# Linearity-based neural network compression

arXiv: https://arxiv.org/abs/2506.21146 · HTML: https://mlsanity.com/paper/2506.21146/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 20 references that are in the map.
- First posted on arXiv 26 Jun 2025.

## Builds on (most cited first, 15 of 15)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [Importance Estimation for Neural Network Pruning](https://mlsanity.com/paper/1906.10771/) (2019)
- [MobileBERT: a Compact Task-Agnostic BERT for Resource-Limited Devices](https://mlsanity.com/paper/2004.02984/) (2020)
- [ThiNet: A Filter Level Pruning Method for Deep Neural Network Compression](https://mlsanity.com/paper/1707.06342/) (2017)
- [NISP: Pruning Networks using Neuron Importance Score Propagation](https://mlsanity.com/paper/1711.05908/) (2017)
- [OpenML Benchmarking Suites](https://mlsanity.com/paper/1708.03731/) (2017)
- [Towards Optimal Structured CNN Pruning via Generative Adversarial Learning](https://mlsanity.com/paper/1903.09291/) (2019)
- [Centripetal SGD for Pruning Very Deep Convolutional Networks with Complicated Structure](https://mlsanity.com/paper/1904.03837/) (2019)
- [An Overview of Neural Network Compression](https://mlsanity.com/paper/2006.03669/) (2020)
- [Neural network relief: a pruning algorithm based on neural activity](https://mlsanity.com/paper/2109.10795/) (2021)
- [NoiseOut: A Simple Way to Prune Neural Networks](https://mlsanity.com/paper/1611.06211/) (2016)

## Built on by (most cited first, 1 of 1)

- [Teacher Geometry Shapes Learnability in Teacher-Student Networks](https://mlsanity.com/paper/2609.09595/) (2026)

## Abstract (arXiv)

In neural network compression, most current methods reduce unnecessary parameters by measuring importance and redundancy. To augment already highly optimized existing solutions, we propose linearity-based compression as a novel way to reduce weights in a neural network. It is based on the intuition that with ReLU-like activation functions, neurons that are almost always activated behave linearly, allowing for merging of subsequent layers. We introduce the theory underlying this compression and evaluate our approach experimentally. Our novel method achieves a lossless compression down to 1/4 of the original model size in over the majority of tested models. Applying our method on already importance-based pruned models shows very little interference between different types of compression, demonstrating the option of successful combination of techniques. Overall, our work lays the foundation for a new type of compression method that enables smaller and ultimately more efficient neural network models.