---
title: "On the Complexity and Typology of Inflectional Morphological"
description: "The authors define i-complexity through information theory. 59 references, cited by 31 papers here."
authors: ["Ryan Cotterell", "Christo Kirov", "Mans Hulden", "Jason Eisner"]
year: 2019
venue: "Transactions of the Association for Computational Linguistics"
source: "https://aclanthology.org/Q19-1021/"
doi: "10.1162/tacl_a_00271"
licence: "CC BY 4.0 (ACL Anthology)"
licence_url: "https://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/cotterell-2019-complexity-typology-inflectional-morphological-systems/"
---
[Elamur Research](https://md.research.elamur.ai/free/en/) · [this page in HTML](https://research.elamur.ai/free/en/papers/cotterell-2019-complexity-typology-inflectional-morphological-systems/)

[home](https://md.research.elamur.ai/free/en/) / [papers](https://md.research.elamur.ai/free/en/papers/) / [2019](https://md.research.elamur.ai/free/en/papers/2019/page/5/) / On the Complexity and Typology of Inflectional Morphological Systems

# On the Complexity and Typology of Inflectional Morphological Systems

**Authors:** [Ryan Cotterell](https://md.research.elamur.ai/free/en/authors/ryan-cotterell/), [Christo Kirov](https://md.research.elamur.ai/free/en/authors/christo-kirov/), [Mans Hulden](https://md.research.elamur.ai/free/en/authors/mans-hulden/) and [Jason Eisner](https://md.research.elamur.ai/free/en/authors/jason-eisner/) · **Year:** 2019 · **Venue:** [Transactions of the Association for Computational Linguistics](https://md.research.elamur.ai/free/en/venues/tacl/) ([Transactions of the Association for Computational Linguistics (TACL) 2019](https://md.research.elamur.ai/free/en/venues/tacl/2019/)) · **Publisher:** [The MIT Press](https://md.research.elamur.ai/free/en/publishers/the-mit-press/) · **Licence:** [CC BY 4.0 (ACL Anthology)](https://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://aclanthology.org/Q19-1021/) · [PDF](https://aclanthology.org/Q19-1021.pdf) · [DOI 10.1162/tacl\_a\_00271](https://doi.org/10.1162/tacl_a_00271) · [OpenAlex](https://openalex.org/W2826525850)

**Citations:** 50 citations (OpenAlex, 2026-10-14) · [31](https://md.research.elamur.ai/free/en/papers/cotterell-2019-complexity-typology-inflectional-morphological-systems/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary
This paper asks how complex a language's inflectional morphology is and whether two kinds of complexity limit each other. The first is enumerative complexity (e-complexity): how many distinct surface forms a paradigm contains. The second is integrative complexity (i-complexity): how irregular, or hard to predict, those forms are. The authors define i-complexity through information theory. It is the conditional entropy of a whole paradigm given its lemma. To estimate it, they fit a probabilistic model: a directed graphical model arranged as a tree, with neural networks serving as its factors and a topology that is learned. A variational bound is used to approximate the measure. The approach needs no segmentation of words into morphemes and is largely theory-neutral. Applied to written noun and verb paradigms from 36 typologically diverse languages, the measurements show a Pareto-style trade-off. A system may have large paradigms or highly irregular ones, but never both. This refines Ackerman and Malouf's low-entropy conjecture. It also suggests that NLP should not equate morphological richness with high OOV rates, since predictable morphology, as in Hungarian, may be easier to process than irregular morphology, as in German.

## Key points
- E-complexity is measured as the average number of *distinct* surface forms per paradigm, not the number of slots. Syncretic slots therefore do not inflate the score. Most English verbs score 4–5, while *be* has 8 forms.
- Paradigms follow the UniMorph annotation scheme and are represented orthographically. The results describe written languages, and spoken forms might give different values.
- Significance comes from a permutation test over 10,000 shuffled scatterplots. It checks whether the high e-complexity, high i-complexity corner is emptier than chance would produce.
- In one training scheme the results are p \< 0.021 for verbs and p \< 0.037 for nouns. In another training scheme they are p \< 0.032 for verbs and p \< 0.024 for nouns.
- Proposed extensions include:
  - modelling frequency effects;
  - joint phonological and orthographic modelling;
  - simulating diachronic transmission;
  - quantifying derivational complexity.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

## Institutions

- [Johns Hopkins University](https://md.research.elamur.ai/free/en/universities/johns-hopkins-university/) — University, Baltimore, United States · 240 works · 96,487 citations
- [University of Colorado Boulder](https://md.research.elamur.ai/free/en/universities/university-of-colorado-boulder/) — University, Boulder, United States · 69 works · 51,069 citations
- [University of Colorado System](https://md.research.elamur.ai/free/en/universities/university-of-colorado-system/) — University, Boulder, United States · 9 works · 1,658 citations
- [University of Colorado Denver](https://md.research.elamur.ai/free/en/universities/university-of-colorado-denver/) — University, Denver, United States · 3 works · 1,046 citations

📚 Shelves (4): [🖥️ Computer Science](https://md.research.elamur.ai/free/en/shelves/computer-science/) · 16,667 works · [🤖 Artificial Intelligence](https://md.research.elamur.ai/free/en/shelves/computer-science/artificial-intelligence/) · 16,194 works · [🎭 Arts and Humanities](https://md.research.elamur.ai/free/en/shelves/arts-and-humanities/) · 16,039 works · [🗣️ Language and Linguistics](https://md.research.elamur.ai/free/en/shelves/arts-and-humanities/language-and-linguistics/) · 15,891 works

🧭 Topics (1): [🧩 Morphology](https://md.research.elamur.ai/free/en/topics/morphology/) · 405 works

💡 Concepts (1): [💡 Word form](https://md.research.elamur.ai/free/en/concepts/word-form/) · 16 works

## Cite

Cite as: Ryan Cotterell, Christo Kirov, Mans Hulden and Jason Eisner. 2019. On the Complexity and Typology of Inflectional Morphological Systems. Transactions of the Association for Computational Linguistics.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@article{cotterell2019complexity,
  title = {{On the Complexity and Typology of Inflectional Morphological Systems}},
  author = {Ryan Cotterell, Christo Kirov, Mans Hulden and Jason Eisner},
  journal = {Transactions of the Association for Computational Linguistics},
  year = {2019},
  doi = {10.1162/tacl\_a\_00271},
  url = {https://doi.org/10.1162/tacl_a_00271}
}
```

- [← previous Mining Discourse Markers for Unsupervised Sentence Representation Learning](https://md.research.elamur.ai/free/en/papers/sileo-2019-mining-discourse-markers-unsupervised-sentence/)
- [next → Pragmatically Informative Text Generation](https://md.research.elamur.ai/free/en/papers/shen-2019-pragmatically-informative-text-generation/)
- [↑ back to papers of 2019](https://md.research.elamur.ai/free/en/papers/2019/page/5/)

## References

59 references, 10 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

1. Farrell Ackerman and Robert Malouf. 2013. Morphological organization: The low conditional entropy conjecture. Language, 89(3):429–464. \#\# Conclusions We have provided clean mathematical formulations of enumerative and integrative complexity of Blake Allen and Michael Becker. 2015. Learning alternati… [find](https://scholar.google.com/scholar?q=Farrell+Ackerman+and+Robert+Malouf%2E+2013%2E+Morphological+organization%3A+The+low+conditional+entropy+conjecture%2E+Language%2C+89%283%29%3A429%E2%80%93464%2E+%5C%23%5C%23+Conclusions+We+have+provided+clean+mathematical+formulations)
2. Lai. 1992. [An estimate of an upper bound for the entropy of English](https://md.research.elamur.ai/free/en/papers/brown-1992-estimate-upper-bound-entropy-english/). Computational Linguistics, 18(1):31–40. phonology. Unpublished manuscript, University of British Columbia and Stony Brook University. Available as [https://ling.auf.net/lingbuzz/](https://ling.auf.net/lingbuzz/) 002503. [↗](https://ling.auf.net/lingbuzz/)
3. Andrew Carstairs-McCarthy. 2010. The Evolution of Morphology, volume 14. Oxford University Press. [find](https://scholar.google.com/scholar?q=Andrew+Carstairs%2DMcCarthy%2E+2010%2E+The+Evolution+of+Morphology%2C+volume+14%2E+Oxford+University+Press%2E)
4. Stephen R. Anderson. 1992. A-Morphous Morphology, volume 62, Cambridge University Press. [find](https://scholar.google.com/scholar?q=Stephen+R%2E+Anderson%2E+1992%2E+A%2DMorphous+Morphology%2C+volume+62%2C+Cambridge+University+Press%2E)
5. C. K. Chow and Cong N. Liu. 1968. Approximating discrete probability distributions with dependence trees. IEEE Transactions on Information Theory, 14(3):462–467. [find](https://scholar.google.com/scholar?q=C%2E+K%2E+Chow+and+Cong+N%2E+Liu%2E+1968%2E+Approximating+discrete+probability+distributions+with+dependence+trees%2E+IEEE+Transactions+on+Information+Theory%2C+14%283%29%3A462%E2%80%93467%2E)
6. Mark Aronoff. 1976. Word Formation in Generative Grammar. Number 1 in Linguistic Inquiry Monographs. MIT Press, Cambridge, MA. [find](https://scholar.google.com/scholar?q=Mark+Aronoff%2E+1976%2E+Word+Formation+in+Generative+Grammar%2E+Number+1+in+Linguistic+Inquiry+Monographs%2E+MIT+Press%2C+Cambridge%2C+MA%2E)
7. Matthew Baerman. 2015. The Oxford Handbook of Inflection. Oxford Handbooks in Linguistic. Part II: Paradigms and their Variants Ryan Cotterell, Christo Kirov, Mans Hulden, and Jason Eisner. 2018a. On the diachronic stability of irregularity in inflectional morphology. arXiv preprint arXiv:1804.08262… — [arXiv:1804.08262](https://arxiv.org/abs/1804.08262) [find](https://scholar.google.com/scholar?q=Matthew+Baerman%2E+2015%2E+The+Oxford+Handbook+of+Inflection%2E+Oxford+Handbooks+in+Linguistic%2E+Part+II%3A+Paradigms+and+their+Variants+Ryan+Cotterell%2C+Christo+Kirov%2C+Mans+Hulden%2C+and+Jason+Eisner%2E+2018a%2E+On+)
8. Matthew Baerman, Dunstan Brown, and Greville G. Corbett. 2015. Understanding and measuring morphological complexity: An introduction. In Matthew Baerman, Dunstan Brown, and Greville G. Corbett, editors, Understanding and measuring morphological complexity. Oxford University Press. [find](https://scholar.google.com/scholar?q=Matthew+Baerman%2C+Dunstan+Brown%2C+and+Greville+G%2E+Corbett%2E+2015%2E+Understanding+and+measuring+morphological+complexity%3A+An+introduction%2E+In+Matthew+Baerman%2C+Dunstan+Brown%2C+and+Greville+G%2E+Corbett%2C+editor)
9. Ryan Cotterell, Christo Kirov, John Sylak-Glassman, Gėraldine Walther, Ekaterina Vylomova, Arya D. McCarthy, Katharina Kann, Sebastian Mielke, Garrett Nicolai, Miikka Silfverberg, David Yarowsky, Jason Eisner, and Mans Hulden. 2018b. [The CoNLL–SIGMORPHON 2018 shared task: Universal morphological re…](https://md.research.elamur.ai/free/en/papers/cotterell-2018-conll-sigmorphon-2018-shared-task/)
10. Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. 2015. [Neural machine translation by jointly learning to align and translate](https://md.research.elamur.ai/free/en/papers/bahdanau-2014-neural-machine-translation-jointly-learning/). In Proceedings of ICLR.
11. RyanCotterell, Christo Kirov, John Sylak-Glassman, Géraldine Walther, Ekaterina Vylomova, Patrick Xia, Manaal Faruqui, Sandra Kübler, David Yarowsky, Jason Eisner, and Mans Hulden. 2017a. [find](https://scholar.google.com/scholar?q=RyanCotterell%2C+Christo+Kirov%2C+John+Sylak%2DGlassman%2C+Ge%CC%81raldine+Walther%2C+Ekaterina+Vylomova%2C+Patrick+Xia%2C+Manaal+Faruqui%2C+Sandra+Ku%CC%88bler%2C+David+Yarowsky%2C+Jason+Eisner%2C+and+Mans+Hulden%2E+2017a%2E)
12. The [CoNLL-SIGMORPHON 2017 shared task: Universal morphological reinflection in 52 languages](https://md.research.elamur.ai/free/en/papers/cotterell-2017-sigmorphon-reinflection-52/). In Proceedings of the CoNLL-SIGMORPHON 2017 Shared Task: Universal Morphological Reinflection, Vancouver.
13. Max Bane. 2008. Quantifying and measuring morphological complexity. In Proceedings of the 26th West Coast Conference on Formal Linguistics, pages 69–76. [find](https://scholar.google.com/scholar?q=Max+Bane%2E+2008%2E+Quantifying+and+measuring+morphological+complexity%2E+In+Proceedings+of+the+26th+West+Coast+Conference+on+Formal+Linguistics%2C+pages+69%E2%80%9376%2E)
14. Jean Berko. 1958. The child’s learning of English morphology. Word, 14(2-3):150–177. [find](https://scholar.google.com/scholar?q=Jean+Berko%2E+1958%2E+The+child%E2%80%99s+learning+of+English+morphology%2E+Word%2C+14%282%2D3%29%3A150%E2%80%93177%2E)
15. Leonard Bloomfield. 1933. Language, University of Chicago Press. Reprint edition (October 15, 1984). [find](https://scholar.google.com/scholar?q=Leonard+Bloomfield%2E+1933%2E+Language%2C+University+of+Chicago+Press%2E+Reprint+edition+%28October+15%2C+1984%29%2E)
16. Ryan Cotterell, Christo Kirov, John Sylak-Glassman, David Yarowsky, Jason Eisner, and Mans Hulden. 2016. [find](https://scholar.google.com/scholar?q=Ryan+Cotterell%2C+Christo+Kirov%2C+John+Sylak%2DGlassman%2C+David+Yarowsky%2C+Jason+Eisner%2C+and+Mans+Hulden%2E+2016%2E)
17. The SIGMORPHON 2016 shared task—morphological reinflection. In Proceedings of the 14th SIGMORPHON Workshop on Computational Research in Phonetics, Phonology, and Morphology, pages 10–22, Berlin. [find](https://scholar.google.com/scholar?q=The+SIGMORPHON+2016+shared+task%E2%80%94morphological+reinflection%2E+In+Proceedings+of+the+14th+SIGMORPHON+Workshop+on+Computational+Research+in+Phonetics%2C+Phonology%2C+and+Morphology%2C+pages+10%E2%80%9322%2C+Berlin%2E)
18. Olivier Bonami and Sarah Beniamine. 2016. Joint predictiveness in inflectional paradigms. Word Structure, 9(2):156–182. [find](https://scholar.google.com/scholar?q=Olivier+Bonami+and+Sarah+Beniamine%2E+2016%2E+Joint+predictiveness+in+inflectional+paradigms%2E+Word+Structure%2C+9%282%29%3A156%E2%80%93182%2E)
19. Alexandre Bouchard-Côté, Percy Liang, Thomas Griffiths, and Dan Klein. 2007. A probabilistic approach to diachronic phonology. In Proceedings of the 2007 Joint Conference on Empirical Methods in Natural Language Processing and Computational Natural Language Learning (EMNLP-CoNLL), pages 887–896, P… [find](https://scholar.google.com/scholar?q=Alexandre+Bouchard%2DCo%CC%82te%CC%81%2C+Percy+Liang%2C+Thomas+Griffiths%2C+and+Dan+Klein%2E+2007%2E+A+probabilistic+approach+to+diachronic+phonology%2E+In+Proceedings+of+the+2007+Joint+Conference+on+Empirical+Methods+in+Nat)
20. Ryan Cotterell, Nanyun Peng, and Jason Eisner. 2014. Stochastic contextual edit distance and probabilistic FSTs. In Proceedings of the 52nd Annual Meeting of the Association for Computational Linguistics (ACL), pages 625–630. Baltimore, MD. [find](https://scholar.google.com/scholar?q=Ryan+Cotterell%2C+Nanyun+Peng%2C+and+Jason+Eisner%2E+2014%2E+Stochastic+contextual+edit+distance+and+probabilistic+FSTs%2E+In+Proceedings+of+the+52nd+Annual+Meeting+of+the+Association+for+Computational+Linguist)
21. Peter F. Brown, Vincent J. Della Pietra, Robert L. Mercer, Stephen A. Della Pietra, and Jennifer C. [find](https://scholar.google.com/scholar?q=Peter+F%2E+Brown%2C+Vincent+J%2E+Della+Pietra%2C+Robert+L%2E+Mercer%2C+Stephen+A%2E+Della+Pietra%2C+and+Jennifer+C%2E)
22. Charles F. Hockett. 1958. A Course In Modern Linguistics. The MacMillan Company. [find](https://scholar.google.com/scholar?q=Charles+F%2E+Hockett%2E+1958%2E+A+Course+In+Modern+Linguistics%2E+The+MacMillan+Company%2E)
23. Ryan Cotterell, Nanyun Peng, and Jason Eisner. 2015. [Modeling word forms using latent underlying morphs and phonology](https://md.research.elamur.ai/free/en/papers/cotterell-2015-modeling-word-forms-latent-underlying/). Transactions of the Association for Computational Linguistics (TACL), 3433–447.
24. Katharina Kann and Hinrich Schütze. 2016. Single-model encoder-decoder with explicit morphological representation for reinflection. In Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics (ACL), pages 555–560, Berlin. [find](https://scholar.google.com/scholar?q=Katharina+Kann+and+Hinrich+Schu%CC%88tze%2E+2016%2E+Single%2Dmodel+encoder%2Ddecoder+with+explicit+morphological+representation+for+reinflection%2E+In+Proceedings+of+the+54th+Annual+Meeting+of+the+Association+for+Co)
25. Ryan Cotterell, John Sylak-Glassman, and Christo Kirov. 2017b. Neural graphical models over strings for principal parts morphological paradigm completion. In Proceedings of the 15th Conference of the European Chapter of the Association for Computational Linguistics (EACL), pages 759–765, Valencia. [find](https://scholar.google.com/scholar?q=Ryan+Cotterell%2C+John+Sylak%2DGlassman%2C+and+Christo+Kirov%2E+2017b%2E+Neural+graphical+models+over+strings+for+principal+parts+morphological+paradigm+completion%2E+In+Proceedings+of+the+15th+Conference+of+the+)
26. Michael J. Kenstowicz. 1994. Phonology in Generative Grammar. Blackwell Oxford. [find](https://scholar.google.com/scholar?q=Michael+J%2E+Kenstowicz%2E+1994%2E+Phonology+in+Generative+Grammar%2E+Blackwell+Oxford%2E)
27. Aleksandr E. Kibrik. 1998, Archi (Caucasian – Daghestanian). In The Handbook of Morphology, pages 455–476, Blackwell Oxford. [find](https://scholar.google.com/scholar?q=Aleksandr+E%2E+Kibrik%2E+1998%2C+Archi+%28Caucasian+%E2%80%93+Daghestanian%29%2E+In+The+Handbook+of+Morphology%2C+pages+455%E2%80%93476%2C+Blackwell+Oxford%2E)
28. Ryan Cotterell, Ekaterina Vylomova, Huda Khayrallah, Christo Kirov, and David Yarowsky. 2017c. Paradigm completion for derivational morphology. In Proceedings of the Conference on Empirical Methods in Natural Language Processing (EMNLP), pages 725–731, Copenhagen. [find](https://scholar.google.com/scholar?q=Ryan+Cotterell%2C+Ekaterina+Vylomova%2C+Huda+Khayrallah%2C+Christo+Kirov%2C+and+David+Yarowsky%2E+2017c%2E+Paradigm+completion+for+derivational+morphology%2E+In+Proceedings+of+the+Conference+on+Empirical+Methods+in)
29. Christo Kirov, Ryan Cotterell, John Sylak-Glassman, Géraldine Walther, Ekaterina Vylomova, Patrick Xia, Manaal Faruqui, Sebastian Mielke, Arya D. McCarthy, Sandra Kübler, David Yarowsky, Jason Eisner, and Mans Hulden. 2018. [UniMorph 2.0: Universal morphology](https://md.research.elamur.ai/free/en/papers/kirov-2018-unimorph-2-0-universal-morphology/). In Proceedings of LREC 2018, Miyazaki,…
30. Markus Dreyer and Jason Eisner. 2009. Graphical models over multiple strings. In Proceedings of the Conference on Empirical Methods in Natural Language Processing (EMNLP), pages 101–110. Singapore. [find](https://scholar.google.com/scholar?q=Markus+Dreyer+and+Jason+Eisner%2E+2009%2E+Graphical+models+over+multiple+strings%2E+In+Proceedings+of+the+Conference+on+Empirical+Methods+in+Natural+Language+Processing+%28EMNLP%29%2C+pages+101%E2%80%93110%2E+Singapore%2E)
31. Guillaume Klein, Yoon Kim, Yuntian Deng, Jean Senellart, and Alexander Rush. 2017. [OpenNMT: Open-source toolkit for neural machine translation](https://md.research.elamur.ai/free/en/papers/klein-2017-opennmt-open-source-toolkit-neural/). In Proceedings of ACL 2017, System Demonstrations, pages 67–72.
32. Markus Dreyer and Jason Eisner. 2011. Discovering morphological paradigms from plain text using a Dirichlet process mixture model. In Proceedings of the Conference on Empirical Methods in Natural Language Processing (EMNLP), pages 616–627, Edinburgh. [find](https://scholar.google.com/scholar?q=Markus+Dreyer+and+Jason+Eisner%2E+2011%2E+Discovering+morphological+paradigms+from+plain+text+using+a+Dirichlet+process+mixture+model%2E+In+Proceedings+of+the+Conference+on+Empirical+Methods+in+Natural+Lang)
33. Warren S. McCulloch and Walter Pitts. 1943. A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics, 5(4):115–133. [find](https://scholar.google.com/scholar?q=Warren+S%2E+McCulloch+and+Walter+Pitts%2E+1943%2E+A+logical+calculus+of+the+ideas+immanent+in+nervous+activity%2E+Bulletin+of+Mathematical+Biophysics%2C+5%284%29%3A115%E2%80%93133%2E)
34. Markus Dreyer, Jason Smith, and Jason Eisner. 2008, October. Latent-variable modeling of string transductions with finite-state methods. In Proceedings of the 2008 Conference on Empirical Methods in Natural Language Processing (EMNLP), pages 1080–1089, Honolulu, HI. [find](https://scholar.google.com/scholar?q=Markus+Dreyer%2C+Jason+Smith%2C+and+Jason+Eisner%2E+2008%2C+October%2E+Latent%2Dvariable+modeling+of+string+transductions+with+finite%2Dstate+methods%2E+In+Proceedings+of+the+2008+Conference+on+Empirical+Methods+in+N)
35. John McWhorter. 2001. The world’s simplest grammars are creole grammars. Linguistic Typology, 5(2):125–66. [find](https://scholar.google.com/scholar?q=John+McWhorter%2E+2001%2E+The+world%E2%80%99s+simplest+grammars+are+creole+grammars%2E+Linguistic+Typology%2C+5%282%29%3A125%E2%80%9366%2E)
36. Yoon Mi Oh. 2015. Linguistic Complexity and Information: Quantitative Approaches. Ph.D. thesis, Université de Lyon, France. [find](https://scholar.google.com/scholar?q=Yoon+Mi+Oh%2E+2015%2E+Linguistic+Complexity+and+Information%3A+Quantitative+Approaches%2E+Ph%2ED%2E+thesis%2C+Universite%CC%81+de+Lyon%2C+France%2E)
37. Jack Edmonds. 1967. Optimum branchings. Journal of Research of the National Bureau of Standards B, 71(4):233–240. [find](https://scholar.google.com/scholar?q=Jack+Edmonds%2E+1967%2E+Optimum+branchings%2E+Journal+of+Research+of+the+National+Bureau+of+Standards+B%2C+71%284%29%3A233%E2%80%93240%2E)
38. Azaria Paz. 2003. Probabilistic Automata, John Wiley and Sons. [find](https://scholar.google.com/scholar?q=Azaria+Paz%2E+2003%2E+Probabilistic+Automata%2C+John+Wiley+and+Sons%2E)
39. David Gil. 1994. The structure of Riau Indonesian. Nordic Journal of Linguistics, 17(2):179–200. [find](https://scholar.google.com/scholar?q=David+Gil%2E+1994%2E+The+structure+of+Riau+Indonesian%2E+Nordic+Journal+of+Linguistics%2C+17%282%29%3A179%E2%80%93200%2E)
40. François Pellegrino, Christophe Coupé, and Egidio Marsico. 2011. A cross-language perspective on speech information rate. Language, 87(3):539–558. [find](https://scholar.google.com/scholar?q=Franc%CC%A7ois+Pellegrino%2C+Christophe+Coupe%CC%81%2C+and+Egidio+Marsico%2E+2011%2E+A+cross%2Dlanguage+perspective+on+speech+information+rate%2E+Language%2C+87%283%29%3A539%E2%80%93558%2E)
41. Mary Hare and Jeffrey L. Elman. 1995. Learning and morphological change. Cognition, 56(1):61–98. [find](https://scholar.google.com/scholar?q=Mary+Hare+and+Jeffrey+L%2E+Elman%2E+1995%2E+Learning+and+morphological+change%2E+Cognition%2C+56%281%29%3A61%E2%80%9398%2E)
42. Kenny Smith, Michael L. Kalish, Thomas L. Griffiths, and Stephan Lewandowsky. 2008. Cultural transmission and the evolution of human behaviour. Philosophical Transactions B. doi.org/10.1098/rstb.2008.0147. — [doi:10.1098/rstb.2008.0147](https://doi.org/10.1098/rstb.2008.0147) [find](https://scholar.google.com/scholar?q=Kenny+Smith%2C+Michael+L%2E+Kalish%2C+Thomas+L%2E+Griffiths%2C+and+Stephan+Lewandowsky%2E+2008%2E+Cultural+transmission+and+the+evolution+of+human+behaviour%2E+Philosophical+Transactions+B%2E+doi%2Eorg%2F10%2E1098%2Frstb%2E2008%2E)
43. Steven Pinker and Alan Prince. 1988. On language and connectionism: Analysis of a parallel distributed processing model of language acquisition. Cognition, 28(1):73–193. [find](https://scholar.google.com/scholar?q=Steven+Pinker+and+Alan+Prince%2E+1988%2E+On+language+and+connectionism%3A+Analysis+of+a+parallel+distributed+processing+model+of+language+acquisition%2E+Cognition%2C+28%281%29%3A73%E2%80%93193%2E)
44. Angela Ralli. 1994. Feature representations and feature-passing operations in Greek nominal inflection. In Proceedings of the 8th Symposium on English and Greek Linguistics, pages 19–46. [find](https://scholar.google.com/scholar?q=Angela+Ralli%2E+1994%2E+Feature+representations+and+feature%2Dpassing+operations+in+Greek+nominal+inflection%2E+In+Proceedings+of+the+8th+Symposium+on+English+and+Greek+Linguistics%2C+pages+19%E2%80%9346%2E)
45. Carolyn P. Sobel and Paul Li. 2013. The Cognitive Sciences: An Interdisciplinary Approach. Sage Publications. [find](https://scholar.google.com/scholar?q=Carolyn+P%2E+Sobel+and+Paul+Li%2E+2013%2E+The+Cognitive+Sciences%3A+An+Interdisciplinary+Approach%2E+Sage+Publications%2E)
46. Angela Ralli. 2002. The role of morphology in gender determination: evidence from Modern Greek. Linguistics, 40(3; ISSU 379):519–552. [find](https://scholar.google.com/scholar?q=Angela+Ralli%2E+2002%2E+The+role+of+morphology+in+gender+determination%3A+evidence+from+Modern+Greek%2E+Linguistics%2C+40%283%3B+ISSU+379%29%3A519%E2%80%93552%2E)
47. Andrew Spencer. 1991. Morphological Theory: An Introduction to Word Structure in Generative Grammar. Wiley-Blackwell. [find](https://scholar.google.com/scholar?q=Andrew+Spencer%2E+1991%2E+Morphological+Theory%3A+An+Introduction+to+Word+Structure+in+Generative+Grammar%2E+Wiley%2DBlackwell%2E)
48. Thomas Stolz, Hitomi Otsuka, Aina Urdze, and Johan van der Auwera. 2012. Irregularity in Morphology (and beyond), volume 11. Walter de Gruyter. [find](https://scholar.google.com/scholar?q=Thomas+Stolz%2C+Hitomi+Otsuka%2C+Aina+Urdze%2C+and+Johan+van+der+Auwera%2E+2012%2E+Irregularity+in+Morphology+%28and+beyond%29%2C+volume+11%2E+Walter+de+Gruyter%2E)
49. Jorma Rissanen and Eric S. Ristad. 1994. Language acquisition in the MDL framework. In Eric S. Ristad, editor, Language Computation. American Mathematical Society, Philadelphia, PA. [find](https://scholar.google.com/scholar?q=Jorma+Rissanen+and+Eric+S%2E+Ristad%2E+1994%2E+Language+acquisition+in+the+MDL+framework%2E+In+Eric+S%2E+Ristad%2C+editor%2C+Language+Computation%2E+American+Mathematical+Society%2C+Philadelphia%2C+PA%2E)
50. Ilya Sutskever, Oriol Vinyals, and Quoc V. Le. 2014. [Sequence to sequence learning with neural networks](https://md.research.elamur.ai/free/en/papers/sutskever-2014-sequence-sequence-learning-neural-networks/). In Advances in Neural Information Processing Systems (NIPS), pages 3104–3112.
51. Robert Henry Robins. 2013. A Short History of Linguistics. Routledge. [find](https://scholar.google.com/scholar?q=Robert+Henry+Robins%2E+2013%2E+A+Short+History+of+Linguistics%2E+Routledge%2E)
52. Benoı̂t Sagot. 2013. Comparing complexity measures. In Computational Approaches to Morphological Complexity, Paris. [find](https://scholar.google.com/scholar?q=Beno%C4%B1%CC%82t+Sagot%2E+2013%2E+Comparing+complexity+measures%2E+In+Computational+Approaches+to+Morphological+Complexity%2C+Paris%2E)
53. John Sylak-Glassman. 2016, The composition and use of the universal morphological feature schema (Unimorph schema). Johns Hopkins University. [find](https://scholar.google.com/scholar?q=John+Sylak%2DGlassman%2E+2016%2C+The+composition+and+use+of+the+universal+morphological+feature+schema+%28Unimorph+schema%29%2E+Johns+Hopkins+University%2E)
54. Edward Sapir. 1921. Language: An Introduction to the Study of Speech. [find](https://scholar.google.com/scholar?q=Edward+Sapir%2E+1921%2E+Language%3A+An+Introduction+to+the+Study+of+Speech%2E)
55. John Sylak-Glassman, Christo Kirov, David Yarowsky, and Roger Que. 2015, July. [A language-independent feature schema for inflectional morphology](https://md.research.elamur.ai/free/en/papers/glassman-2015-language-independent-feature-schema-inflectional/). In Proceedings of the 53rd Annual Meeting of the Association for Computational Linguistics and the 7th International Joint Conference on Natural Language…
56. Claude E. Shannon. 1948. A mathematical theory of communication. Bell Systems Technical Journal, 27. [find](https://scholar.google.com/scholar?q=Claude+E%2E+Shannon%2E+1948%2E+A+mathematical+theory+of+communication%2E+Bell+Systems+Technical+Journal%2C+27%2E)
57. Hava T. Siegelmann and Eduardo D. Sontag. 1991. Turing computability with neural nets. Applied Mathematics Letters, 4(6):77–80. [find](https://scholar.google.com/scholar?q=Hava+T%2E+Siegelmann+and+Eduardo+D%2E+Sontag%2E+1991%2E+Turing+computability+with+neural+nets%2E+Applied+Mathematics+Letters%2C+4%286%29%3A77%E2%80%9380%2E)
58. Hava T. Siegelmann and Eduardo D. Sontag. 1995. On the computational power of neural nets. Journal of Computer and System Sciences, 50(1):132–150. [find](https://scholar.google.com/scholar?q=Hava+T%2E+Siegelmann+and+Eduardo+D%2E+Sontag%2E+1995%2E+On+the+computational+power+of+neural+nets%2E+Journal+of+Computer+and+System+Sciences%2C+50%281%29%3A132%E2%80%93150%2E)
59. Matthew D. Zeiler. 2012. [ADADELTA: An adaptive learning rate method](https://md.research.elamur.ai/free/en/papers/zeiler-2012-adadelta-adaptive-learning-rate-method/). arXiv preprint arXiv:1212.5701v1.

*Updated 30 October 2026*