@inproceedings{zhang-etal-2026-beyond-input,
title = "Beyond Input Understanding: Diagnosing Multilingual Mathematical Reasoning with Directed Acyclic Trace Graphs",
author = "Zhang, Jiaqiao and
Li, Zhoujun and
Zhao, Raoyuan and
Lan, Jian and
Seidl, Thomas and
Hedderich, Michael A. and
Schuetze, Hinrich and
Liu, Yihong",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.emnlp-main.463/",
pages = "10615--10639",
ISBN = "979-8-89176-459-0",
abstract = "Large reasoning models (LRMs) achieve strong mathematical reasoning performance in English, but remain much less reliable in many low- and medium-resource languages. This gap is often explained as a failure to understand non-English problem statements. We show that this view is incomplete: even when the problem is given in English, controlling the model{'}s reasoning language can substantially reduce accuracy, suggesting that language also affects reasoning execution itself. To study this effect, we introduce DATG, a Directed Acyclic Trace Graph framework that maps reasoning traces to language-independent mathematical anchors and dependencies. This allows us to align target-language traces with reference DAGs and measure whether they cover required mathematical nodes, respect dependency edges, and avoid harmful mathematical actions. Experiments on the Qwen3 series across 12 languages show that non-English reasoning often suffers from reduced anchor coverage and weaker dependency fidelity, especially in low-resource languages. Motivated by this diagnosis, we propose Loop-Retry and Formula-Retry, two simple test-time controls targeting DATG-exposed failure modes, and show that they consistently improve target-language reasoning performance in low-resource languages."
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<abstract>Large reasoning models (LRMs) achieve strong mathematical reasoning performance in English, but remain much less reliable in many low- and medium-resource languages. This gap is often explained as a failure to understand non-English problem statements. We show that this view is incomplete: even when the problem is given in English, controlling the model’s reasoning language can substantially reduce accuracy, suggesting that language also affects reasoning execution itself. To study this effect, we introduce DATG, a Directed Acyclic Trace Graph framework that maps reasoning traces to language-independent mathematical anchors and dependencies. This allows us to align target-language traces with reference DAGs and measure whether they cover required mathematical nodes, respect dependency edges, and avoid harmful mathematical actions. Experiments on the Qwen3 series across 12 languages show that non-English reasoning often suffers from reduced anchor coverage and weaker dependency fidelity, especially in low-resource languages. Motivated by this diagnosis, we propose Loop-Retry and Formula-Retry, two simple test-time controls targeting DATG-exposed failure modes, and show that they consistently improve target-language reasoning performance in low-resource languages.</abstract>
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%0 Conference Proceedings
%T Beyond Input Understanding: Diagnosing Multilingual Mathematical Reasoning with Directed Acyclic Trace Graphs
%A Zhang, Jiaqiao
%A Li, Zhoujun
%A Zhao, Raoyuan
%A Lan, Jian
%A Seidl, Thomas
%A Hedderich, Michael A.
%A Schuetze, Hinrich
%A Liu, Yihong
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F zhang-etal-2026-beyond-input
%X Large reasoning models (LRMs) achieve strong mathematical reasoning performance in English, but remain much less reliable in many low- and medium-resource languages. This gap is often explained as a failure to understand non-English problem statements. We show that this view is incomplete: even when the problem is given in English, controlling the model’s reasoning language can substantially reduce accuracy, suggesting that language also affects reasoning execution itself. To study this effect, we introduce DATG, a Directed Acyclic Trace Graph framework that maps reasoning traces to language-independent mathematical anchors and dependencies. This allows us to align target-language traces with reference DAGs and measure whether they cover required mathematical nodes, respect dependency edges, and avoid harmful mathematical actions. Experiments on the Qwen3 series across 12 languages show that non-English reasoning often suffers from reduced anchor coverage and weaker dependency fidelity, especially in low-resource languages. Motivated by this diagnosis, we propose Loop-Retry and Formula-Retry, two simple test-time controls targeting DATG-exposed failure modes, and show that they consistently improve target-language reasoning performance in low-resource languages.
%U https://aclanthology.org/2026.emnlp-main.463/
%P 10615-10639
Markdown (Informal)
[Beyond Input Understanding: Diagnosing Multilingual Mathematical Reasoning with Directed Acyclic Trace Graphs](https://aclanthology.org/2026.emnlp-main.463/) (Zhang et al., EMNLP 2026)
ACL
- Jiaqiao Zhang, Zhoujun Li, Raoyuan Zhao, Jian Lan, Thomas Seidl, Michael A. Hedderich, Hinrich Schuetze, and Yihong Liu. 2026. Beyond Input Understanding: Diagnosing Multilingual Mathematical Reasoning with Directed Acyclic Trace Graphs. In Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing, pages 10615–10639, Budapest, Hungary. Association for Computational Linguistics.