GRRR: The Geometry of Reshaping, Rotation, and Routing in Decoder LLM post-training
We study how post-training changes the weights of Large Language Models (LLMs) relative to their pretrained weights. Across 12 post-training chains with supervised fine-tuning (SFT) and reinforcement learning (RL), we express each weight update in the pretrained matrix's singular value decomposition (SVD) frame. This decomposition separates the changes of three geometrically distinct components: diagonal values, which reshapes singular values; off-diagonal values, which rotates the coupling between pretrained input and output directions; and null-space values, which routes outside the matrix's original nonzero SVD core. On a math evaluation suite, we find that removing the diagonal compon...
| Authors | Jianing Qi, Hao Tang, Zhigang Zhu |
|---|---|
| Primary category | cs.LG |
| Published | 26 August 2026 |
| Last updated at source | 26 August 2026 |
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