# Beyond Input Understanding: Diagnosing Multilingual Mathematical Reasoning with Directed Acyclic Trace Graphs

arXiv: https://arxiv.org/abs/2605.27715 · HTML: https://mlsanity.com/paper/2605.27715/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 13 of its 42 references that are in the map.
- First posted on arXiv 26 May 2026.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 13 of 13)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Thought Anchors: Which LLM Reasoning Steps Matter?](https://mlsanity.com/paper/2506.19143/) (2025)
- [PolyMath: Evaluating Mathematical Reasoning in Multilingual Contexts](https://mlsanity.com/paper/2504.18428/) (2025)
- [Crosslingual Reasoning through Test-Time Scaling](https://mlsanity.com/paper/2505.05408/) (2025)
- [Language Matters: How Do Multilingual Input and Reasoning Paths Affect Large Reasoning Models?](https://mlsanity.com/paper/2505.17407/) (2025)
- [Long Chain-of-Thought Reasoning Across Languages](https://mlsanity.com/paper/2508.14828/) (2025)
- [Think Natively: Unlocking Multilingual Reasoning with Consistency-Enhanced Reinforcement Learning](https://mlsanity.com/paper/2510.07300/) (2025)
- [ReasoningFlow: Semantic Structure of Complex Reasoning Traces](https://mlsanity.com/paper/2506.02532/) (2025)
- [Why Do Multilingual Reasoning Gaps Emerge in Reasoning Language Models?](https://mlsanity.com/paper/2510.27269/) (2025)
- [Crosslingual On-Policy Self-Distillation for Multilingual Reasoning](https://mlsanity.com/paper/2605.09548/) (2026)
- [Large Reasoning Models Are (Not Yet) Multilingual Latent Reasoners](https://mlsanity.com/paper/2601.02996/) (2026)
- [What Makes Good Multilingual Reasoning? Disentangling Traces with Measurable Features](https://mlsanity.com/paper/2604.04720/) (2026)

## Abstract (arXiv)

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.