Reasoning over Grammar: Can Synthetic Linguistic Reasoning Traces Enhance Low-Resource Machine Translation?

Large language models (LLMs) offer a promising approach to machine translation (MT) for extremely low-resource languages by incorporating linguistic resources through in-context learning. However, LLMs often struggle to apply grammatical information effectively during translation. Inspired by recent progress in chain-of-thought reasoning, we investigate whether low-resource MT can benefit from structured intermediate steps of linguistic analysis and grammatical reasoning. We propose a pipeline for automatically generating step-by-step linguistic reasoning traces from Universal Dependencies treebanks, dictionaries, and grammar-rule banks. We evaluate these traces in three settings: in-context learning (ICL), supervised fine-tuning (SFT), and reinforcement fine-tuning (RFT), on Xibe and Chintang as test cases. Our results show that linguistic reasoning traces are most effective as inference-time guidance: in ICL, reliable sentence-specific traces substantially improve translation performance across most models, languages, and metrics. In contrast, using the linguistic reasoning traces as training data yields smaller and less consistent gains, as models learn the trace format but often generate erroneous content. These findings suggest that LLMs can leverage grammatical information for low-resource MT when given reliable linguistic analyses, while learning to generate such analyses remains a major bottleneck.

Expert-Aware Causal Tracing of Factual Recall in Sparse MoE Language Models

Causal tracing of factual recall has been studied predominantly in dense transformer language models, where interventions localize information flow to layers or feed-forward modules. Sparse mixture-of-experts (MoE) language models introduce a sharper question: when a factual prediction is mediated by a routed MoE block, which routed expert contributions matter? We formulate expert-aware causal tracing for sparse MoE language models. Using CounterFact facts, we first corrupt the model's factual preference by adding noise to subject-token embeddings, and then test whether clean MoE-block outputs or clean expert-level updates restore the true-vs-foil logit contrast. For Qwen3-30B-A3B-Base, a layer sweep selects and validates layer 44, and expert-level tracing identifies L44E069 as an expert repeatedly selected in the clean run whose held-out patch outperforms other active same-layer expert patches. For Mixtral-8x7B-v0.1, layer-level tracing validates a mid-layer signal, but the signal is not localized to the selected singleton expert; a coalition check instead recovers it with routed multi-expert updates. These results suggest that MoE factual tracing can be made expert-aware, while also showing that expert-level localization is model- and protocol-dependent rather than universal.

Understanding LLM Behavior in Multi-Target Cross-Lingual Summarization

Multi-target cross-lingual text summarization (MTXLS), which summarizes a source document into multiple target languages, is increasingly important as users consume content in diverse languages, but remains underexplored. To address this gap, we introduce multi-target cross-lingual element-aware (MEA), a new MTXLS benchmark covering 24 target languages. We benchmark end-to-end and pipeline approaches across various LLMs and show that MTXLS performance still substantially lags behind English monolingual summarization. To better understand MTXLS in LLMs, we propose a layer-wise analysis framework for investigating how LLMs internally perform MTXLS. Our analyses suggest that translation and summarization behaviors emerge jointly within later layers rather than as distinctly decomposed stages. Most task-relevant processing occurs within these layers, and errors also tend to arise at similar depths. Motivated by these findings, we introduce an inference-time activation steering method that leverages hidden representations from English summarization to guide MTXLS generation. Experiments show that our method consistently improves MTXLS quality across target languages.

ReverseMath: Answer Inversion for Scalable and Verifiable Mathematical Problem Generation

Mathematical reasoning benchmarks are vital for evaluating large language models (LLMs), but many are static and repeatedly exposed through public evaluation and training pipelines, making it difficult to separate genuine reasoning from memorization. Meanwhile, manually constructing new math problems with reliable answers remains costly. We introduce ReverseMath, a scalable method for generating new math problems through answer inversion. Given a problem and its answer, ReverseMath masks a numerical value in the original problem, treats the original answer as a known condition, and rewrites the problem so that the masked value becomes the new answer. The generated problem reverses the original input-output relation, making its answer known by construction. We study ReverseMath for both evaluation and training. For evaluation, paired original/reversed problems reveal substantial behavioral shifts: models sometimes fail on reversed problems and even incorrectly output the original answer, suggesting memorization-like behavior. For training, ReverseMath provides automatically labeled reversed problems as data augmentation for reinforcement learning (RL). Experiments show that including ReverseMath-generated data improves mathematical reasoning performance across multiple benchmarks, demonstrating its value as both an analysis tool and a scalable source of verifiable training data.

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

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.

Enhancing Multilingual Counterfactual Generation through Alignment-as-Preference Optimization

Self-generated counterfactual explanations (SCEs) are minimally modified inputs (minimality) generated by large language models (LLMs) that flip their own predictions (validity), offering a causally grounded approach to unraveling black-box LLM behavior. Yet extending them beyond English remains challenging: existing methods struggle to produce valid SCEs in non-dominant languages, and a persistent trade-off between validity and minimality undermines explanation quality. We introduce Macro, a preference alignment framework that applies Direct Preference Optimization (DPO) to multilingual SCE generation, using a composite scoring function to construct preference pairs that effectively translate the trade-off into measurable preference signals. Experiments across four LLMs and seven typologically diverse languages show that Macro improves validity by 12.55\% on average over the chain-of-thought baseline without degrading minimality, while avoiding the severe minimality violations of the translation-based baseline. Compared to supervised fine-tuning, Macro achieves superior performance on both metrics, confirming that explicit preference optimization is essential for balancing this trade-off. Further analyses reveal that Macro increases cross-lingual perturbation alignment and mitigates common generation errors. Our results highlight preference optimization as a promising direction for enhancing multilingual model explanations.

Crosslingual On-Policy Self-Distillation for Multilingual Reasoning

Large language models (LLMs) have achieved remarkable progress in mathematical reasoning, but this ability is not equally accessible across languages. Especially low-resource languages exhibit much lower reasoning performance. To address this, we propose Crosslingual On-Policy Self-Distillation (COPSD), which transfers a model's own high-resource reasoning behavior to low-resource languages. COPSD uses the same model as student and teacher: the student sees only the low-resource problem, while the teacher receives privileged crosslingual context, including the problem translation and reference solution in English. Training minimizes full-distribution token-level divergence on the student's own rollouts, providing dense supervision while avoiding the sparsity and instability of outcome-only reinforcement learning (RL). Experiments on 17 low-resource African languages show that COPSD consistently improves low-resource mathematical reasoning across model sizes and substantially outperforms Group Relative Policy Optimization (GRPO). Further analyses show that COPSD improves answer-format adherence, strengthens test-time scaling, and generalizes to harder multilingual reasoning benchmarks, with especially large gains for lower-resource languages. We make our code and data available at: https://github.com/cisnlp/COPSD.

Why Better Cross-Lingual Alignment Fails for Better Cross-Lingual Transfer: Case of Encoders

Better cross-lingual alignment is often assumed to yield better cross-lingual transfer. However, explicit alignment techniques -- despite increasing embedding similarity -- frequently fail to improve token-level downstream performance. In this work, we show that this mismatch arises because alignment and downstream task objectives are largely orthogonal, and because the downstream benefits from alignment vary substantially across languages and task types. We analyze four XLM-R encoder models aligned on different language pairs and fine-tuned for either POS Tagging or Sentence Classification. Using representational analyses, including embedding distances, gradient similarities, and gradient magnitudes for both task and alignment losses, we find that: (1) embedding distances alone are unreliable predictors of improvements (or degradations) in task performance and (2) alignment and task gradients are often close to orthogonal, indicating that optimizing one objective may contribute little to optimizing the other. Taken together, our findings explain why ``better'' alignment often fails to translate into ``better'' cross-lingual transfer. Based on these insights, we provide practical guidelines for combining cross-lingual alignment with task-specific fine-tuning, highlighting the importance of careful loss selection.

Evaluating Contextually Mediated Factual Recall in Multilingual Large Language Models

Large language models (LLMs) can recall a wide range of factual knowledge across languages. However, existing factual recall evaluations primarily assess fact retrieval in isolation, where the queried entity is explicitly named and the fact is requested directly. In natural language use, facts are often accessed through context, where the relevant entity is introduced only indirectly. In this work, we study contextually mediated factual recall, asking whether LLMs can reliably retrieve factual knowledge when the target entity is embedded in a naturalistic context rather than queried explicitly, across languages. We construct controlled prompts that preserve the underlying fact while introducing referential mediation through contextual sentences. To disentangle contextual effects from name-specific associations, we further compare performance using synthetic names and real names across languages. Evaluating multiple model families in five languages, we find that contextual mediation consistently degrades factual recall, with substantial variation across relations. Larger models are more robust to contextual mediation, exhibiting a reduced performance gap relative to direct queries, while the effect of real names and name origin is mixed and unsystematic. These findings highlight a gap between isolated factual recall and context-dependent language understanding in multilingual LLMs.

Relational Linearity is a Predictor of Hallucinations

Hallucination is a central failure mode in large language models (LLMs). We focus on hallucinations of answers to questions like: "Which instrument did Glenn Gould play?", but we ask these questions for synthetic entities that are unknown to the model. Surprisingly, we find that medium-size models like Gemma-7B-IT frequently hallucinate, i.e., they have difficulty recognizing that the hallucinated fact is not part of their knowledge. We hypothesize that an important factor in causing these hallucinations is the linearity of the relation: linear relations tend to be stored more abstractly, making it difficult for the LLM to assess its knowledge; the facts of nonlinear relations tend to be stored more directly, making knowledge assessment easier. To investigate this hypothesis, we create SyntHal, a dataset of 6000 synthetic entities for six relations. In our experiments with four models, we determine, for each relation, the hallucination rate on SyntHal and also measure its linearity, using $Δ\cos$. We find a strong correlation ($r \in [.78,.82]$) between relational linearity and hallucination rate, providing evidence for our hypothesis that the underlying storage of triples of a relation is a factor in how well a model can self-assess its knowledge. This finding has implications for how to manage hallucination behavior and suggests new research directions for improving the representation of factual knowledge in LLMs.