Are crossing dependencies really scarce?

Abstract

The syntactic structure of a sentence can be modelled as a tree, where vertices correspond to words and edges indicate syntactic dependencies. It has been claimed recurrently that the number of edge crossings in real sentences is small. However, a baseline or null hypothesis has been lacking. Here we quantify the amount of crossings of real sentences and compare it to the predictions of a series of baselines. We conclude that crossings are really scarce in real sentences. Their scarcity is unexpected by the hubiness of the trees. Indeed, real sentences are close to linear trees, where the potential number of crossings is maximized.

Scarcity of crossing dependencies: A direct outcome of a specific constraint?

“…2). Indeed, the hubiness of real syntactic dependencies is close to trees from the ensemble of uniformly random trees, for which h tends to zero as n increases [18].…”

“…The simplest null hypothesis assumes a uniformly random permutation of the words of a sentence and predicts that the expected edge length is (n + 1)/3, where n is the number of vertices of the tree (the length of the sentence in words) [9,17]. Second, their hubiness coefficient does not exceed 25% [18]. h, the hubiness coefficient is a normalized variance of vertex degrees.…”

“…24]. Indeed, the actual number of crossings per sentence does not reach 3.5 across languages and is only above 1 in a few of them [18]. However, how small a number is depends on the scale of measurement and a null model is required.…”

“…A rigorous demonstration that crossings are really scarce has been missing for decades. Recently, statistical evidence that crossings are significantly small has been provided [18]. Furthermore, sentences where dependencies are shorter tend to have fewer crossings [25].…”

“…Research on syntactic dependency networks parallels research on non-spatial networks: as the statistical properties of many real networks have been compared against the predictions of null models, the Erdős-Rényi graph being one of the most simple and popular examples [26], the statistical properties of syntactic dependency networks have been compared against the predictions of null models with increasing levels of complexity for the length of syntactic dependencies [9,15,16] or for the number of crossings [18,27,28].…”