Inflectional morphology with linear mappings

This methodological study provides a step-by-step introduction to a computational implementation of word and paradigm

morphology using linear mappings between vector spaces for form and meaning. Taking as starting point the linear regression model, the main

concepts underlying linear mappings are introduced and illustrated with R code. It is then shown how vector spaces can be set up for Latin

verb conjugations, using 672 inflected variants of two verbs each from the four main conjugation classes. It turns out that mappings from form

to meaning (comprehension), and from meaning to form (production) can be carried out loss-free. This study concludes with a demonstration

that when the graph of triphones, the units that underlie the form space, is mapped onto a 2-dimensional space with a self-organising

algorithm from physics (graphopt), morphological functions show topological clustering, even though morphemic units do not play any role

whatsoever in the model. It follows, first, that evidence for morphemes emerging from experimental studies using, for instance, fMRI, to

localize morphemes in the brain, does not guarantee the existence of morphemes in the brain, and second, that potential topological

organization of morphological form in the cortex may depend to a high degree on the morphological system of a language.