Article published in:
The Mental Lexicon
Vol. 13:2 (2018) ► pp. 230–268
Methodological and analytic considerations

Inflectional morphology with linear mappings

| University of Tübingen
| University of Tübingen
| University of Cambridge
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.
Keywords: inflectional morphology, linear discriminative learning, word and paradigm morphology, linear mappings, 2-D network topology, graphopt
Article outline
  • 1.Introduction
  • 2.Latin conjugations
  • 3.Introduction to the mathematics of linear mappings
  • 4.Matrices for form and meaning in Latin
  • 5.Mappings between form and meaning
    • 5.1Comprehension: From form to meaning
    • 5.2Production: from meaning to form
  • 6.A novel perspective on traditional evidence for morphemes
  • 7.Concluding remarks
  • References
Available under the Creative Commons Attribution (CC BY) 4.0 license.

For any use beyond this license, please contact the publisher at rights@benjamins.nl.

Published online: 10 January 2019
https://doi.org/10.1075/ml.18010.baa
References
Ackerman, F., Blevins, J. P., and Malouf, R.
(2009) Parts and wholes: Implicative patterns in inflectional paradigms. In Blevins, J. P. and Blevins, J., editors, Analogy in grammar: Form and acquisition, pages 54–82. Oxford Univ. Press Oxford, UK. CrossrefGoogle Scholar
Arnold, D., Tomaschek, F., Lopez, F., Sering, T., and Baayen, R. H.
(2017) Words from spontaneous conversational speech can be recognized with human-like accuracy by an error-driven learning algorithm that discriminates between meanings straight from smart acoustic features, bypassing the phoneme as recognition unit. PLOS ONE, 12(4):e0174623. CrossrefGoogle Scholar
Aronoff, M. and Fudeman, K.
(2011) What is morphology?, volume 81. John Wiley & Sons.Google Scholar
Baayen, R. H., Chuang, Y.-Y., Shafaei-Bajestan, E., and Blevins, J.
(2018) The discriminative lexicon: A unified computational model for the lexicon and lexical processing in comprehension and production grounded not in (de)composition but in linear discriminative learning. Complexity, accepted for publication.Google Scholar
Beard, R.
(1977) On the extent and nature of irregularity in the lexicon. Lingua, 421:305–341. CrossrefGoogle Scholar
Bertram, R., Tønnessen, F. E., Strömqvist, S., Hyönä, J., and Niemi, P.
(2015) Cascaded processing in written compound word production. Frontiers in human neuroscience, 9:207.Google Scholar
Blevins, J. P.
(2003) Stems and paradigms. Language, 791:737–767. CrossrefGoogle Scholar
(2006) Word-based morphology. Journal of Linguistics, 42(03):531–573. CrossrefGoogle Scholar
(2016) Word and paradigm morphology. Oxford University Press. CrossrefGoogle Scholar
Booij, G.
(2012) The grammar of words: An introduction to linguistic morphology. Oxford University Press.Google Scholar
Booij, G. E.
(2016) Construction morphology. In Hippisley, A. and Stump, G., editors, The Cambridge Handbook of Morphology, pages 424–448. Cambridge University Press, Cambridge. CrossrefGoogle Scholar
Booij, G.
(2018) The Construction of Words: Advances in Construction Morphology, volume 41. Springer. CrossrefGoogle Scholar
Bozic, M. and Marslen-Wilson, W.
(2010) Neurocognitive contexts for morphological complexity: Dissociating inflection and derivation. Language and Linguistics Compass, 4(11):1063–1073. CrossrefGoogle Scholar
Bozic, M., Tyler, L. K., Ives, D. T., Randall, B., and Marslen-Wilson, W. D.
(2010) Bihemispheric foundations for human speech comprehension. Proceedings of the National Academy of Sciences, 107(40):17439–17444. CrossrefGoogle Scholar
Brown, D. and Hippisley, A.
(2012) Network morphology: A defaults-based theory of word structure, volume 1331. Cambridge University Press. CrossrefGoogle Scholar
Button, K. S., Ioannidis, J. P., Mokrysz, C., Nosek, B. A., Flint, J., Robinson, E. S., and Munafò, M. R.
(2013) Power failure: Why small sample size undermines the reliability of neuroscience. Nature Reviews Neuroscience, 14(5): 365–376. CrossrefGoogle Scholar
Butz, M. V. and Kutter, E. F.
(2016) How the mind comes into being: Introducing cognitive science from a functional and computational perspective. Oxford University Press.Google Scholar
Cahill, L. and Gazdar, G.
(1999) German noun inflection. Journal of Linguistics, 35(1):1–42. CrossrefGoogle Scholar
Chersi, F., Ferro, M., Pezzulo, G., and Pirrelli, V.
(2014) Topological self-organization and prediction learning support both action and lexical chains in the brain. Topics in cognitive science, 6(3):476–491. CrossrefGoogle Scholar
Cibelli, E. S., Leonard, M. K., Johnson, K., and Chang, E. F.
(2015) The influence of lexical statistics on temporal lobe cortical dynamics during spoken word listening. Brain and language, 1471:66–75. CrossrefGoogle Scholar
Corbett, G. G. and Fraser, N. M.
(1993) Network morphology: a datr account of russian nominal inflection. Journal of linguistics, 29(1):113–142. CrossrefGoogle Scholar
Csardi, G. and Nepusz, T.
(2006) The igraph software package for complex network research. Inter Journal, Complex Systems:1695.Google Scholar
Dabrowska, E.
(2001) Learning a morphological system without a default: the Polish genitive. Journal of child language, 281:545–574. CrossrefGoogle Scholar
Divjak, D. and Milin, P.
(2018) Language, learning and usage-based linguistics. Invited talk at the Philological Society, London, February 9 2018.Google Scholar
Erelt, M.
editor (2003) Estonian language. Estonian academy publishers, Tallinn.Google Scholar
Ernestus, M., Baayen, R. H., and Schreuder, R.
(2002) The recognition of reduced word forms. Brain and Language, 811:162–173. CrossrefGoogle Scholar
Ferro, M., Marzi, C., and Pirrelli, V.
(2011) A self-organizing model of word storage and processing: implications for morphology learning. Lingue e linguaggio, 10(2):209–226.Google Scholar
Firth, J. R.
(1968) Selected papers of J R Firth, 1952–59. Indiana University Press.Google Scholar
Gahl, S.
(2008) Time and thyme are not homophones: The effect of lemma frequency on word durations in spontaneous speech. Language, 84(3):474–496. CrossrefGoogle Scholar
Hay, J. B.
(2002) From speech perception to morphology: Affix-ordering revisited. Language, 781:527–555. CrossrefGoogle Scholar
Hay, J. B. and Baayen, R. H.
(2003) Phonotactics, parsing and productivity. Italian Journal of Linguistics, 11:99–130.Google Scholar
Hickok, G.
(2014) The architecture of speech production and the role of the phoneme in speech processing. Language, Cognition and Neuroscience, 29(1):2–20. CrossrefGoogle Scholar
Hockett, C.
(1960) The origin of speech. Scientific American, 2031:89–97. CrossrefGoogle Scholar
Jackendoff, R.
(1990) Semantic Structures. MIT Press, Cambridge.Google Scholar
Johnson, K.
(2004) Massive reduction in conversational American English. In Spontaneous speech: data and analysis. Proceedings of the 1st session of the 10th international symposium, pages 29–54, Tokyo, Japan. The National International Institute for Japanese Language.Google Scholar
Juola, P.
(2000) Double dissociations and neurophysiological expectations. Brain and cognition, 43(1–3):257–262.Google Scholar
Karlsson, F.
(1986) Frequency considerations in morphology. STUF-Language Typology and Universals, 39(1–4):19–28. CrossrefGoogle Scholar
Kaye, R. and Wilson, R.
(1998) Linear Algebra. Oxford University Press.Google Scholar
Kemps, R., Ernestus, M., Schreuder, R., and Baayen, R. H.
(2004) Processing reduced word forms: The suffix restoration effect. Brain and Language, 191:117–127. CrossrefGoogle Scholar
Landauer, T. and Dumais, S.
(1997) A solution to Plato’s problem: The latent semantic analysis theory of acquisition, induction and representation of knowledge. Psychological Review, 104(2):211–240. CrossrefGoogle Scholar
Lardier, D.
(2014) Words and their parts. In Fasold, R. W. and Connor-Linton, J., editors, An introduction to language and linguistics. Cambridge University Press, Cambridge.Google Scholar
Levelt, W., Roelofs, A., and Meyer, A. S.
(1999) A theory of lexical access in speech production. Behavioral and Brain Sciences, 221:1–38. CrossrefGoogle Scholar
Lieber, R.
(1980) On the Organization of the Lexicon. PhD thesis, MIT, Cambridge.Google Scholar
Loo, K., Jaervikivi, J., and Baayen, R.
(2018a) Whole-word frequency and inflectional paradigm size facilitate estonian case-inflected noun processing. Cognition, 1751:20–25. CrossrefGoogle Scholar
Loo, K., Jaervikivi, J., Tomaschek, F., Tucker, B., and Baayen, R.
(2018b) Production of estonian case-inflected nouns shows whole-word frequency and paradigmatic effects. Morphology, 1(28):71–97. CrossrefGoogle Scholar
Marantz, A.
(2013) No escape from morphemes in morphological processing. Language and Cognitive Processes, 28(7):905–916. CrossrefGoogle Scholar
Marelli, M. and Baroni, M.
(2015) Affixation in semantic space: Modeling morpheme meanings with compositional distributional semantics. Psychological Review, 122(3):485. CrossrefGoogle Scholar
Matthews, P. H.
(1974) Morphology. An Introduction to the Theory of Word Structure. Cambridge University Press, Cambridge.Google Scholar
(1991) Morphology. An Introduction to the Theory of Word Structure. Cambridge University Press, Cambridge.Google Scholar
Mikolov, T., Sutskever, I., Chen, K., Corrado, G. S., and Dean, J.
(2013) Distributed representations of words and phrases and their compositionality. In Advances in neural information processing systems, pages 3111–3119.Google Scholar
Open Science Collaboration
(2015) Estimating the reproducibility of psychological science. Science, 349(6251):aac4716. CrossrefGoogle Scholar
Pham, H. and Baayen, R. H.
(2015) Vietnamese compounds show an anti-frequency effect in visual lexical decision. Language, Cognition, and Neuroscience, 30(9):1077–1095. CrossrefGoogle Scholar
Pirrelli, V., Ferro, M., and Marzi, C.
(2015) Computational complexity of abstractive morphology. In Bearman, M., Brown, D., and Corbett, G. G., editors, Understanding and measuring morphological complexity, pages 141–166. Oxford University Press Oxford. CrossrefGoogle Scholar
Plag, I.
(2003) Word-formation in English. Cambridge University Press, Cambridge. CrossrefGoogle Scholar
Plag, I., Homann, J., and Kunter, G.
(2017) Homophony and morphology: The acoustics of word-final S in English. Journal of Linguistics, 53(1):181–216. CrossrefGoogle Scholar
R Core Team
(2017) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.Google Scholar
Seidenberg, M.
(1987) Sublexical structures in visual word recognition: Access units or orthographic redundancy. In Coltheart, M., editor, Attention and Performance XII, pages 245–264. Lawrence Erlbaum Associates, Hove.Google Scholar
Shafaei Bajestan, E. and Baayen, R. H.
(2018) Wide learning for auditory comprehension. In Interspeech. CrossrefGoogle Scholar
Shaoul, C. and Westbury, C.
(2010) Exploring lexical co-occurrence space using hidex. Behavior Research Methods, 42(2):393–413. CrossrefGoogle Scholar
Spencer, A.
(1991) Morphological Theory: An Introduction to Word Structure in Generative Grammar. Cambridge University Press, Cambridge.Google Scholar
Stump, G.
(2001) Inflectional Morphology: A Theory of Paradigm Structure. Cambridge University Press. CrossrefGoogle Scholar
Taft, M.
(1994) Interactive-activation as a framework for understanding morphological processing. LCP, 9(3):271–294.Google Scholar
Weaver, W.
(1955) Translation. In Locke, W. N. and Booth, A. D., editors, Machine Translation of Languages: Fourteen Essays, pages 15–23. MIT Press, Cambridge.Google Scholar
Weingarten, R., Nottbusch, G., and Will, U.
(2004) Morphemes, syllables and graphemes in written word production. In Pechmann, T. and Habel, C., editors, Multidisciplinary approaches to speech production, pages 529–572. Mouton de Gruyter, Berlin. CrossrefGoogle Scholar
Zwitserlood, P.
(2018) Processing and representation of morphological complexity in native language comprehension and production. In Booij, G. E., editor, The construction of words. Advances in construction morphology, pages 583–602. Springer.Google Scholar

Full-text

Inflectional morphology with linear mappings
Cited by

Cited by 20 other publications

Amenta, Simona, Davide Crepaldi & Marco Marelli
2020. Consistency measures individuate dissociating semantic modulations in priming paradigms: A new look on semantics in the processing of (complex) words. Quarterly Journal of Experimental Psychology 73:10 ► pp. 1546 ff. Crossref logo
Baayen, R. Harald & Eva Smolka
2020. Modeling Morphological Priming in German With Naive Discriminative Learning. Frontiers in Communication 5 Crossref logo
Chuang, Yu-Ying, Kaidi Lõo, James P. Blevins & R. Harald Baayen
2020.  In Complex Words, ► pp. 119 ff. Crossref logo
Chuang, Yu-Ying, Marie Lenka Vollmer, Elnaz Shafaei-Bajestan, Susanne Gahl, Peter Hendrix & R. Harald Baayen
2021. The processing of pseudoword form and meaning in production and comprehension: A computational modeling approach using linear discriminative learning. Behavior Research Methods 53:3 ► pp. 945 ff. Crossref logo
Chuang, Yu‐Ying, Melanie J. Bell, Isabelle Banke & R. Harald Baayen
2021. Bilingual and Multilingual Mental Lexicon: A Modeling Study With Linear Discriminative Learning. Language Learning 71:S1 ► pp. 219 ff. Crossref logo
Divjak, Dagmar, Petar Milin, Adnane Ez-zizi, Jarosław Józefowski & Christian Adam
2021. What is learned from exposure: an error-driven approach to productivity in language. Language, Cognition and Neuroscience 36:1 ► pp. 60 ff. Crossref logo
Don, Jan & Martin Everaert
2020.  In Complex Words, ► pp. 1 ff. Crossref logo
Gutierrez-Vasques, Ximena & Victor Mijangos
2019. Productivity and Predictability for Measuring Morphological Complexity. Entropy 22:1 ► pp. 48 ff. Crossref logo
Guzmán Naranjo, Matías & Olivier Bonami
2021. Overabundance and inflectional classification: Quantitative evidence from Czech. Glossa: a journal of general linguistics 6:1 Crossref logo
Heitmeier, Maria & R. Harald Baayen
2020. Simulating phonological and semantic impairment of English tense inflection with linear discriminative learning. The Mental Lexicon 15:3 ► pp. 385 ff. Crossref logo
Heitmeier, Maria, Yu-Ying Chuang & R. Harald Baayen
2021. Modeling Morphology With Linear Discriminative Learning: Considerations and Design Choices. Frontiers in Psychology 12 Crossref logo
Lívia Körtvélyessy & Pavol Štekauer
2020.  In Complex Words, Crossref logo
Nieder, Jessica, Fabian Tomaschek, Enum Cohrs & Ruben van de Vijver
2022. Modelling Maltese noun plural classes without morphemes. Language, Cognition and Neuroscience 37:3 ► pp. 381 ff. Crossref logo
Nieder, Jessica, Ruben van de Vijver & Holger Mitterer
2021. Knowledge of Maltese singular–plural mappings. Morphology 31:2 ► pp. 147 ff. Crossref logo
Nikolaev, Alexandre, Sameer Ashaie, Merja Hallikainen, Tuomo Hänninen, Eve Higby, JungMoon Hyun, Minna Lehtonen & Hilkka Soininen
2019. Effects of morphological family on word recognition in normal aging, mild cognitive impairment, and Alzheimer's disease. Cortex 116 ► pp. 91 ff. Crossref logo
Shafaei-Bajestan, Elnaz, Masoumeh Moradipour-Tari, Peter Uhrig & R. Harald Baayen
2021. LDL-AURIS: a computational model, grounded in error-driven learning, for the comprehension of single spoken words. Language, Cognition and Neuroscience ► pp. 1 ff. Crossref logo
Stein, Simon David & Ingo Plag
2022. How relative frequency and prosodic structure affect the acoustic duration of English derivatives. Laboratory Phonology 13:1 Crossref logo
TOMASCHEK, FABIAN, INGO PLAG, MIRJAM ERNESTUS & R. HARALD BAAYEN
2021. Phonetic effects of morphology and context: Modeling the duration of word-final S in English with naïve discriminative learning. Journal of Linguistics 57:1 ► pp. 123 ff. Crossref logo
Tomaschek, Fabian, Benjamin V. Tucker, Michael Ramscar & R. Harald Baayen
2021. Paradigmatic enhancement of stem vowels in regular English inflected verb forms. Morphology 31:2 ► pp. 171 ff. Crossref logo
van de Weijer, Jeroen, Weiyun Wei, Yumeng Wang, Guangyuan Ren & Yunyun Ran
2020. Words are constructions, too: A construction-based approach to English ablaut reduplication. Linguistics 58:6 ► pp. 1701 ff. Crossref logo

This list is based on CrossRef data as of 10 april 2022. Please note that it may not be complete. Sources presented here have been supplied by the respective publishers. Any errors therein should be reported to them.