Post-training gains mostly reroute LLM weights, not reshape their scale
A study of 12 SFT and reinforcement-learning chains suggests LLM post-training improves models mainly by reconfiguring and extending existing weight pathways, not by substantially changing their singular values. The authors split each update in the pretrained matrix’s SVD frame: diagonal changes reshape singular values, off-diagonal changes rotate connections, and null-space changes route beyond the original core. On a math evaluation suite, removing the diagonal component usually preserved most gains.