3 research outputs found
A Language and Its Dimensions: Intrinsic Dimensions of Language Fractal Structures
The present paper introduces a novel object of study - a language fractal
structure. We hypothesize that a set of embeddings of all -grams of a
natural language constitutes a representative sample of this fractal set. (We
use the term Hailonakea to refer to the sum total of all language fractal
structures, over all ). The paper estimates intrinsic (genuine) dimensions
of language fractal structures for the Russian and English languages. To this
end, we employ methods based on (1) topological data analysis and (2) a minimum
spanning tree of a data graph for a cloud of points considered (Steele
theorem). For both languages, for all , the intrinsic dimensions appear to
be non-integer values (typical for fractal sets), close to 9 for both of the
Russian and English language.Comment: Preprint. Under revie
Formal concept analysis for evaluating intrinsic dimension of a natural language
Some results of a computational experiment for determining the intrinsic
dimension of linguistic varieties for the Bengali and Russian languages are
presented. At the same time, both sets of words and sets of bigrams in these
languages were considered separately. The method used to solve this problem was
based on formal concept analysis algorithms. It was found that the intrinsic
dimensions of these languages are significantly less than the dimensions used
in popular neural network models in natural language processing.Comment: Preprint, 10th International Conference on Pattern Recognition and
Machine Intelligence (PReMI 2023