# Swap distance minimization beyond entropy minimization in word order variation

arXiv: https://arxiv.org/abs/2404.14192 · HTML: https://mlsanity.com/paper/2404.14192/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 61 references that are in the map.
- First posted on arXiv 22 Apr 2024.

## Builds on (most cited first, 9 of 9)

- [Anti dependency distance minimization in short sequences. A graph theoretic approach](https://mlsanity.com/paper/1906.05765/) (2019)
- [The placement of the head that maximizes predictability. An information theoretic approach](https://mlsanity.com/paper/1705.09932/) (2017)
- [The placement of the head that minimizes online memory: a complex systems approach](https://mlsanity.com/paper/1309.1939/) (2013)
- [Optimization models of natural communication](https://mlsanity.com/paper/1412.2486/) (2014)
- [Kauffman's adjacent possible in word order evolution](https://mlsanity.com/paper/1512.05582/) (2015)
- [Swap distance minimization in SOV languages. Cognitive and mathematical foundations](https://mlsanity.com/paper/2312.04219/) (2023)
- [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)
- [The optimality of attaching unlinked labels to unlinked meanings](https://mlsanity.com/paper/1310.5884/) (2013)
- [The advent and fall of a vocabulary learning bias from communicative efficiency](https://mlsanity.com/paper/2105.11519/) (2021)

## Built on by (most cited first, 4 of 4)

- [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)
- [Vocabulary shapes cross-lingual variation of word-order learnability in language models](https://mlsanity.com/paper/2603.19427/) (2026)
- [Swap distance minimization shapes the order of subject, object and verb in languages of the world](https://mlsanity.com/paper/2604.26726/) (2026)

## Abstract (arXiv)

Consider a linguistic structure formed by n elements, for instance, subject, direct object and verb (n=3) or subject, direct object, indirect object and verb (n=4). We investigate whether the frequency of the n! possible orders is constrained by two principles. First, entropy minimization, a principle that has been suggested to shape natural communication systems at distinct levels of organization. Second, swap distance minimization, namely a preference for word orders that require fewer swaps of adjacent elements to be produced from a source order. We present average swap distance, a novel score for research on swap distance minimization. We find strong evidence of pressure for entropy minimization and swap distance minimization with respect to a die rolling experiment in distinct linguistic structures with n=3 or n=4. Evidence with respect to a Polya urn process is strong for n=4 but weaker for n=3. We still find evidence consistent with the action of swap distance minimization when word order frequencies are shuffled, indicating that swap distance minimization effects are beyond pressure to reduce word order entropy.