---
title: "Vertical Routing: A Cost-Efficient Collaboration Routing Framework"
description: "The authors show that lightweight difficulty predictors do barely better than chance, while stronger evaluators are costly. 36 references."
authors: ["Si Shen", "Peijun Shen", "Danhao Zhu"]
year: 2026
venue: "Transactions of the Association for Computational Linguistics"
source: "https://aclanthology.org/2026.tacl-1.104/"
doi: "10.1162/tacl.a.802"
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/shen-2026-vertical-routing-cost-efficient-collaboration/"
---
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# Vertical Routing: A Cost-Efficient Collaboration Routing Framework

**Authors:** Si Shen, Peijun Shen and Danhao Zhu · **Year:** 2026 · **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) 2026](https://md.research.elamur.ai/free/en/venues/tacl/2026/)) · **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/2026.tacl-1.104/) · [PDF](https://aclanthology.org/2026.tacl-1.104.pdf) · [DOI 10.1162/tacl.a.802](https://doi.org/10.1162/tacl.a.802) · [OpenAlex](https://openalex.org/W7207797061)

**Citations:** 0 citations (OpenAlex, 2026-10-14)

## Summary
Systems that split work between large and small language models usually guess, before generation starts, how hard a query is and then give the whole query to one model. The authors show that lightweight difficulty predictors do barely better than chance, while stronger evaluators are costly. Their alternative, Vertical Routing, divides a single response into stages and gives the large model only the parts that matter most. Domain templates encode task structure with criticality scores, such as planning before solving in math or choosing keywords before translating. A default template has the large model write a budgeted opening prefix, after which the small model finishes. A template is chosen once per dataset using a short checklist, and large-model tokens are then allocated greedily under a cost budget. On GSM8K, MATH and WMT, the method scores slightly higher than RouterDC while using about half the tokens and showing much less run-to-run variance. This points to cheaper and more predictable LLM deployment.

## Key points
- When tested on sets split evenly between easy and hard queries in translation, math and code, lightweight query-level routers perform scarcely better than the 50% achieved by random guessing. This motivates routing at the stage level instead of the query level.
- Against RouterDC, Vertical Routing reaches an average score of 60.4 versus 58.4. Token usage falls from 929.1 to 474.5 (−48.9%). The large model's share of output drops from 46.0% to 26.8% (41.7% relative), and standard deviation across runs is 87.5% lower.
- A domain template is used only if three conditions hold: stages are shared, later stages depend on earlier ones, and stages clearly differ in criticality. Otherwise the prefix-first default applies. Cost is measured as weighted token counts, with the large-to-small cost ratio estimated from decoding latency.
- On MBPP, under matched large-model budgets, the method helps most when the budget is low. The small model's arithmetic and constraint errors remain a bottleneck, and all experiments use a single model family.
- Data and code are released at github.com/shenpeijun0212/Vertical-Routing.

*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

- [Nanjing University of Science and Technology](https://md.research.elamur.ai/free/en/universities/nanjing-university-of-science-and-technology/) — University, Nanjing, China · 14 works · 1,590 citations

Also on the byline: [Shanghai Police College](https://ror.org/0479fds27) · [Jiangsu Police Officer College](https://ror.org/04k1m2t10).

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## Cite

Cite as: Si Shen, Peijun Shen and Danhao Zhu. 2026. Vertical Routing: A Cost-Efficient Collaboration Routing Framework. Transactions of the Association for Computational Linguistics.

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

```bibtex
@article{shen2026vertical,
  title = {{Vertical Routing: A Cost-Efficient Collaboration Routing Framework}},
  author = {Si Shen, Peijun Shen and Danhao Zhu},
  journal = {Transactions of the Association for Computational Linguistics},
  year = {2026},
  doi = {10.1162/tacl.a.802},
  url = {https://doi.org/10.1162/tacl.a.802}
}
```

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- [next → VET: Verifiable Execution Tracing for Reliable Text-to-SQL Generation](https://md.research.elamur.ai/free/en/papers/wang-2026-vet-verifiable-execution-tracing-reliable/)
- [↑ back to papers of 2026](https://md.research.elamur.ai/free/en/papers/2026/page/47/)

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*Updated 1 November 2026*