# Beyond Layer Importance in Layer-wise Sparsity: An Inter-Layer Perturbation-Absorption Perspective

arXiv: https://arxiv.org/abs/2606.15161 · HTML: https://mlsanity.com/paper/2606.15161/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 28 references that are in the map.
- First posted on arXiv 13 Jun 2026.

## Builds on (most cited first, 18 of 18)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [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)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [Channel Pruning for Accelerating Very Deep Neural Networks](https://mlsanity.com/paper/1707.06168/) (2017)
- [ThiNet: A Filter Level Pruning Method for Deep Neural Network Compression](https://mlsanity.com/paper/1707.06342/) (2017)
- [Discrimination-aware Channel Pruning for Deep Neural Networks](https://mlsanity.com/paper/1810.11809/) (2018)
- [Outlier Weighed Layerwise Sparsity (OWL): A Missing Secret Sauce for Pruning LLMs to High Sparsity](https://mlsanity.com/paper/2310.05175/) (2023)
- [EvoPress: Accurate Dynamic Model Compression via Evolutionary Search](https://mlsanity.com/paper/2410.14649/) (2024)
- [OSSCAR: One-Shot Structured Pruning in Vision and Language Models with Combinatorial Optimization](https://mlsanity.com/paper/2403.12983/) (2024)
- [Determining Layer-wise Sparsity for Large Language Models Through a Theoretical Perspective](https://mlsanity.com/paper/2502.14770/) (2025)
- [Do All MobileNets Quantize Poorly? Gaining Insights into the Effect of Quantization on Depthwise Separable Convolutional Networks Through the Eyes of Multi-scale Distributional Dynamics](https://mlsanity.com/paper/2104.11849/) (2021)
- [Maximum Redundancy Pruning: A Principle-Driven Layerwise Sparsity Allocation for LLMs](https://mlsanity.com/paper/2503.18377/) (2025)

## Built on by (most cited first, 1 of 1)

- [RippleKV: Cross-Layer KV Cache Allocation via Perturbation Propagation](https://mlsanity.com/paper/2608.08684/) (2026)

## Abstract (arXiv)

The considerable layer-wise redundancy in large language models (LLMs) has established non-uniform sparsity allocation across layers as the standard pruning approach for efficient compression. Existing layer-wise allocation methods that estimate allocation strategy from local signals such as activation outliers or weight spectra mainly derive from local layer importance, whereas the final post-pruning performance is also influenced by the network's subsequent compensatory capacity. In this paper, we directly characterize this property through controlled perturbation experiments. We make the following empirical findings. First, layers exhibit highly heterogeneous responses to pruning-scale perturbations. In most cases, early layers amplify perturbations, while middle and late layers actively absorb them, with relative L2 drift decreasing monotonically across depth and direction realigning toward the unperturbed hidden-state trajectory. Second, absorption is a large-perturbation phenomenon. Under small perturbations the network exhibits amplification across all layers, and the transition to absorption occurs smoothly as perturbation magnitude grows to pruning scale. This enriches the linearized accumulation theory underlying related works. Building on these findings, we define an absorption coefficient per layer and propose absorption-aware correction, an orthogonal augmentation that improves OWL and AlphaPruning by reducing perplexity by 7.13% and boosting zero-shot accuracy by 1.02% across multiple model families at 70% sparsity.