As the post-training of large language models (LLMs) advances from instruction-following to complex reasoning tasks, understanding how different data affect finetuning dynamics remains largely unexplored. In this paper, we present a spectral analysis of layer-wise gradients induced by low/high-quality instruction and reasoning data for LLM post-training. Our analysis reveals that widely-studied metrics for data evaluation, e.g., IFD, InsTag, Difficulty, and Reward, can be explained and unified by spectral properties computed from gradients' singular value decomposition (SVD). Specifically, higher-quality data are usually associated with lower nuclear norms and higher effective ranks. Notably, effective rank exhibits better robustness and resolution than nuclear norm in capturing subtle quality differences. For example, reasoning data achieves substantially higher effective ranks than instruction data, implying richer gradient structures on more complex tasks. Our experiments also highlight that models within the same family share similar gradient patterns regardless of their sizes, whereas different model families diverge significantly. Providing a unified view on the effects of data quality across instruction and reasoning data, this work illuminates the interplay between data quality and training stability, shedding novel insights into developing better data exploration strategies for post-training.

本研究探讨了不同质量的数据如何影响大语言模型的后期训练动态，填补了这一领域的研究空白。通过层级梯度的光谱分析，发现高质量的数据通常与更低的核范数和更高的有效秩相关。此外，本研究表明推理数据在复杂任务中展示出显著更高的有效秩，揭示了数据质量与训练稳定性之间的相互影响。

指令和推理数据如何塑造后期训练：通过层级梯度透视数据质量