# The placement of the head that minimizes online memory: a complex systems approach

arXiv: https://arxiv.org/abs/1309.1939 · HTML: https://mlsanity.com/paper/1309.1939/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Sep 2013.

## Built on by (most cited first, 8 of 8)

- [The optimal placement of the head in the noun phrase. The case of demonstrative, numeral, adjective and noun](https://mlsanity.com/paper/2402.10311/) (2024)
- [Swap distance minimization beyond entropy minimization in word order variation](https://mlsanity.com/paper/2404.14192/) (2024)
- [Predictability maximization and the origins of word order harmony](https://mlsanity.com/paper/2408.16570/) (2024)
- [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 Maximum Linear Arrangement Problem for trees under projectivity and planarity](https://mlsanity.com/paper/2206.06924/) (2022)
- [Does Dependency Locality Predict Non-canonical Word Order in Hindi?](https://mlsanity.com/paper/2405.07730/) (2024)
- [Ease of dependency distance minimization in star-like structures](https://mlsanity.com/paper/2604.28034/) (2026)

## Abstract (arXiv)

It is well known that the length of a syntactic dependency determines its online memory cost. Thus, the problem of the placement of a head and its dependents (complements or modifiers) that minimizes online memory is equivalent to the problem of the minimum linear arrangement of a star tree. However, how that length is translated into cognitive cost is not known. This study shows that the online memory cost is minimized when the head is placed at the center, regardless of the function that transforms length into cost, provided only that this function is strictly monotonically increasing. Online memory defines a quasi-convex adaptive landscape with a single central minimum if the number of elements is odd and two central minima if that number is even. We discuss various aspects of the dynamics of word order of subject (S), verb (V) and object (O) from a complex systems perspective and suggest that word orders tend to evolve by swapping adjacent constituents from an initial or early SOV configuration that is attracted towards a central word order by online memory minimization. We also suggest that the stability of SVO is due to at least two factors, the quasi-convex shape of the adaptive landscape in the online memory dimension and online memory adaptations that avoid regression to SOV. Although OVS is also optimal for placing the verb at the center, its low frequency is explained by its long distance to the seminal SOV in the permutation space.