Ease of dependency distance minimization in star-like structures

TL;DR

This paper investigates the complexity of dependency distance minimization in star-like syntactic structures, showing that the optimization landscape is convex and exploring reasons for anti-minimization effects.

Contribution

It demonstrates that dependency distance minimization in star structures is easier than previously thought due to convexity and discusses why anti-minimization effects occur.

Findings

The optimization landscape of star structures is convex.

Dependency distance minimization is simpler in star and quasistar trees.

Anti-minimization effects are likely due to competing principles, not optimization difficulty.

Abstract

The syntactic structure of a sentence can be represented as a tree where edges indicate syntactic dependencies between words. When that structure is a star, it has been demonstrated that the head should be placed in the middle of the linear arrangement according to the principle of syntactic dependency distance minimization. However, hubs of stars tend to be put at one of the ends, against that principle. Here we address two questions: (1) How difficult is it to minimize dependency distance? (2) Why anti dependency distance minimization effects have been found in star structures but not in path structures? The ease of optimization is determined by the shape of the optimization landscape. It was demonstrated that the landscape of star structures is quasiconvex (Ferrer-i-Cancho 2015, Language Dynamics and Change). As for (1), here we show that it is indeed convex (a particular case of quasiconvexity) both for star trees and quasistar trees and thus the distance-based optimization problem is simpler than previously believed. As for (2), we argue that (a) competing principles, rather than the difficulty of optimization, must be the actual reason for anti-dependency distance minimization effects and that (b) dependency distance minimization on star-like structures is less rewarding compared to other structures.