Geometrical morphology

TL;DR

This paper presents a geometric model of inflectional morphology, where morpheme selection is based on a vector space approach that finds the closest match to feature specifications.

Contribution

It introduces a novel geometric framework for understanding morphological inflection as a vector optimization problem in feature space.

Findings

Morpheme selection corresponds to maximizing inner product with feature vectors.

The model unifies discrete morphemes with continuous feature representations.

Provides a new perspective on the relationship between morphology and feature geometry.

Abstract

We explore inflectional morphology as an example of the relationship of the discrete and the continuous in linguistics. The grammar requests a form of a lexeme by specifying a set of feature values, which corresponds to a corner M of a hypercube in feature value space. The morphology responds to that request by providing a morpheme, or a set of morphemes, whose vector sum is geometrically closest to the corner M. In short, the chosen morpheme $\mu$ is the morpheme (or set of morphemes) that maximizes the inner product of $\mu$ and M.