Effect of PiSSA Probe Rank on Gradient Alignment

Conduct a systematic study of how the rank of the low-rank PiSSA gradient probe affects the resulting token weights and how closely low-rank gradient alignment tracks full-parameter gradient alignment.

Background

GAW-PO computes rejected-token weights by measuring gradient alignment in the parameter space of a low-rank PiSSA adapter rather than in the full parameter space of the LLM. The authors use this probe as a tractable approximation because computing token-level gradients over all parameters is prohibitively expensive, and they report that the resulting weights are informative in their experiments.

The unresolved issue is whether the chosen probe rank materially changes the token weights and whether alignment measured in the low-rank subspace reliably represents alignment in the full parameter space. Resolving this would help assess the robustness and validity of the gradient-alignment approximation used by GAW-PO.