# Weight Concentration Regularization for Improving Pruning Robustness Under High Sparsity

arXiv: https://arxiv.org/abs/2511.14282 · HTML: https://mlsanity.com/paper/2511.14282/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 37 references that are in the map.
- First posted on arXiv 18 Nov 2025.

## Builds on (most cited first, 27 of 27)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [Channel Pruning for Accelerating Very Deep Neural Networks](https://mlsanity.com/paper/1707.06168/) (2017)
- [Rethinking the Value of Network Pruning](https://mlsanity.com/paper/1810.05270/) (2018)
- [Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networks](https://mlsanity.com/paper/2102.00554/) (2021)
- [Pruning neural networks without any data by iteratively conserving synaptic flow](https://mlsanity.com/paper/2006.05467/) (2020)
- [Picking Winning Tickets Before Training by Preserving Gradient Flow](https://mlsanity.com/paper/2002.07376/) (2020)
- [PyHessian: Neural Networks Through the Lens of the Hessian](https://mlsanity.com/paper/1912.07145/) (2019)
- [On the Linear Speedup Analysis of Communication Efficient Momentum SGD for Distributed Non-Convex Optimization](https://mlsanity.com/paper/1905.03817/) (2019)
- [Handbook of Convergence Theorems for (Stochastic) Gradient Methods](https://mlsanity.com/paper/2301.11235/) (2023)
- [Association of genomic subtypes of lower-grade gliomas with shape features automatically extracted by a deep learning algorithm](https://mlsanity.com/paper/1906.03720/) (2019)
- [Can We Gain More from Orthogonality Regularizations in Training Deep CNNs?](https://mlsanity.com/paper/1810.09102/) (2018)
- [All You Need is Beyond a Good Init: Exploring Better Solution for Training Extremely Deep Convolutional Neural Networks with Orthonormality and Modulation](https://mlsanity.com/paper/1703.01827/) (2017)
- [DeepHoyer: Learning Sparser Neural Network with Differentiable Scale-Invariant Sparsity Measures](https://mlsanity.com/paper/1908.09979/) (2019)
- [Train Flat, Then Compress: Sharpness-Aware Minimization Learns More Compressible Models](https://mlsanity.com/paper/2205.12694/) (2022)

## Abstract (arXiv)

Deep neural networks achieve outstanding performance across vision and language tasks, yet their large parameter counts limit deployment in resource-constrained settings. One-shot pruning reduces model size without retraining, but models trained with standard objectives often suffer substantial accuracy drops under aggressive sparsity. Prior work mitigates this drop along two directions: regularizers such as ℓ1 and DeepHoyer that shape the weight distribution during training, and pruning-robust optimizers such as SAM, CrAM, and S2SAM that flatten the loss landscape. However, existing regularizers either shrink all weights uniformly (ℓ1) or induce scale-invariant sparsity (DeepHoyer), without concentrating weight energy onto a small set of informative parameters. We propose a Weight Concentration Regularizer (WCR), a training-time regularizer that amplifies the magnitude of a small subset of parameters while driving the remainder toward zero, so that magnitude pruning predominantly removes parameters with negligible functional contribution. We provide a convergence analysis and evaluate WCR on LLM fine-tuning, image classification, and medical segmentation, demonstrating consistent improvements in pruning robustness across architectures and compatibility with existing pruning-robust optimizers.