# Layerwise Decoupling for Stable Structured Sparsification of Fully Connected Layers

arXiv: https://arxiv.org/abs/2609.21126 · HTML: https://mlsanity.com/paper/2609.21126/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 39 of its 44 references that are in the map.
- First posted on arXiv 17 Sep 2026.

## Builds on (most cited first, 30 of 39)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [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)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [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)
- [Rethinking the Value of Network Pruning](https://mlsanity.com/paper/1810.05270/) (2018)
- [The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems](https://mlsanity.com/paper/1710.00211/) (2017)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [Learning Structured Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1608.03665/) (2016)
- [Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networks](https://mlsanity.com/paper/2102.00554/) (2021)
- [HAQ: Hardware-Aware Automated Quantization with Mixed Precision](https://mlsanity.com/paper/1811.08886/) (2018)
- [Filter Pruning via Geometric Median for Deep Convolutional Neural Networks Acceleration](https://mlsanity.com/paper/1811.00250/) (2018)
- [In Search of the Real Inductive Bias: On the Role of Implicit Regularization in Deep Learning](https://mlsanity.com/paper/1412.6614/) (2014)
- [Dynamic Network Surgery for Efficient DNNs](https://mlsanity.com/paper/1608.04493/) (2016)
- [NISP: Pruning Networks using Neuron Importance Score Propagation](https://mlsanity.com/paper/1711.05908/) (2017)
- [Network Trimming: A Data-Driven Neuron Pruning Approach towards Efficient Deep Architectures](https://mlsanity.com/paper/1607.03250/) (2016)
- [Data-Driven Sparse Structure Selection for Deep Neural Networks](https://mlsanity.com/paper/1707.01213/) (2017)
- [Learning to Quantize Deep Networks by Optimizing Quantization Intervals with Task Loss](https://mlsanity.com/paper/1808.05779/) (2018)
- [Layer-adaptive sparsity for the Magnitude-based Pruning](https://mlsanity.com/paper/2010.07611/) (2020)
- [Mixed Precision Quantization of ConvNets via Differentiable Neural Architecture Search](https://mlsanity.com/paper/1812.00090/) (2018)
- [Group Sparse Regularization for Deep Neural Networks](https://mlsanity.com/paper/1607.00485/) (2016)
- [Exploring Sparsity in Recurrent Neural Networks](https://mlsanity.com/paper/1704.05119/) (2017)
- [What Kinds of Functions do Deep Neural Networks Learn? Insights from Variational Spline Theory](https://mlsanity.com/paper/2105.03361/) (2021)
- [Initialization and Regularization of Factorized Neural Layers](https://mlsanity.com/paper/2105.01029/) (2021)
- [The Generalization-Stability Tradeoff In Neural Network Pruning](https://mlsanity.com/paper/1906.03728/) (2019)

## Abstract (arXiv)

We propose a decoupled, layerwise method for structurally sparsifying the fully connected layers of pretrained neural networks. Rather than penalizing all layers jointly, our approach extracts shallow two-layer subnetworks, normalizes the inner weights, and applies a structured group penalty to the outer weight matrix of each block, processing layers sequentially to prune neurons and reduce the width of each layer. We prove that the constrained decoupled objective is equivalent at optimality to a specific joint penalty on the inner and outer weights, for any positively homogeneous activation, and thus admits a clean projected and proximal formulation. Our central finding is that this decoupled reformulation is more robust than coupled methods. In numerical experiments it provides a wider usable range of the regularization strength and a lower rate of catastrophic over-pruning than the tested joint baseline while maintaining comparable accuracy. We establish these properties in controlled classification and sparse-recovery studies, and examine their scope in a high-dimensional PINN stress test and in the feed-forward layers of OPT-1.3B.