QK-Wanda: Coupling Queries and Keys for Unstructured Pruning

Abstract: Wanda (Sun et al., 2024) prunes LLMs by scoring weights independently within each linear projection, although queries and keys interact through dot products. We introduce QK-Wanda, which scores query and key weights by their individual deletion costs under an unmasked pre-RoPE reconstruction objective. It augments Wanda scores with information from the opposite projection (keys for query weights, and queries for key weights), allowing both projections to share a pruning budget. Its closed-form scores require no gradients or weight updates; full pruning takes 1.3% longer than Wanda on A100 and 3.1% longer on H200 with the calibration used in our main experiments. We evaluate QK-only pruning across 15 models from TinyLlama, Llama 2, Llama 3, and Qwen2.5, spanning 0.5B-72B parameters. Relative to Wanda, QK-Wanda reduces QK reconstruction error by an average of 60% at 50% sparsity and 45% at 80%. Downstream gains depend on the model. At 80% sparsity on Llama 2 70B, WikiText-2 and C4 perplexity decrease by 20.3% and 13.5%, while mean zero-shot accuracy rises by 5.94 percentage points. Qwen2.5-72B also improves, but Llama-3.1-70B has substantially higher perplexity despite lower reconstruction error. These results show both the promise of coupled pruning criteria and the limits of local reconstruction as a predictor of model quality.