger number of less frequent verbs for languages with a larger sample size would mean a stronger confound. ## discussion results across 79 languages provide strong support to our hypothesis of a positive correlation between a verb's frequency and the diversity of its valency frame. by controlling for the circularity confound, we are able to determine that this correlation stands even after we exclude the effect of the more frequent verbs having more opportunities to appear. the cross-linguistic coverage further confirms that the results indicate a general trend and are not specific to individual languages. while the correlational nature of our findings precludes us from drawing definitive conclusions as to which causal pathway is behind the observed regularities, the results match predictions made by efficiency-based theories and thus corroborate them. as we have detailed in §2, considerations from learnability in language acquisition, online production and comprehension converge to predict the correlation between verb frequency and valency frame diversity and provide possible casual explanations for them. in particular, our results complement a number of existing studies focusing a correlation between word frequency and number of meanings (as a measure of semantic ambiguity) @xcite but test our hypothesis independently on the morphosyntax; seen from a processing perspective, the valency frames may serve as additional morphosyntactic disambiguation for verbs with multiple or broad meanings, suggesting a close interaction between lexical semantics and morphosyntax. in this way, our study extends previous work on natural language lexicons and shows that they are optimized for efficiency not just in word-internal proprieties but also in their interface with grammar. additionally, our findings show that different syntactic relations differ in their impact on the correlation, but do not support a clear-cut distinction between core and non-core dependents, otherwise understood as arguments and adjuncts. the quantitative trend was supported both by core and non-core dependents, and larger sets of relations strengthened the observed correlation. this is evidence in support of a more graded distinction between different verb dependencies rather than a binary one. while the predicted pattern holds across languages, we observe variation in correlation strength between languages. understanding whether these differences reflect typologically meaningful variation is an interesting task for future work. one possibility is that the ud annotation scheme does not sufficiently account for cross-linguistic differences in argument encoding: e.g. in chinese, many outlier verbs that have high frequency but low vfe are coverbs, which serve semantic functions similar to prepositions in english while are syntactically verbs (e.g., 自'from', 隨'follow / with'). their have narrow semantic functions and are associated with a relatively small number of valency frames compared to similarly frequent verbs. this brings into question the strictness of word category boundaries, and fuller picture may need to better situate the verb category within the overall lexicon. ## conclusion across 79 languages, we have provided evidence for a cross-linguistic quantitative trend in the organization of valency: more frequent verbs are associated with a larger diversity of valency frames, both when estimated by count-based or entropy-based metrics. crucially, we showed that this pattern is not driven by differences in the number of observations between high-and low-frequency verbs, and persists even when equalizing the number of observations available for each verb. extending a recent line of research studying the lexicon's efficiency for human communication and language use, these results suggest that such considerations apply not just to word-internal structure, but also to the way words are integrated within the sentence.