# Application of discrete Ricci curvature in pruning randomly wired neural networks: A case study with chest x-ray classification of COVID-19

arXiv: https://arxiv.org/abs/2509.05322 · HTML: https://mlsanity.com/paper/2509.05322/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 38 of its 97 references that are in the map.
- First posted on arXiv 30 Aug 2025.

## Builds on (most cited first, 30 of 38)

- [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)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [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)
- [Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning](https://mlsanity.com/paper/1602.07261/) (2016)
- [CheXpert: A Large Chest Radiograph Dataset with Uncertainty Labels and Expert Comparison](https://mlsanity.com/paper/1901.07031/) (2019)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [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)
- [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)
- [Efficient Processing of Deep Neural Networks: A Tutorial and Survey](https://mlsanity.com/paper/1703.09039/) (2017)
- [COVID-Net: A Tailored Deep Convolutional Neural Network Design for Detection of COVID-19 Cases from Chest X-Ray Images](https://mlsanity.com/paper/2003.09871/) (2020)
- [A Comprehensive Survey of Neural Architecture Search: Challenges and Solutions](https://mlsanity.com/paper/2006.02903/) (2020)
- [Hierarchical Neural Architecture Search for Deep Stereo Matching](https://mlsanity.com/paper/2010.13501/) (2020)
- [Designing Energy-Efficient Convolutional Neural Networks using Energy-Aware Pruning](https://mlsanity.com/paper/1611.05128/) (2016)
- [Exploring Randomly Wired Neural Networks for Image Recognition](https://mlsanity.com/paper/1904.01569/) (2019)
- [COVID-19 Image Data Collection](https://mlsanity.com/paper/2003.11597/) (2020)
- [CoroNet: A deep neural network for detection and diagnosis of COVID-19 from chest x-ray images](https://mlsanity.com/paper/2004.04931/) (2020)
- [Graph Structure of Neural Networks](https://mlsanity.com/paper/2007.06559/) (2020)
- [Deep-COVID: Predicting COVID-19 From Chest X-Ray Images Using Deep Transfer Learning](https://mlsanity.com/paper/2004.09363/) (2020)
- [COVIDX-Net: A Framework of Deep Learning Classifiers to Diagnose COVID-19 in X-Ray Images](https://mlsanity.com/paper/2003.11055/) (2020)
- [Classification of COVID-19 in chest X-ray images using DeTraC deep convolutional neural network](https://mlsanity.com/paper/2003.13815/) (2020)
- [Recent Advances on Neural Network Pruning at Initialization](https://mlsanity.com/paper/2103.06460/) (2021)
- [COVID-CAPS: A Capsule Network-based Framework for Identification of COVID-19 cases from X-ray Images](https://mlsanity.com/paper/2004.02696/) (2020)

## Abstract (arXiv)

Randomly Wired Neural Networks (RWNNs) serve as a valuable testbed for investigating the impact of network topology in deep learning by capturing how different connectivity patterns impact both learning efficiency and model performance. At the same time, they provide a natural framework for exploring edge-centric network measures as tools for pruning and optimization. In this study, we investigate three edge-centric network measures: Forman-Ricci curvature (FRC), Ollivier-Ricci curvature (ORC), and edge betweenness centrality (EBC), to compress RWNNs by selectively retaining important synapses (or edges) while pruning the rest. As a baseline, RWNNs are trained for COVID-19 chest x-ray image classification, aiming to reduce network complexity while preserving performance in terms of accuracy, specificity, and sensitivity. We extend prior work on pruning RWNN using ORC by incorporating two additional edge-centric measures, FRC and EBC, across three network generators: Erd"os-R'enyi (ER) model, Watts-Strogatz (WS) model, and Barab'asi-Albert (BA) model. We provide a comparative analysis of the pruning performance of the three measures in terms of compression ratio and theoretical speedup. A central focus of our study is to evaluate whether FRC, which is computationally more efficient than ORC, can achieve comparable pruning effectiveness. Along with performance evaluation, we further investigate the structural properties of the pruned networks through modularity and global efficiency, offering insights into the trade-off between modular segregation and network efficiency in compressed RWNNs. Our results provide initial evidence that FRC-based pruning can effectively simplify RWNNs, offering significant computational advantages while maintaining performance comparable to ORC.