Shu-Han Zhou

Preference-Gradient Subspaces for Memory-Efficient Zeroth-Order Alignment of Large Language Models

The capture ratio ρ is introduced as a measurable quality index of a subspace, it is proved that the expected per-step progress of subspace ZO-SGD scales as ρ/(k+2) with a loss floor governed by 1 – ρ, and it is shown that random subspaces (ρ ≈ k/D) provide no advantage over full-space ZO.