Reproduce “Spectral Rank and Step-Direction Dynamics in Language-Model Post-Training” on OpenResearch
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About this paper
Khurram Khalil, Khaza Anuarul Hoque
The paper distinguishes spectral concentration from energy coverage and compares consecutive post-training weight changes by cosine. Its example PPO query update has stable rank 9.58, yet needs 532 singular components to capture 80% of its energy. Across public RLVR stages, all 131 adjacent pairs had negative cosines. Three paired runs showed lower alignment after changing the advantage package, without establishing the cause.
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