Arithmetics-Based Decomposition of Numeral Words -- Arithmetic Conditions give the Unpacking Strategy
This addresses the challenge of unsupervised grammar induction for numeral systems across many languages, with incremental improvements in compactness and accuracy.
The paper tackled the problem of decomposing numeral words by developing a novel numeral decomposer based on arithmetic criteria derived from Hurford's Packing Strategy, which was tested on 273 languages and produced grammars that were often close to expert-made and more compact than those from a state-of-the-art tool.
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.