---
title: "Learning Latent Representations with — Paramore 2026"
description: "The paper tackles a learnability problem in morphophonology."
authors: ["Jonathan Charles Paramore"]
year: 2026
venue: "Proceedings of the Society for Computation in Linguistics 2026"
source: "https://aclanthology.org/2026.scil-main.5/"
doi: "10.18653/v1/2026.scil-main.5"
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/paramore-2026-learning-latent-representations-progressive-hypothesis/"
---
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# Learning Latent Representations with Progressive Hypothesis Space Expansion

**Authors:** Jonathan Charles Paramore · **Year:** 2026 · **Venue:** Proceedings of the Society for Computation in Linguistics 2026 · **Licence:** [CC BY 4.0 (ACL Anthology)](https://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://aclanthology.org/2026.scil-main.5/) · [PDF](https://aclanthology.org/2026.scil-main.5.pdf) · [DOI 10.18653/v1/2026.scil-main.5](https://doi.org/10.18653/v1/2026.scil-main.5) · [OpenAlex](https://openalex.org/W7166802243)

**Citations:** 0 citations (openalex-snapshot · 2026-10-14)

## Summary
The paper tackles a learnability problem in morphophonology. Some analyses need underlying representations (URs) that differ from every surface form of a morpheme. Allowing that much abstraction raises two issues: the learner may not settle on the least abstract adequate UR, and the candidate space can grow without limit. Earlier models either fixed a finite UR set by hand or, as in Wang and Hayes (2025), failed at high abstraction levels.

Paramore proposes the UR PHaSE learner, which combines MaxEnt with expectation-maximization. Building on Tesar's ordering of URs by disparity count, it starts with fully concrete UR candidates. It moves to more abstract batches only when a likelihood threshold is not met. New candidates are generated selectively, using constraints whose weights signal unresolved uncertainty.

Tested on Pakistani Punjabi vowel nasality, the learner finds the abstract URs that parallel-search learners miss. The result suggests that limits on abstraction can come from the search procedure itself rather than from an external stipulation.

## Key points
- Learning has four stages, with stages 2–4 repeated until every morpheme passes the threshold:
  - phonotactic MaxEnt learning (weights start at 50 within [0, 100], with an L2 prior favoring a restrictive grammar),
  - EM over URs with up to n disparities,
  - a likelihood-threshold check,
  - targeted generation of (n+1)-disparity candidates.
- Case study: in Pakistani Punjabi (about 110 million speakers), vowels before tautomorphemic nasals are always nasal on the surface but do not trigger regressive nasal harmony. Contrastive nasal vowels do trigger it. This motivates underlyingly oral URs for pre-N vowels.
- After 1-disparity EM, the learner gives full posterior probability (1.00) to /sA/ for 'breath' and to the abstract /tAVAn/ for 'penalty'.
- Predicted likelihoods for the observed surface forms are 1.00, 0.96 and 1.00. These depend on high weights for *VN and ID[NAS]/_V.
- Planned future work:
  - testing on other cases said to need abstract URs (e.g., O'Hara 2017; Wang and Hayes 2025),
  - finding the point where deep disparity levels become computationally intractable.

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

Fields: [Linguistics & languages](https://md.research.elamur.ai/free/en/shelves/linguistics/)

## Cite

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

```bibtex
@inproceedings{paramore2026learning,
  title = {{Learning Latent Representations with Progressive Hypothesis Space Expansion}},
  author = {Paramore, Jonathan Charles},
  booktitle = {Proceedings of the Society for Computation in Linguistics 2026},
  year = {2026},
  doi = {10.18653/v1/2026.scil-main.5},
  url = {https://doi.org/10.18653/v1/2026.scil-main.5}
}
```

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## References

12 references, 0 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

1. Caleb Belth. 2026. A learning-based account of phonological tiers. Linguistic Inquiry, 57(2):229–265. [find](https://scholar.google.com/scholar?q=Caleb+Belth%2E+2026%2E+A+learning%2Dbased+account+of+phonological+tiers%2E+Linguistic+Inquiry%2C+57%282%29%3A229%E2%80%93265%2E)
2. John J. McCarthy. 2007. Hidden Generalizations: Phonological Opacity in Optimality Theory. Sheffield: Equinox. [find](https://scholar.google.com/scholar?q=John+J%2E+McCarthy%2E+2007%2E+Hidden+Generalizations%3A+Phonological+Opacity+in+Optimality+Theory%2E+Sheffield%3A+Equinox%2E)
3. Arthur P. Dempster, Nan M. Laird, and Donald B. Rubin. 1977. Maximum likelihood from incomplete data via the EM algorithm. In Royal Statistical Society. [find](https://scholar.google.com/scholar?q=Arthur+P%2E+Dempster%2C+Nan+M%2E+Laird%2C+and+Donald+B%2E+Rubin%2E+1977%2E+Maximum+likelihood+from+incomplete+data+via+the+EM+algorithm%2E+In+Royal+Statistical+Society%2E)
4. Charlie O’Hara. 2017. How abstract is more abstract? learning abstract underlying representations. Phonology, 34(2):325–345. [find](https://scholar.google.com/scholar?q=Charlie+O%E2%80%99Hara%2E+2017%2E+How+abstract+is+more+abstract%3F+learning+abstract+underlying+representations%2E+Phonology%2C+34%282%29%3A325%E2%80%93345%2E)
5. Madeline Gilbert. 2023. Testing for underlying representations: Segments and clusters in Sevillian Span-Jonathan Charles Paramore. 2025. Learning covert URs via disparity minimization. In Eighth Annual Meeting of the Society for Computation in Linguistics (SCiL), volume 8. ii. *N AS O BS (Walker, 20… [find](https://scholar.google.com/scholar?q=Madeline+Gilbert%2E+2023%2E+Testing+for+underlying+representations%3A+Segments+and+clusters+in+Sevillian+Span%2DJonathan+Charles+Paramore%2E+2025%2E+Learning+covert+URs+via+disparity+minimization%2E+In+Eighth+Annua)
6. Jonathan Charles Paramore and Ryan T. Bennett. 2025. Covert URs: evidence from nasalization in Pakistani Punjabi. Manuscript, UC Santa Cruz. iii. *N AS G (Walker, 2003, p.51) Assign a violation for every glide that dominates a [+ NAS ] feature. [find](https://scholar.google.com/scholar?q=Jonathan+Charles+Paramore+and+Ryan+T%2E+Bennett%2E+2025%2E+Covert+URs%3A+evidence+from+nasalization+in+Pakistani+Punjabi%2E+Manuscript%2C+UC+Santa+Cruz%2E+iii%2E+%2AN+AS+G+%28Walker%2C+2003%2C+p%2E51%29+Assign+a+violation+for+ev)
7. Alan Prince and Paul Smolensky. 1993/2004. Optimality Theory: constraint interaction in Generative grammar. Malden, Mass: Blackwell Publishers. iv. *N AS V (Walker, 2003, p.51) Assign a violation for every vowel that dominates a [+ NAS ] feature. [find](https://scholar.google.com/scholar?q=Alan+Prince+and+Paul+Smolensky%2E+1993%2F2004%2E+Optimality+Theory%3A+constraint+interaction+in+Generative+grammar%2E+Malden%2C+Mass%3A+Blackwell+Publishers%2E+iv%2E+%2AN+AS+V+%28Walker%2C+2003%2C+p%2E51%29+Assign+a+violation+for+)
8. Herbert A. Simon. 1955. A behavioral model of rational choice. The Quarterly Journal of Economics, 69(1):99–118. v. *VN Assign a violation for every vowel that dominates a [- NAS ] feature when directly preceding a nasal consonant. [find](https://scholar.google.com/scholar?q=Herbert+A%2E+Simon%2E+1955%2E+A+behavioral+model+of+rational+choice%2E+The+Quarterly+Journal+of+Economics%2C+69%281%29%3A99%E2%80%93118%2E+v%2E+%2AVN+Assign+a+violation+for+every+vowel+that+dominates+a+%5B%2D+NAS+%5D+feature+when+direct)
9. Herbert A. Simon. 1956. Rational choice and the structure of the environment. Psychological Review, 63(2):129–138. vi. I D [ NAS ] For every segment, A, assign a violation if the output value for the [ NAS ] feature dominated by A does not match the input value for the [ NAS ] feature dominated by A… [find](https://scholar.google.com/scholar?q=Herbert+A%2E+Simon%2E+1956%2E+Rational+choice+and+the+structure+of+the+environment%2E+Psychological+Review%2C+63%282%29%3A129%E2%80%93138%2E+vi%2E+I+D+%5B+NAS+%5D+For+every+segment%2C+A%2C+assign+a+violation+if+the+output+value+for+the+)
10. Bruce Tesar. 2014. Output-Driven Phonology. Cambridge: Cambridge University Press. [find](https://scholar.google.com/scholar?q=Bruce+Tesar%2E+2014%2E+Output%2DDriven+Phonology%2E+Cambridge%3A+Cambridge+University+Press%2E)
11. Bruce Tesar. 2016. Phonological learning with output-driven maps. Language Acquisition, 24(2):148–167. [find](https://scholar.google.com/scholar?q=Bruce+Tesar%2E+2016%2E+Phonological+learning+with+output%2Ddriven+maps%2E+Language+Acquisition%2C+24%282%29%3A148%E2%80%93167%2E)
12. Rachel Walker. 2003. Reinterpreting transparency in nasal harmony, pages 37–72. Amsterdam: John Benjamins. [find](https://scholar.google.com/scholar?q=Rachel+Walker%2E+2003%2E+Reinterpreting+transparency+in+nasal+harmony%2C+pages+37%E2%80%9372%2E+Amsterdam%3A+John+Benjamins%2E)