# COPS: Controlled Pruning Before Training Starts

arXiv: https://arxiv.org/abs/2107.12673 · HTML: https://mlsanity.com/paper/2107.12673/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 31 references that are in the map.
- First posted on arXiv 27 Jul 2021.

## Builds on (most cited first, 20 of 20)

- [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)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [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)
- [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)
- [EIE: Efficient Inference Engine on Compressed Deep Neural Network](https://mlsanity.com/paper/1602.01528/) (2016)
- [Compressing Neural Networks with the Hashing Trick](https://mlsanity.com/paper/1504.04788/) (2015)
- [Deep Rewiring: Training very sparse deep networks](https://mlsanity.com/paper/1711.05136/) (2017)
- [A Signal Propagation Perspective for Pruning Neural Networks at Initialization](https://mlsanity.com/paper/1906.06307/) (2019)
- [Faster Dynamic Matrix Inverse for Faster LPs](https://mlsanity.com/paper/2004.07470/) (2020)
- [Pruning via Iterative Ranking of Sensitivity Statistics](https://mlsanity.com/paper/2006.00896/) (2020)
- [FreezeNet: Full Performance by Reduced Storage Costs](https://mlsanity.com/paper/2011.14087/) (2020)

## Built on by (most cited first, 6 of 6)

- [Interspace Pruning: Using Adaptive Filter Representations to Improve Training of Sparse CNNs](https://mlsanity.com/paper/2203.07808/) (2022)
- [Dimensionality Reduced Training by Pruning and Freezing Parts of a Deep Neural Network, a Survey](https://mlsanity.com/paper/2205.08099/) (2022)
- [CNN Mixture-of-Depths](https://mlsanity.com/paper/2409.17016/) (2024)
- [One-shot Network Pruning at Initialization with Discriminative Image Patches](https://mlsanity.com/paper/2209.05683/) (2022)
- [PROM: Prioritize Reduction of Multiplications Over Lower Bit-Widths for Efficient CNNs](https://mlsanity.com/paper/2505.03254/) (2025)
- [HASTE: A Framework for Training-Free, Dynamic, and Steerable Compression of Pre-Trained Convolutional Neural Networks](https://mlsanity.com/paper/2606.30516/) (2026)

## Abstract (arXiv)

State-of-the-art deep neural network (DNN) pruning techniques, applied one-shot before training starts, evaluate sparse architectures with the help of a single criterion -- called pruning score. Pruning weights based on a solitary score works well for some architectures and pruning rates but may also fail for other ones. As a common baseline for pruning scores, we introduce the notion of a generalized synaptic score (GSS). In this work we do not concentrate on a single pruning criterion, but provide a framework for combining arbitrary GSSs to create more powerful pruning strategies. These COmbined Pruning Scores (COPS) are obtained by solving a constrained optimization problem. Optimizing for more than one score prevents the sparse network to overly specialize on an individual task, thus COntrols Pruning before training Starts. The combinatorial optimization problem given by COPS is relaxed on a linear program (LP). This LP is solved analytically and determines a solution for COPS. Furthermore, an algorithm to compute it for two scores numerically is proposed and evaluated. Solving COPS in such a way has lower complexity than the best general LP solver. In our experiments we compared pruning with COPS against state-of-the-art methods for different network architectures and image classification tasks and obtained improved results.