# Relative Kinetic Utility for Reasoning-Aware Structural Pruning in Large Language Models

arXiv: https://arxiv.org/abs/2605.09008 · HTML: https://mlsanity.com/paper/2605.09008/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 42 of its 46 references that are in the map.
- First posted on arXiv 9 May 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 42)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [Analyzing Multi-Head Self-Attention: Specialized Heads Do the Heavy Lifting, the Rest Can Be Pruned](https://mlsanity.com/paper/1905.09418/) (2019)
- [Are Sixteen Heads Really Better than One?](https://mlsanity.com/paper/1905.10650/) (2019)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [LLM-Pruner: On the Structural Pruning of Large Language Models](https://mlsanity.com/paper/2305.11627/) (2023)
- [Importance Estimation for Neural Network Pruning](https://mlsanity.com/paper/1906.10771/) (2019)
- [Sheared LLaMA: Accelerating Language Model Pre-training via Structured Pruning](https://mlsanity.com/paper/2310.06694/) (2023)
- [SliceGPT: Compress Large Language Models by Deleting Rows and Columns](https://mlsanity.com/paper/2401.15024/) (2024)
- [ShortGPT: Layers in Large Language Models are More Redundant Than You Expect](https://mlsanity.com/paper/2403.03853/) (2024)
- [Block Pruning For Faster Transformers](https://mlsanity.com/paper/2109.04838/) (2021)
- [Structured Pruning Learns Compact and Accurate Models](https://mlsanity.com/paper/2204.00408/) (2022)
- [Outlier Weighed Layerwise Sparsity (OWL): A Missing Secret Sauce for Pruning LLMs to High Sparsity](https://mlsanity.com/paper/2310.05175/) (2023)
- [Fluctuation-based Adaptive Structured Pruning for Large Language Models](https://mlsanity.com/paper/2312.11983/) (2023)
- [LoRAPrune: Structured Pruning Meets Low-Rank Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2305.18403/) (2023)
- [ZipLM: Inference-Aware Structured Pruning of Language Models](https://mlsanity.com/paper/2302.04089/) (2023)
- [BESA: Pruning Large Language Models with Blockwise Parameter-Efficient Sparsity Allocation](https://mlsanity.com/paper/2402.16880/) (2024)
- [DISP-LLM: Dimension-Independent Structural Pruning for Large Language Models](https://mlsanity.com/paper/2410.11988/) (2024)
- [SparseLLM: Towards Global Pruning for Pre-trained Language Models](https://mlsanity.com/paper/2402.17946/) (2024)
- [Is C4 Dataset Optimal for Pruning? An Investigation of Calibration Data for LLM Pruning](https://mlsanity.com/paper/2410.07461/) (2024)
- [DarwinLM: Evolutionary Structured Pruning of Large Language Models](https://mlsanity.com/paper/2502.07780/) (2025)
- [SlimLLM: Accurate Structured Pruning for Large Language Models](https://mlsanity.com/paper/2505.22689/) (2025)
- [Instruction-Following Pruning for Large Language Models](https://mlsanity.com/paper/2501.02086/) (2025)
- [Beware of Calibration Data for Pruning Large Language Models](https://mlsanity.com/paper/2410.17711/) (2024)
- [Probe Pruning: Accelerating LLMs through Dynamic Pruning via Model-Probing](https://mlsanity.com/paper/2502.15618/) (2025)
- [Alternating Gradient Flows: A Theory of Feature Learning in Two-layer Neural Networks](https://mlsanity.com/paper/2506.06489/) (2025)
- [From LLMs to LRMs: Rethinking Pruning for Reasoning-Centric Models](https://mlsanity.com/paper/2601.18091/) (2026)

## Abstract (arXiv)

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.