# Dep-L0: Improving L0-based Network Sparsification via Dependency Modeling

arXiv: https://arxiv.org/abs/2107.00070 · HTML: https://mlsanity.com/paper/2107.00070/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 48 references that are in the map.
- First posted on arXiv 30 Jun 2021.

## Builds on (most cited first, 30 of 34)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [Learning Efficient Convolutional Networks through Network Slimming](https://mlsanity.com/paper/1708.06519/) (2017)
- [To prune, or not to prune: exploring the efficacy of pruning for model compression](https://mlsanity.com/paper/1710.01878/) (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)
- [Importance Estimation for Neural Network Pruning](https://mlsanity.com/paper/1906.10771/) (2019)
- [The State of Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1902.09574/) (2019)
- [AMC: AutoML for Model Compression and Acceleration on Mobile Devices](https://mlsanity.com/paper/1802.03494/) (2018)
- [Deep Learning with Limited Numerical Precision](https://mlsanity.com/paper/1502.02551/) (2015)
- [Filter Pruning via Geometric Median for Deep Convolutional Neural Networks Acceleration](https://mlsanity.com/paper/1811.00250/) (2018)
- [Soft Filter Pruning for Accelerating Deep Convolutional Neural Networks](https://mlsanity.com/paper/1808.06866/) (2018)
- [Exploiting Linear Structure Within Convolutional Networks for Efficient Evaluation](https://mlsanity.com/paper/1404.0736/) (2014)
- [HRank: Filter Pruning using High-Rank Feature Map](https://mlsanity.com/paper/2002.10179/) (2020)
- [Speeding up Convolutional Neural Networks with Low Rank Expansions](https://mlsanity.com/paper/1405.3866/) (2014)
- [Variational Dropout Sparsifies Deep Neural Networks](https://mlsanity.com/paper/1701.05369/) (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)
- [Discrimination-aware Channel Pruning for Deep Neural Networks](https://mlsanity.com/paper/1810.11809/) (2018)
- [Towards Optimal Structured CNN Pruning via Generative Adversarial Learning](https://mlsanity.com/paper/1903.09291/) (2019)
- [Gate Decorator: Global Filter Pruning Method for Accelerating Deep Convolutional Neural Networks](https://mlsanity.com/paper/1909.08174/) (2019)
- [Rethinking the Smaller-Norm-Less-Informative Assumption in Channel Pruning of Convolution Layers](https://mlsanity.com/paper/1802.00124/) (2018)
- [Network Pruning via Transformable Architecture Search](https://mlsanity.com/paper/1905.09717/) (2019)

## Abstract (arXiv)

Training deep neural networks with an L0 regularization is one of the prominent approaches for network pruning or sparsification. The method prunes the network during training by encouraging weights to become exactly zero. However, recent work of Gale et al. reveals that although this method yields high compression rates on smaller datasets, it performs inconsistently on large-scale learning tasks, such as ResNet50 on ImageNet. We analyze this phenomenon through the lens of variational inference and find that it is likely due to the independent modeling of binary gates, the mean-field approximation, which is known in Bayesian statistics for its poor performance due to the crude approximation. To mitigate this deficiency, we propose a dependency modeling of binary gates, which can be modeled effectively as a multi-layer perceptron (MLP). We term our algorithm Dep-L0 as it prunes networks via a dependency-enabled L0 regularization. Extensive experiments on CIFAR10, CIFAR100 and ImageNet with VGG16, ResNet50, ResNet56 show that our Dep-L0 outperforms the original L0-HC algorithm of Louizos et al. by a significant margin, especially on ImageNet. Compared with the state-of-the-arts network sparsification algorithms, our dependency modeling makes the L0-based sparsification once again very competitive on large-scale learning tasks. Our source code is available at https://github.com/leo-yangli/dep-l0.