# The scarcity of crossing dependencies: a direct outcome of a specific constraint?

arXiv: https://arxiv.org/abs/1601.03210 · HTML: https://mlsanity.com/paper/1601.03210/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jan 2016.

## Built on by (most cited first, 7 of 7)

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- [The expected sum of edge lengths in planar linearizations of trees. Theory and applications](https://mlsanity.com/paper/2207.05564/) (2022)
- [How to measure the optimality of word or gesture order with respect to the principle of swap distance minimization](https://mlsanity.com/paper/2604.01938/) (2026)
- [Dependency distance minimization predicts compression](https://mlsanity.com/paper/2109.08900/) (2021)
- [The Impact of Edge Displacement Vaserstein Distance on UD Parsing Performance](https://mlsanity.com/paper/2209.07139/) (2022)

## Abstract (arXiv)

The structure of a sentence can be represented as a network where vertices are words and edges indicate syntactic dependencies. Interestingly, crossing syntactic dependencies have been observed to be infrequent in human languages. This leads to the question of whether the scarcity of crossings in languages arises from an independent and specific constraint on crossings. We provide statistical evidence suggesting that this is not the case, as the proportion of dependency crossings of sentences from a wide range of languages can be accurately estimated by a simple predictor based on a null hypothesis on the local probability that two dependencies cross given their lengths. The relative error of this predictor never exceeds 5% on average, whereas the error of a baseline predictor assuming a random ordering of the words of a sentence is at least 6 times greater. Our results suggest that the low frequency of crossings in natural languages is neither originated by hidden knowledge of language nor by the undesirability of crossings per se, but as a mere side effect of the principle of dependency length minimization.