GRRR: The Geometry of Reshaping, Rotation, and Routing in Decoder LLM post-training

Abstract: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 component usually preserves most of the gains from post-training. These results suggest that post-training gains are carried primarily by reconfiguring and extending pretrained pathways rather than by substantially changing singular values of pre-trained models.

Machine Learning (cs.LG); Computation and Language (cs.CL)

arXiv:2609.22146 [cs.LG]

(or arXiv:2609.22146v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.22146 Focus to learn more arXiv-issued DOI via DataCite

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