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

2025-08-30

AI Summary

This study addresses model compression for Random Wired Neural Networks (RWNNs) in COVID-19 chest X-ray classification. We propose a discrete Ricci curvature-based edge pruning method, introducing Forman-Ricci curvature—computationally more efficient than Ollivier-Ricci curvature—into neural network pruning for the first time, while preserving pruning efficacy. The method is further enhanced by integrating edge betweenness centrality and systematically evaluated across Erdős–Rényi, Watts–Strogatz, and Barabási–Albert topologies to demonstrate robustness. Experiments show that our approach significantly reduces parameter count and theoretical computational cost—yielding higher speedup—while maintaining classification accuracy, sensitivity, and specificity. Moreover, it achieves a superior trade-off between preserving modular structure and sustaining global information propagation efficiency.

Technology Category

• Machine Learning: Learning on the Edge & Model Compression
• Computer Vision: Other Foundations of Computer Vision
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

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: Erdös-Rényi (ER) model, Watts-Strogatz (WS) model, and Barabási-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.

Problem

• Pruning randomly wired neural networks using discrete Ricci curvature
• Evaluating edge-centric measures for network compression and performance
• Comparing Forman-Ricci curvature with Ollivier-Ricci for computational efficiency

Innovation

• Using Forman-Ricci curvature for efficient network pruning
• Comparing three edge measures across different network generators
• Pruning randomly wired networks while preserving classification performance