Instruction tuning is crucial for aligning Large Language Models (LLMs), yet the quality of instruction-following data varies significantly. While high-quality data is paramount, it is often scarce; conversely, abundant low-quality data is frequently discarded, leading to substantial information loss. Existing data augmentation methods struggle to augment this low-quality data effectively, and the evaluation of such techniques remains poorly defined. To address this, we formally define the task of Instruction Distillation: distilling multiple low-quality and redundant inputs into high-quality and coherent instruction-output pairs. This process uses three complementary reward signals: quality, semantic alignment, and format compliance, via Group Relative Policy Optimization (GRPO). We demonstrate that LM-Mixup effectively augments imperfect datasets: fine-tuning LLMs on its distilled data, which accounts for only about 3% of the entire dataset, not only surpasses full-dataset training but also competes with state-of-the-art high-quality data selection methods across multiple benchmarks. Our work establishes that low-quality data is a valuable resource when properly distilled and augmented with LM-Mixup, significantly enhancing the efficiency and performance of instruction-tuned LLMs. The code and the dataset are available at: https://github.com/yuu250/LM-mixup. In recent years, large language models (LLMs) have achieved notable progress in natural language processing and multimodal understanding (Team et al., 2023; Singhal et al., 2023; Deng et al., 2025; Li et al., 2024b; 2025a; Pang et al., 2025b). This progress stems not only from improved architectures and larger scales but also from more efficient ways for models to learn and apply knowledge (Patil & Jadon, 2025; Dredze, 2025). While the conventional view holds that high-quality human alignment requires massive annotated data (Kim et al., 2024; K opf et al., 2023), recent studies show that LLMs acquire most knowledge during pre-training (Brown et al., 2020; Roberts et al., 2020). This shifts the research focus from "more data" to "better data", emphasizing efficient high-quality data selection for model improvement. However, high-quality samples are scarce and costly, while real-world datasets contain abundant redundant or low-quality data, leading to significant information waste.

Experiments show that training on the high-quality data selected by our method can often outperform other data selection methods for collaborative fine-tuning of LLMs, across diverse private domain datasets, in medical, multilingual and financial settings.

Recent research has highlighted the importance of data quality in scaling large language models (LLMs). However, automated data quality control faces unique challenges in collaborative settings where sharing is not allowed directly between data silos. To tackle this issue, this paper proposes a novel data quality control technique based on the notion of data influence on the training dynamics of LLMs, that high quality data are more likely to have similar training dynamics to the anchor dataset. We then leverage the influence of the training dynamics to select high-quality data from different private domains, with centralized model updates on the server side in a collaborative training fashion by either model merging or federated learning. As for the data quality indicator, we compute the per-sample gradients with respect to the private data and the anchor dataset, and use the trace of the accumulated inner products as a measurement of data quality. In addition, we develop a quality control evaluation tailored for collaborative settings with heterogeneous domain data. Experiments show that training on the high-quality data selected by our method can often outperform other data selection methods for collaborative fine-tuning of LLMs, across diverse private domain datasets, in medical, multilingual and financial settings. Our code is released at github.com/Ryan0v0/CLUES.

Decentralized federated learning (DFL) enables devices to collaboratively train models over complex network topologies without relying on a central controller. In this setting, local data remains private, but its quality and quantity can vary significantly across nodes. The extent to which a fully decentralized system is vulnerable to poor-quality or corrupted data remains unclear, but several factors could contribute to potential risks. Without a central authority, there can be no unified mechanism to detect or correct errors, and each node operates with a localized view of the data distribution, making it difficult for the node to assess whether its perspective aligns with the true distribution. Moreover, models trained on low-quality data can propagate through the network, amplifying errors. To explore the impact of low-quality data on DFL, we simulate two scenarios with degraded data quality -- one where the corrupted data is evenly distributed in a subset of nodes and one where it is concentrated on a single node -- using a decentralized implementation of FedAvg. Our results reveal that averaging-based decentralized learning is remarkably robust to localized bad data, even when the corrupted data resides in the most influential nodes of the network. Counterintuitively, this robustness is further enhanced when the corrupted data is concentrated on a single node, regardless of its centrality in the communication network topology. This phenomenon is explained by the averaging process, which ensures that no single node -- however central -- can disproportionately influence the overall learning process.

By leveraging massively distributed data, federated learning (FL) enables collaborative instruction tuning of large language models (LLMs) in a privacy-preserving way. While FL effectively expands the data quantity, the issue of data quality remains under-explored in the current literature on FL for LLMs. To address this gap, we propose a new framework of federated instruction tuning of LLMs with data quality control (FedDQC), which measures data quality to facilitate the subsequent filtering and hierarchical training processes. Our approach introduces an efficient metric to assess each client's instruction-response alignment (IRA), identifying potentially noisy data through single-shot inference. Low-IRA samples are potentially noisy and filtered to mitigate their negative impacts. To further utilize this IRA value, we propose a quality-aware hierarchical training paradigm, where LLM is progressively fine-tuned from high-IRA to low-IRA data, mirroring the easy-to-hard learning process. We conduct extensive experiments on 4 synthetic and a real-world dataset, and compare our method with baselines adapted from centralized setting. Results show that our method consistently and significantly improves the performance of LLMs trained on mix-quality data in FL.

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.

The PubMedQA task is designed to answer research questions with responses categorized as yes/no/maybe, effectively framing it as a multiple-choice question format. The dataset is divided into three subsets: 1,000 manually labeled question-answer pairs (denoted as PQA-L), 61,200 unlabeled pairs (PQA-U), and 211,300 pairs that have been artificially generated (PQA-A). Consistent with previous studies (Diao et al., 2023; Singhal et al., 2023), we employ the PQA-L subset as the test set for evaluating the model's performance. USMLE USMLE (Jin et al., 2021) consists of multiple-choice questions (with 4 choices per question) that are based on the United States Medical Licensing Exams. This dataset has been compiled from questions used in professional medical board examinations and is unique in its multilingual composition, including English, Simplified Chinese, and Traditional Chinese versions. It contains 12,724 questions in English, 34,251 in Simplified Chinese, and 14,123 in Traditional Chinese. For our purposes, we focus on the English component of the dataset, which is further divided into 10,178 questions for the training set, 1,273 for the validation set, and 1,273 for the test set, adhering to the official distribution of the dataset.