# Effective Sparsification of Neural Networks with Global Sparsity Constraint

arXiv: https://arxiv.org/abs/2105.01571 · HTML: https://mlsanity.com/paper/2105.01571/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 41 references that are in the map.
- First posted on arXiv 3 May 2021.

## Builds on (most cited first, 30 of 36)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (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)
- [Channel Pruning for Accelerating Very Deep Neural Networks](https://mlsanity.com/paper/1707.06168/) (2017)
- [To prune, or not to prune: exploring the efficacy of pruning for model compression](https://mlsanity.com/paper/1710.01878/) (2017)
- [Rethinking the Value of Network Pruning](https://mlsanity.com/paper/1810.05270/) (2018)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [Rigging the Lottery: Making All Tickets Winners](https://mlsanity.com/paper/1911.11134/) (2019)
- [The State of Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1902.09574/) (2019)
- [Picking Winning Tickets Before Training by Preserving Gradient Flow](https://mlsanity.com/paper/2002.07376/) (2020)
- [ThiNet: A Filter Level Pruning Method for Deep Neural Network Compression](https://mlsanity.com/paper/1707.06342/) (2017)
- [Scalable Training of Artificial Neural Networks with Adaptive Sparse Connectivity inspired by Network Science](https://mlsanity.com/paper/1707.04780/) (2017)
- [SNAS: Stochastic Neural Architecture Search](https://mlsanity.com/paper/1812.09926/) (2018)
- [Variational Dropout Sparsifies Deep Neural Networks](https://mlsanity.com/paper/1701.05369/) (2017)
- [Comparing Rewinding and Fine-tuning in Neural Network Pruning](https://mlsanity.com/paper/2003.02389/) (2020)
- [What's Hidden in a Randomly Weighted Neural Network?](https://mlsanity.com/paper/1911.13299/) (2019)
- [Dynamic Network Surgery for Efficient DNNs](https://mlsanity.com/paper/1608.04493/) (2016)
- [Sparse Networks from Scratch: Faster Training without Losing Performance](https://mlsanity.com/paper/1907.04840/) (2019)
- [Deconstructing Lottery Tickets: Zeros, Signs, and the Supermask](https://mlsanity.com/paper/1905.01067/) (2019)
- [Structured Pruning of Large Language Models](https://mlsanity.com/paper/1910.04732/) (2019)
- [Parameter Efficient Training of Deep Convolutional Neural Networks by Dynamic Sparse Reparameterization](https://mlsanity.com/paper/1902.05967/) (2019)

## Built on by (most cited first, 30 of 45)

- [CODA: A Real-World Road Corner Case Dataset for Object Detection in Autonomous Driving](https://mlsanity.com/paper/2203.07724/) (2022)
- [Deep Differentiable Logic Gate Networks](https://mlsanity.com/paper/2210.08277/) (2022)
- [Advancing Model Pruning via Bi-level Optimization](https://mlsanity.com/paper/2210.04092/) (2022)
- [Model Agnostic Sample Reweighting for Out-of-Distribution Learning](https://mlsanity.com/paper/2301.09819/) (2023)
- [Exploring Diffusion Time-steps for Unsupervised Representation Learning](https://mlsanity.com/paper/2401.11430/) (2024)
- [Efficient Neural Network Training via Forward and Backward Propagation Sparsification](https://mlsanity.com/paper/2111.05685/) (2021)
- [Not All Models Are Equal: Predicting Model Transferability in a Self-challenging Fisher Space](https://mlsanity.com/paper/2207.03036/) (2022)
- [NTK-SAP: Improving neural network pruning by aligning training dynamics](https://mlsanity.com/paper/2304.02840/) (2023)
- [Probabilistic Bilevel Coreset Selection](https://mlsanity.com/paper/2301.09880/) (2023)
- [Effective Model Sparsification by Scheduled Grow-and-Prune Methods](https://mlsanity.com/paper/2106.09857/) (2021)
- [Controlled Sparsity via Constrained Optimization or: How I Learned to Stop Tuning Penalties and Love Constraints](https://mlsanity.com/paper/2208.04425/) (2022)
- [Write and Paint: Generative Vision-Language Models are Unified Modal Learners](https://mlsanity.com/paper/2206.07699/) (2022)
- [Efficient Joint Optimization of Layer-Adaptive Weight Pruning in Deep Neural Networks](https://mlsanity.com/paper/2308.10438/) (2023)
- [Mask in the Mirror: Implicit Sparsification](https://mlsanity.com/paper/2408.09966/) (2024)
- [Connectivity Matters: Neural Network Pruning Through the Lens of Effective Sparsity](https://mlsanity.com/paper/2107.02306/) (2021)
- [Deep Weight Factorization: Sparse Learning Through the Lens of Artificial Symmetries](https://mlsanity.com/paper/2502.02496/) (2025)
- [Dimensionality Reduced Training by Pruning and Freezing Parts of a Deep Neural Network, a Survey](https://mlsanity.com/paper/2205.08099/) (2022)
- [A Unified Framework for Soft Threshold Pruning](https://mlsanity.com/paper/2302.13019/) (2023)
- [VLUE: A Multi-Task Benchmark for Evaluating Vision-Language Models](https://mlsanity.com/paper/2205.15237/) (2022)
- [Efficient Symbolic Policy Learning with Differentiable Symbolic Expression](https://mlsanity.com/paper/2311.02104/) (2023)
- [Are Straight-Through gradients and Soft-Thresholding all you need for Sparse Training?](https://mlsanity.com/paper/2212.01076/) (2022)
- [Hadamard product in deep learning: Introduction, Advances and Challenges](https://mlsanity.com/paper/2504.13112/) (2025)
- [Spartan: Differentiable Sparsity via Regularized Transportation](https://mlsanity.com/paper/2205.14107/) (2022)
- [Balanced Training for Sparse GANs](https://mlsanity.com/paper/2302.14670/) (2023)
- [Balance is Essence: Accelerating Sparse Training via Adaptive Gradient Correction](https://mlsanity.com/paper/2301.03573/) (2023)
- [Magnitude Attention-based Dynamic Pruning](https://mlsanity.com/paper/2306.05056/) (2023)
- [Multi-Objective Optimization for Sparse Deep Multi-Task Learning](https://mlsanity.com/paper/2308.12243/) (2023)
- [SAFE: Finding Sparse and Flat Minima to Improve Pruning](https://mlsanity.com/paper/2506.06866/) (2025)
- [GraphTOP: Graph Topology-Oriented Prompting for Graph Neural Networks](https://mlsanity.com/paper/2510.22451/) (2025)
- [Exploring Structural Sparsity in Neural Image Compression](https://mlsanity.com/paper/2202.04595/) (2022)

## Abstract (arXiv)

Weight pruning is an effective technique to reduce the model size and inference time for deep neural networks in real-world deployments. However, since magnitudes and relative importance of weights are very different for different layers of a neural network, existing methods rely on either manual tuning or handcrafted heuristic rules to find appropriate pruning rates individually for each layer. This approach generally leads to suboptimal performance. In this paper, by directly working on the probability space, we propose an effective network sparsification method called it probabilistic masking (ProbMask), which solves a natural sparsification formulation under global sparsity constraint. The key idea is to use probability as a global criterion for all layers to measure the weight importance. An appealing feature of ProbMask is that the amounts of weight redundancy can be learned automatically via our constraint and thus we avoid the problem of tuning pruning rates individually for different layers in a network. Extensive experimental results on CIFAR-10/100 and ImageNet demonstrate that our method is highly effective, and can outperform previous state-of-the-art methods by a significant margin, especially in the high pruning rate situation. Notably, the gap of Top-1 accuracy between our ProbMask and existing methods can be up to 10%. As a by-product, we show ProbMask is also highly effective in identifying supermasks, which are subnetworks with high performance in a randomly weighted dense neural network.