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.

Unsupervised paraphrase generation is a challenging task that benefits a variety of downstream NLP applications. Current unsupervised methods for paraphrase generation typically employ round-trip translation or denoising, which require translation corpus and result in paraphrases overly similar to the original sentences in surface structure. Most of these methods lack explicit control over the similarity between the original and generated sentences, and the entities are also less correctly kept. To obviate the reliance on translation data and prompt greater variations in surface structure, we propose a self-supervised pseudo-data construction method that generates diverse pseudo-paraphrases in distinct surface structures for a given sentence. To control the similarity and generate accurate entities, we propose an unsupervised paraphrasing model that encodes the sentence meaning and the entities with discrete and continuous variables, respectively. The similarity can be controlled by sampling discrete variables and the entities are kept substantially accurate due to the specific modeling of entities using continuous variables. Experimental results on two benchmark datasets demonstrate the advantages of our pseudo-data construction method compared to round-trip translation, and the superiority of our paraphrasing model over the state-of-the-art unsupervised methods.