# Arithmetics-Based Decomposition of Numeral Words -- Arithmetic Conditions give the Unpacking Strategy

arXiv: https://arxiv.org/abs/2312.10097 · HTML: https://mlsanity.com/paper/2312.10097/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 34 references that are in the map.
- First posted on arXiv 14 Dec 2023.

## Builds on (most cited first, 6 of 6)

- [Ordered Neurons: Integrating Tree Structures into Recurrent Neural Networks](https://mlsanity.com/paper/1810.09536/) (2018)
- [Compound Probabilistic Context-Free Grammars for Grammar Induction](https://mlsanity.com/paper/1906.10225/) (2019)
- [Unsupervised Latent Tree Induction with Deep Inside-Outside Recursive Autoencoders](https://mlsanity.com/paper/1904.02142/) (2019)
- [Finding Dataset Shortcuts with Grammar Induction](https://mlsanity.com/paper/2210.11560/) (2022)
- [Reinforcement Learning of Minimalist Numeral Grammars](https://mlsanity.com/paper/1906.04447/) (2019)
- [Discovering Textual Structures: Generative Grammar Induction using Template Trees](https://mlsanity.com/paper/2009.04530/) (2020)

## Abstract (arXiv)

This paper presents a novel numeral decomposer based on arithmetic criteria. The criteria are not dependent on a base-10 assumption but only on Hurford's Packing Strategy. Hurford's Packing Strategy constitutes numerals by packing factors and summands to multiplicators. We found out that a numeral of value n has a multiplicator larger than sqrt(n), a summand smaller than n/2 and a factor smaller than sqrt(n). Using these findings, the numeral decomposer attempts to detect and unpack factors and summand in order to reverse Hurford's Packing strategy. We tested its applicability for incremental unsupervised grammar induction in 273 languages. This way, grammars were obtained with sensible mathematical attributes that explain the structure of produced numerals. The numeral-decomposer-induced grammars are often close to expert-made and more compact than numeral grammars induced by a modern state-of-the-art grammar induction tool. Furthermore, this paper contains a report about the few cases of incorrect induced mathematical attributes, which are often linked to linguistic peculiarities like context sensitivity.