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# Learning Non-Isomorphic Tree Mappings for Machine Translation

**Authors:** [Jason Eisner](https://md.mova.elamur.ai/free/en/docs/papers/authors/jason-eisner/) · **Year:** 2003 · **Venue:** The Companion Volume to the Proceedings of the 41st Annual Meeting of the ACL **Link:** [aclanthology.org/P03-2041](https://aclanthology.org/P03-2041/) · **Licence:** [CC BY-NC-SA 3.0](https://creativecommons.org/licenses/by-nc-sa/3.0/) — summary only

[**240** citations](https://openalex.org/works?filter=cites:W2143008661) openalex · 2026-10-19[**114** citations in our library](https://md.mova.elamur.ai/free/en/docs/papers/cited-by/eisner-2003-learning-non-isomorphic-tree-mappings/) of the 140673 papers whose bibliographies we read[The Companion Volume to the Proceedings of 41st Annual Meeting of the Association for Computational Linguistics](https://aclanthology.org/volumes/P03-2/)[licence](https://creativecommons.org/licenses/by-nc-sa/3.0/)

- [Publisher's page](https://aclanthology.org/P03-2041/)
- [PDF](https://aclanthology.org/P03-2041.pdf)
- [DOI 10.3115/1075178.1075217](https://doi.org/10.3115/1075178.1075217)
- [OpenAlex](https://openalex.org/W2143008661)

**Authors (1)**

1. [Eisner, Jason](https://openalex.org/A5052467896) [ORCID](https://orcid.org/0000-0002-8861-0772) · [Semantic Scholar](https://www.semanticscholar.org/author/145043214) · h 51 · 8141 citations · 307 works

Citations and author metrics from openalex (2026-10-19); authors with the same name are not always told apart.

## What it is about

Eisner proposes learning a mapping between two trees that need not have the same shape. The model is a synchronous tree substitution grammar (STSG): a set of pairs of elementary trees, each pair with a state for every open position, which combine into a pair of derived trees. He gives a probabilistic form, a tree parsing algorithm that finds all ways to cut a tree into elementary trees with bounded size (for dependency trees, at most three internal nodes), and EM training with an inside-outside pass over all derivations, so unaligned tree pairs can be used. Empty elementary trees handle free-translation mismatches, such as a deleted quantifier or an inserted adverb, and a matching between frontier nodes allows a chunk to be aligned to a non-isomorphic chunk. The paper is a short sketch. It reports the algorithms and an implementation status, but no experiments and no numbers.

## Ideas

- I1. Empty meta tokens for deletions and insertions. A verse pair often adds or drops a word (*and*, *the*, a pronoun). Give the reader a null-concept meta token for each side, so a dropped word is recorded as a deletion, not lost. Count these per author (open problem 4).
- I2. Chunk-to-chunk pairs learned from unaligned verse pairs. Enumerate the decompositions of the two trees into bounded chunks, weight them by the current counts, and keep a chunk pair (*give a kiss to* to *kiss*) only when it lowers the residual. This is the count-based version of the residual-driven lexicon (open problem 2).
- I3. Put number and person into the states of the chunk table. The paper uses states such as (plural, third person) for a subject slot, which is the UD FEATS idea of open problem 5 for meta tokens.
- I4. Prune matchings whose inside score is low, and compare the pruned and full search on a dev set of verses. The control is the exact encoder output: pruning must leave it unchanged on dev.

## For Mova

The relevant code is `tools/translate` (`meta.rs` for the chunk pairs and the null tokens, `profile.rs` for the encoder). The paper's EM is not needed as such: the counted decompositions of verse pairs can be kept as integer counts in ordered maps. Since the paper has no results, the first step is a measurement, not a claim: count how many verse pairs need a null token on each side.

Topics: [Machine translation](https://md.mova.elamur.ai/free/en/docs/papers/topics/machine-translation/)

## Cite

The paper itself, not this card. BibTeX from the library's record of the work. [DOI 10.3115/1075178.1075217](https://doi.org/10.3115/1075178.1075217)

```
@inproceedings{eisner2003learning,
  title = {{Learning Non-Isomorphic Tree Mappings for Machine Translation}},
  author = {Eisner, Jason},
  booktitle = {The Companion Volume to the Proceedings of 41st Annual Meeting of the Association for Computational Linguistics},
  year = {2003},
  doi = {10.3115/1075178.1075217},
  url = {https://doi.org/10.3115/1075178.1075217}
}
```

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