# Unifying Depth and Width Pruning for LLMs via Binary Knapsack Optimization

arXiv: https://arxiv.org/abs/2608.12953 · HTML: https://mlsanity.com/paper/2608.12953/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 61 of its 72 references that are in the map.
- First posted on arXiv 13 Aug 2026.

## Builds on (most cited first, 30 of 61)

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- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
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- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [What Disease does this Patient Have? A Large-scale Open Domain Question Answering Dataset from Medical Exams](https://mlsanity.com/paper/2009.13081/) (2020)
- [TinyBERT: Distilling BERT for Natural Language Understanding](https://mlsanity.com/paper/1909.10351/) (2019)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [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)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [Phi-4 Technical Report](https://mlsanity.com/paper/2412.08905/) (2024)
- [CoQA: A Conversational Question Answering Challenge](https://mlsanity.com/paper/1808.07042/) (2018)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [LLM-Pruner: On the Structural Pruning of Large Language Models](https://mlsanity.com/paper/2305.11627/) (2023)
- [BLiMP: The Benchmark of Linguistic Minimal Pairs for English](https://mlsanity.com/paper/1912.00582/) (2019)
- [Gender Bias in Coreference Resolution](https://mlsanity.com/paper/1804.09301/) (2018)
- [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)

## Abstract (arXiv)

Structured pruning is a promising approach for compressing large language models (LLMs), yet existing methods rely heavily on greedy heuristics that produce myopic decisions, and often fail to precisely meet target compression budgets. We present SNIPER, a two-stage structured pruning framework that solves a knapsack optimization over coarse-granularity components to yield conditionally optimal parameter allocations with respect to fixed importance estimates, followed by a fine-grained pruning stage to meet strict budget constraints. We introduce the Compression Ratio Adherence Factor (CRAFT) to quantify budget fidelity, showing that while existing pruners deviate from target compression ratios by up to 33%, SNIPER achieves near-exact adherence with a CRAFT score of 0.98. Evaluations across four diverse architectures over a set of 18 tasks spanning five domains demonstrate SNIPER's consistent improvements in average performance retention and task-level stability over six state-of-the-art pruners. Across all pruning configurations, SNIPER achieves an excellent mean rank of 1.25, indicating its robust cross-architectural generalizability and excellent reliability.