Zeroth-order (ZO) optimization enables memory-efficient fine-tuning of large language models through forward-only evaluations, but high-dimensional random perturbations can limit optimization efficiency. Sparse perturbations reduce the search dimension, making the selection of informative coordinates critical.

We propose Wanda-Importance Sparsity-MeZO (WIS-MeZO), which uses Wanda weight--activation saliency to construct task-conditioned sparse perturbation masks while keeping the pretrained model dense. We analyze support quality through gradient energy capture and relate it to gradient estimation and convergence.

Across 16 benchmarks with LLaMA and Qwen models ranging from 3B to 32B parameters, WIS-MeZO achieves higher aggregate scores than MeZO and reaches comparable validation losses in fewer optimization steps. Comparisons with random and magnitude-based sparse perturbations further highlight the importance of informative support selection.