This study explores methods to increase data volume for low-resource languages using techniques such as crowdsourcing, pseudo-labeling, advanced data preprocessing and various permissive data sources such as audiobooks, Common Voice, YouTube. While these methods are well-explored for highresource languages, their application for low-resource languages remains underexplored. Using Armenian and Georgian as case studies, we demonstrate how linguistic and resource-specific characteristics influence the success of these methods. This work provides practical guidance for researchers to choose cost-effective and quality-driven dataset extension strategies for low-resource languages. The key takeaway from various data extension approaches is that paid crowd-sourcing offers the best balance between cost and quality, outperforming volunteer crowd-sourcing, open-source audiobooks, and unlabeled data usage. Ablation study shows that models trained on the expanded datasets outperform existing baselines and achieve 5.73% for Gergian and 9.9% for Armenian ASR word error rate using a relatively small FastConformer architecture. We open-sourced both the Armenian and Georgian models to allow further research and practical applications.

Mathematical reasoning continues to be a critical challenge in large language model (LLM) development with significant interest. However, most of the cutting-edge progress in mathematical reasoning with LLMs has become \emph{closed-source} due to lack of access to training data. This lack of data access limits researchers from understanding the impact of different choices for synthesizing and utilizing the data. With the goal of creating a high-quality finetuning (SFT) dataset for math reasoning, we conduct careful ablation experiments on data synthesis using the recently released \texttt{Llama3.1} family of models. Our experiments show that: (a) solution format matters, with excessively verbose solutions proving detrimental to SFT performance, (b) data generated by a strong teacher outperforms equally-sized data generated by a weak student model, (c) SFT is robust to low-quality solutions, allowing for imprecise data filtering, and (d) question diversity is crucial for achieving data scaling gains. Based on these insights, we create the OpenMathInstruct-2 dataset, which consists of 14M question-solution pairs ($\approx$ 600K unique questions), making it nearly eight times larger than the previous largest open-source math reasoning dataset. Finetuning the \texttt{Llama-3.1-8B-Base} using OpenMathInstruct-2 outperforms \texttt{Llama3.1-8B-Instruct} on MATH by an absolute 15.9\% (51.9\% $\rightarrow$ 67.8\%). Finally, to accelerate the open-source efforts, we release the code, the finetuned models, and the OpenMathInstruct-2 dataset under a commercially permissive license.