Data Quality in Focus: How Instruction and Reasoning Data Influence Post-Training of Large Language Models

The post-training of large language models (LLMs) has evolved from simply following instructions to complex reasoning tasks. However, the question of how different data influences the fine-tuning of these models remains largely unexplored. A recent research article sheds light on this connection and analyzes the impact of data quality on the gradients in different layers of an LLM during post-training.

The study examines the spectral properties of layer-wise gradients induced by high-quality and low-quality instruction and reasoning data. Using singular value decomposition (SVD) of these gradients, established metrics for data evaluation, such as IFD, InsTag, Difficulty, and Reward, can be explained and unified. It shows that higher-quality data is generally associated with lower nuclear norms and higher effective ranks.

The effective rank, in particular, proves to be more robust and precise than the nuclear norm in capturing subtle quality differences. For example, reasoning data achieves significantly higher effective ranks than instruction data, suggesting richer gradient structures for more complex tasks.

The study's experiments also show that models within the same model family exhibit similar gradient patterns, regardless of their size. In contrast, the gradient patterns of different model families differ significantly. These findings provide a unified understanding of the impact of data quality on instruction and reasoning data and illuminate the interplay between data quality and training stability.

The Importance of Gradient Analysis

Gradients play a crucial role in training neural networks. They indicate the direction of steepest descent on the error surface and thus determine how the network's weights are adjusted to improve performance. Analyzing the gradients provides insights into the model's learning processes and can help to better understand the effects of the training data.

Spectral Analysis and Data Quality

Spectral analysis, particularly singular value decomposition (SVD), offers a powerful tool for examining gradients. SVD decomposes a matrix into its fundamental components and allows for the identification of the most important directions of variance in the data. In the context of LLM post-training, SVD of the gradients can reveal how different data influences the adjustment of model parameters.

Implications for Practice

The results of this study have important implications for the development and application of LLMs. They underscore the importance of data quality for post-training and offer new approaches to evaluating and selecting training data. The insights into the relationship between data quality and training stability can contribute to the development of more efficient and robust training procedures.

The research findings suggest that developing better data exploration strategies for the post-training of LLMs is essential. By considering the spectral properties of the gradients, developers can better assess the quality of the training data and optimize the performance of the models. This opens up new possibilities for developing more powerful and reliable LLMs for a variety of applications.

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