In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower bound on the critical sample complexity required for reliable model selection. More specifically, we show that distinguishing a $k$-component mixture from a simpler model necessitates a sample size scaling of $Ω(Δ^{-(4k-4)})$. We then propose a thresholding-based estimation algorithm that evaluates the spectral gap of an empirical covariance matrix constructed from random Fourier measurement vectors. This parameter-free estimator operates with an efficient time complexity of $\mathcal{O}(k^2 n)$, scaling linearly with the sample size. We demonstrate that the sample complexity of our method matches the established lower bound, confirming its minimax optimality with respect to the component separation distance $Δ$. Conditioned on the estimated model order, we subsequently introduce a gradient-based minimization method for parameter estimation. To effectively navigate the non-convex objective landscape, we employ a data-driven, score-based initialization strategy that guarantees rapid convergence. We prove that this method achieves the optimal parametric convergence rate of $\mathcal{O}_p(n^{-1/2})$ for estimating the component means. To enhance the algorithm's efficiency in high-dimensional regimes where the ambient dimension exceeds the number of mixture components (i.e., \(d > k\)), we integrate principal component analysis (PCA) for dimension reduction. Numerical experiments demonstrate that our Fourier-based algorithmic framework outperforms conventional Expectation-Maximization (EM) methods in both estimation accuracy and computational time.

Large Language Models (LLMs) have demonstrated strong translation abilities through prompting, even without task-specific training. However, their effectiveness in dialectal and low-resource contexts remains underexplored. This study presents the first systematic investigation of LLM-based machine translation (MT) for Sylheti, a dialect of Bangla that is itself low-resource. We evaluate five advanced LLMs (GPT-4.1, GPT-4.1, LLaMA 4, Grok 3, and DeepSeek V3.2) across both translation directions (Bangla $\Leftrightarrow$ Sylheti), and find that these models struggle with dialect-specific vocabulary. To address this, we introduce Sylheti-CAP (Context-Aware Prompting), a three-step framework that embeds a linguistic rulebook, a dictionary (2{,}260 core vocabulary items and idioms), and an authenticity check directly into prompts. Extensive experiments show that Sylheti-CAP consistently improves translation quality across models and prompting strategies. Both automatic metrics and human evaluations confirm its effectiveness, while qualitative analysis reveals notable reductions in hallucinations, ambiguities, and awkward phrasing, establishing Sylheti-CAP as a scalable solution for dialectal and low-resource MT. Dataset link: \href{https://github.com/TabiaTanzin/LLMs-for-Low-Resource-Dialect-Translation-Using-Context-Aware-Prompting-A-Case-Study-on-Sylheti.git}{https://github.com/TabiaTanzin/LLMs-for-Low-Resource-Dialect-Translation-Using-Context-Aware-Prompting-A-Case-Study-on-Sylheti.git}

Large language models have significantly advanced Multilingual Machine Translation (MMT), yet the broad language coverage, consistent translation quality, and English-centric bias remain open challenges. To address these challenges, we introduce \textbf{LMT}, a suite of \textbf{L}arge-scale \textbf{M}ultilingual \textbf{T}ranslation models centered on both Chinese and English, covering 60 languages and 234 translation directions. During development, we identify a previously overlooked phenomenon of \textbf{directional degeneration}, where symmetric multi-way fine-tuning data overemphasize reverse directions (X $\to$ En/Zh), leading to excessive many-to-one mappings and degraded translation quality. We propose \textbf{Strategic Downsampling}, a simple yet effective method to mitigate this degeneration. In addition, we design \textbf{Parallel Multilingual Prompting (PMP)}, which leverages typologically related auxiliary languages to enhance cross-lingual transfer. Through rigorous data curation and refined adaptation strategies, LMT achieves SOTA performance among models of comparable language coverage, with our 4B model (LMT-60-4B) surpassing the much larger Aya-101-13B and NLLB-54B models by a substantial margin. We release LMT in four sizes (0.6B/1.7B/4B/8B) to catalyze future research and provide strong baselines for inclusive, scalable, and high-quality MMT \footnote{\href{https://github.com/NiuTrans/LMT}{https://github.com/NiuTrans/LMT}}.

The linguistic diversity of India poses significant machine translation challenges, especially for underrepresented tribal languages like Bhili, which lack high-quality linguistic resources. This paper addresses the gap by introducing Bhili-Hindi-English Parallel Corpus (BHEPC), the first and largest parallel corpus worldwide comprising 110,000 meticulously curated sentences across Bhili, Hindi, and English. The corpus was created with the assistance of expert human translators. BHEPC spans critical domains such as education, administration, and news, establishing a valuable benchmark for research in low resource machine translation. To establish a comprehensive Bhili Machine Translation benchmark, we evaluated a wide range of proprietary and open-source Multilingual Large Language Models (MLLMs) on bidirectional translation tasks between English/Hindi and Bhili. Comprehensive evaluation demonstrates that the fine-tuned NLLB-200 distilled 600M variant model outperforms others, highlighting the potential of multilingual models in low resource scenarios. Furthermore, we investigated the generative translation capabilities of multilingual LLMs on BHEPC using in-context learning, assessing performance under cross-domain generalization and quantifying distributional divergence. This work bridges a critical resource gap and promotes inclusive natural language processing technologies for low-resource and marginalized languages globally.

We present ACADATA, a high-quality parallel dataset for academic translation, that consists of two subsets: ACAD-TRAIN, which contains approximately 1.5 million author-generated paragraph pairs across 96 language directions and ACAD-BENCH, a curated evaluation set of almost 6,000 translations covering 12 directions. To validate its utility, we fine-tune two Large Language Models (LLMs) on ACAD-TRAIN and benchmark them on ACAD-BENCH against specialized machine-translation systems, general-purpose, open-weight LLMs, and several large-scale proprietary models. Experimental results demonstrate that fine-tuning on ACAD-TRAIN leads to improvements in academic translation quality by +6.1 and +12.4 d-BLEU points on average for 7B and 2B models respectively, while also improving long-context translation in a general domain by up to 24.9% when translating out of English. The fine-tuned top-performing model surpasses the best propietary and open-weight models on academic translation domain. By releasing ACAD-TRAIN, ACAD-BENCH and the fine-tuned models, we provide the community with a valuable resource to advance research in academic domain and long-context translation.

Prior research diverges on language diversity in LLM fine-tuning: Some studies report benefits while others find no advantages. Through controlled fine-tuning experiments across 132 translation directions, we systematically resolve these disparities. We find that expanding language diversity during fine-tuning improves translation quality for both unsupervised and -- surprisingly -- supervised pairs, despite less diverse models being fine-tuned exclusively on these supervised pairs. However, benefits plateau or decrease beyond a certain diversity threshold. We show that increased language diversity creates more language-agnostic representations. These representational adaptations help explain the improved performance in models fine-tuned with greater diversity.

We show that translation quality can be predicted with surprising accuracy \textit{without ever running the translation system itself}. Using only a handful of features, token fertility ratios, token counts, and basic linguistic metadata (language family, script, and region), we can forecast ChrF scores for GPT-4o translations across 203 languages in the FLORES-200 benchmark. Gradient boosting models achieve favorable performance ($R^{2}=0.66$ for XX$\rightarrow$English and $R^{2}=0.72$ for English$\rightarrow$XX). Feature importance analyses reveal that typological factors dominate predictions into English, while fertility plays a larger role for translations into diverse target languages. These findings suggest that translation quality is shaped by both token-level fertility and broader linguistic typology, offering new insights for multilingual evaluation and quality estimation.

In-Image Machine Translation (IIMT) aims to translate images containing texts from one language to another. Current research of end-to-end IIMT mainly conducts on synthetic data, with simple background, single font, fixed text position, and bilingual translation, which can not fully reflect real world, causing a significant gap between the research and practical conditions. To facilitate research of IIMT in real-world scenarios, we explore Practical In-Image Multilingual Machine Translation (IIMMT). In order to convince the lack of publicly available data, we annotate the PRIM dataset, which contains real-world captured one-line text images with complex background, various fonts, diverse text positions, and supports multilingual translation directions. We propose an end-to-end model VisTrans to handle the challenge of practical conditions in PRIM, which processes visual text and background information in the image separately, ensuring the capability of multilingual translation while improving the visual quality. Experimental results indicate the VisTrans achieves a better translation quality and visual effect compared to other models. The code and dataset are available at: https://github.com/BITHLP/PRIM.

Document level Machine Translation (DocMT) approaches often struggle with effectively capturing discourse level phenomena. Existing approaches rely on heuristic rules to segment documents into discourse units, which rarely align with the true discourse structure required for accurate translation. Otherwise, they fail to maintain consistency throughout the document during translation. To address these challenges, we propose Graph Augmented Agentic Framework for Document Level Translation (GRAFT), a novel graph based DocMT system that leverages Large Language Model (LLM) agents for document translation. Our approach integrates segmentation, directed acyclic graph (DAG) based dependency modelling, and discourse aware translation into a cohesive framework. Experiments conducted across eight translation directions and six diverse domains demonstrate that GRAFT achieves significant performance gains over state of the art DocMT systems. Specifically, GRAFT delivers an average improvement of 2.8 d BLEU on the TED test sets from IWSLT2017 over strong baselines and 2.3 d BLEU for domain specific translation from English to Chinese. Moreover, our analyses highlight the consistent ability of GRAFT to address discourse level phenomena, yielding coherent and contextually accurate translations.

Large language models (LLMs) have demonstrated impressive translation capabilities even without being explicitly trained on parallel data. This remarkable property has led some to believe that parallel data is no longer necessary for building multilingual language models. While some attribute this to the emergent abilities of LLMs due to scale, recent work suggests that it is actually caused by incidental bilingual signals present in the training data. Various methods have been proposed to maximize the utility of parallel data to enhance the multilingual capabilities of multilingual encoder-based and encoder-decoder language models. However, some decoder-based LLMs opt to ignore parallel data instead. In this work, we conduct a systematic study on the impact of adding parallel data on LLMs' multilingual capabilities, focusing specifically on translation and multilingual common-sense reasoning. Through controlled experiments, we demonstrate that parallel data can significantly improve LLMs' multilingual capabilities.