QK-Wanda: Coupling Queries and Keys for Unstructured Pruning

One-shot post-training pruning is the most energy-frugal compression strategy for largelanguage models (LLMs), yet existing approaches trade either quality (WANDA) or compute cost (SPARSEGPT). We introduce F-WANDA, a drop-in modification of WANDA that reallocates the per-row keep budget across output neurons in proportion to the empirical Fisher information of the pre-activation. The Fisher signal is collected in a single additional backward pass over the same calibration corpus WANDA already uses; no weights are updated. On LLAMA-2-7B at 50 % unstructured sparsity, F-WANDA attains WikiText-2 perplexity of 6.85, matches WANDA fluency, and improves 5-shot MMLU by +1.6 pp over WANDA and +1.1 pp over SPARSEGPT, while incurring only one-third of SPARSEGPT pruning wall-clock and energy. The headline trade-off is achieved without extra calibration data or fine-tuning, placing F-WANDA on the Pareto frontier of quality versus pruning cost for sustainable LLM compression.

Global structured pruning requires channels from different layers to compete under a shared sparsity budget, raising two coupled challenges: identifying which channels should be retained and making their scores comparable across layers. Raw channel scores can contain block-common scale that leaves within-block ordering unchanged but distorts model-wide competition. Our experiment indicates that similar layer-wise allocations can retain substantially different FFN channels, so layer allocation alone does not determine channel identity. Motivated by this separation, we introduce Global Relative Kinetic Utility (Global RKU), a label-free criterion that separates channel importance estimation from cross-layer comparison. Global RKU measures channel participation using a final-hidden-state activation-gradient signal, then applies block-relative normalization to mitigate block-common scale while preserving within-block ordering, requires only unlabeled calibration inputs, and produces a static pruning topology in a single calibration stage. Under questions-only calibration on Qwen-2.5-7B, RKU-GISP Mean3 margins are -0.98, +3.79, and +8.61 points at 30%, 40%, and 50% sparsity, respectively (average +3.81). Additional Qwen evaluations cover non-mathematical reasoning, recovery, held-out transfer, and physical deployment. Separately, replacing Wiki16K with questions-only Q16K improves RKU's Mean3 at every tested sparsity on Qwen, Llama, and Gemma. Our ablation study shows relative-normalization gains of 14.42 and 5.53 Mean3 points at 40% and 50% sparsity, respectively; the common-seed audit is positive in all 27 seed-task comparisons.

Structured pruning of large language models (LLMs) offers hardware-efficient compression, yet existing methods require calibration data, gradient computation, or large auxiliary policy networks at pruning time. LILA (\emph{Latent-Informed Layer Analysis}) scores neuron importance via the Kolmogorov--Smirnov (KS) distance between empirical singular value distributions of the full and neuron-ablated feed-forward network (FFN) weight matrix, providing a closed-form spectral rule requiring no training, calibration data, or auxiliary network. Without any fine-tuning, LILA surpasses PruneNet (45M-parameter RL policy) by 1.57pp in zero-shot accuracy on LLaMA-2-7B at 25% sparsity, and outperforms WikiText-2-calibrated SliceGPT by up to 6.0pp across all sparsity levels, while preserving the original architecture. After one epoch of LoRA recovery fine-tuning, LILA achieves highly competitive performance, matching the heavily calibrated SliceGPT baseline to within a 0.48~pp margin across LLaMA-2-7B and Phi-2, despite using zero calibration data. A Neural Tangent Kernel analysis confirms a 22$\times$ reduction in functional distortion versus random pruning, providing theoretical grounding for the spectral importance criterion. Finally, extending LILA to dynamically allocate sparsity budgets via KS-scores yields state-of-the-art generative preservation at moderate compression, while uncovering fundamental single-layer architectural bottlenecks at higher compression regimes.