# Scaling Up Exact Neural Network Compression by ReLU Stability

arXiv: https://arxiv.org/abs/2102.07804 · HTML: https://mlsanity.com/paper/2102.07804/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 61 of its 105 references that are in the map.
- First posted on arXiv 15 Feb 2021.

## Builds on (most cited first, 30 of 61)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [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)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [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)
- [Rethinking the Value of Network Pruning](https://mlsanity.com/paper/1810.05270/) (2018)
- [What is the State of Neural Network Pruning?](https://mlsanity.com/paper/2003.03033/) (2020)
- [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)
- [ThiNet: A Filter Level Pruning Method for Deep Neural Network Compression](https://mlsanity.com/paper/1707.06342/) (2017)
- [On the Number of Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1402.1869/) (2014)
- [Stronger generalization bounds for deep nets via a compression approach](https://mlsanity.com/paper/1802.05296/) (2018)
- [Exploiting Linear Structure Within Convolutional Networks for Efficient Evaluation](https://mlsanity.com/paper/1404.0736/) (2014)
- [On the Expressive Power of Deep Neural Networks](https://mlsanity.com/paper/1606.05336/) (2016)
- [Speeding up Convolutional Neural Networks with Low Rank Expansions](https://mlsanity.com/paper/1405.3866/) (2014)
- [Comparing Rewinding and Fine-tuning in Neural Network Pruning](https://mlsanity.com/paper/2003.02389/) (2020)
- [NISP: Pruning Networks using Neuron Importance Score Propagation](https://mlsanity.com/paper/1711.05908/) (2017)
- [Predicting Parameters in Deep Learning](https://mlsanity.com/paper/1306.0543/) (2013)
- [Learning to Prune Deep Neural Networks via Layer-wise Optimal Brain Surgeon](https://mlsanity.com/paper/1705.07565/) (2017)
- [Algorithms for Verifying Deep Neural Networks](https://mlsanity.com/paper/1903.06758/) (2019)
- [Speeding-up Convolutional Neural Networks Using Fine-tuned CP-Decomposition](https://mlsanity.com/paper/1412.6553/) (2014)
- [Compressing BERT: Studying the Effects of Weight Pruning on Transfer Learning](https://mlsanity.com/paper/2002.08307/) (2020)
- [Pruning Neural Networks at Initialization: Why are We Missing the Mark?](https://mlsanity.com/paper/2009.08576/) (2020)
- [What Do Compressed Deep Neural Networks Forget?](https://mlsanity.com/paper/1911.05248/) (2019)
- [Complexity of Linear Regions in Deep Networks](https://mlsanity.com/paper/1901.09021/) (2019)

## Built on by (most cited first, 19 of 19)

- [Structured Pruning for Deep Convolutional Neural Networks: A survey](https://mlsanity.com/paper/2303.00566/) (2023)
- [Going Beyond Linear Mode Connectivity: The Layerwise Linear Feature Connectivity](https://mlsanity.com/paper/2307.08286/) (2023)
- [The Combinatorial Brain Surgeon: Pruning Weights That Cancel One Another in Neural Networks](https://mlsanity.com/paper/2203.04466/) (2022)
- [When Deep Learning Meets Polyhedral Theory: A Survey](https://mlsanity.com/paper/2305.00241/) (2023)
- [Pruning's Effect on Generalization Through the Lens of Training and Regularization](https://mlsanity.com/paper/2210.13738/) (2022)
- [Parameter identifiability of a deep feedforward ReLU neural network](https://mlsanity.com/paper/2112.12982/) (2021)
- [Optimization Over Trained Neural Networks: Taking a Relaxing Walk](https://mlsanity.com/paper/2401.03451/) (2024)
- [Recall Distortion in Neural Network Pruning and the Undecayed Pruning Algorithm](https://mlsanity.com/paper/2206.02976/) (2022)
- [Getting Away with More Network Pruning: From Sparsity to Geometry and Linear Regions](https://mlsanity.com/paper/2301.07966/) (2023)
- [Universal approximation and model compression for radial neural networks](https://mlsanity.com/paper/2107.02550/) (2021)
- [Computational Tradeoffs of Optimization-Based Bound Tightening in ReLU Networks](https://mlsanity.com/paper/2312.16699/) (2023)
- [Quiver neural networks](https://mlsanity.com/paper/2207.12773/) (2022)
- [Training Thinner and Deeper Neural Networks: Jumpstart Regularization](https://mlsanity.com/paper/2201.12795/) (2022)
- [Relaxation-Informed Training of Neural Network Surrogate Models](https://mlsanity.com/paper/2604.22746/) (2026)
- [Multi-Objective Linear Ensembles for Robust and Sparse Training of Few-Bit Neural Networks](https://mlsanity.com/paper/2212.03659/) (2022)
- [Towards Global Neural Network Abstractions with Locally-Exact Reconstruction](https://mlsanity.com/paper/2210.12054/) (2022)
- [Tightening convex relaxations of trained neural networks: a unified approach for convex and S-shaped activations](https://mlsanity.com/paper/2410.23362/) (2024)
- [Optimization over Trained (and Sparse) Neural Networks: A Surrogate within a Surrogate](https://mlsanity.com/paper/2505.01985/) (2025)
- [Uncovering the Limits of Proof Sharing for Neural Networks](https://mlsanity.com/paper/2608.19351/) (2026)

## Abstract (arXiv)

We can compress a rectifier network while exactly preserving its underlying functionality with respect to a given input domain if some of its neurons are stable. However, current approaches to determine the stability of neurons with Rectified Linear Unit (ReLU) activations require solving or finding a good approximation to multiple discrete optimization problems. In this work, we introduce an algorithm based on solving a single optimization problem to identify all stable neurons. Our approach is on median 183 times faster than the state-of-art method on CIFAR-10, which allows us to explore exact compression on deeper (5 x 100) and wider (2 x 800) networks within minutes. For classifiers trained under an amount of L1 regularization that does not worsen accuracy, we can remove up to 56% of the connections on the CIFAR-10 dataset. The code is available at the following link, https://github.com/yuxwind/ExactCompression.