{"ID":2867765,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.17866","arxiv_id":"2509.17866","title":"Understanding Post-Training Structural Changes in Large Language Models","abstract":"Post-training fundamentally alters the behavior of large language models (LLMs), yet its impact on the internal parameter space remains poorly understood. In this work, we conduct a systematic singular value decomposition (SVD) analysis of principal linear layers in pretrained LLMs, focusing on two widely adopted post-training methods: instruction tuning and long-chain-of-thought (Long-CoT) distillation. Our analysis reveals two unexpected and robust structural changes: (1) a near-uniform geometric scaling of singular values across layers; and (2) highly consistent orthogonal transformations are applied to the left and right singular vectors of each matrix. Based on these findings, We propose a simple yet effective framework to describe the coordinated dynamics of parameters in LLMs, which elucidates why post-training inherently relies on the foundational capabilities developed during pre-training. Further experiments demonstrate that singular value scaling underpins the temperature-controlled regulatory mechanisms of post-training, while the coordinated rotation of singular vectors encodes the essential semantic alignment. These results challenge the prevailing view of the parameter space in large models as a black box, uncovering the first clear regularities in how parameters evolve during training, and providing a new perspective for deeper investigation into model parameter changes.","short_abstract":"Post-training fundamentally alters the behavior of large language models (LLMs), yet its impact on the internal parameter space remains poorly understood. In this work, we conduct a systematic singular value decomposition (SVD) analysis of principal linear layers in pretrained LLMs, focusing on two widely adopted post-...","url_abs":"https://arxiv.org/abs/2509.17866","url_pdf":"https://arxiv.org/pdf/2509.17866v4","authors":"[\"Xinyu He\",\"Xianghui Cao\"]","published":"2025-09-22T15:03:36Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\"]","methods":"[\"Large Language Model\",\"Language Model\"]","has_code":false}