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

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.

💡 Research Summary

This paper investigates the use of edge‑centric graph‑theoretic measures to prune randomly wired neural networks (RWNNs) and evaluates the resulting trade‑offs in model size, computational cost, and classification performance on a COVID‑19 chest X‑ray dataset. RWNNs differ from conventional convolutional networks by generating their internal connectivity with three classic random graph models: Erdős‑Rényi (ER), Watts‑Strogatz (WS), and Barabási‑Albert (BA). Each model produces a directed acyclic graph that is mapped onto a series of “stage blocks” containing 32 nodes, forming the backbone of the network. Ten instances of each graph type were built using parameters (ER p = 0.2, WS k = 4, p = 0.75, BA m = 5) that were previously shown to yield strong baseline performance. All networks were trained for 100 epochs with stochastic gradient descent (learning rate = 0.1) in PyTorch.

The authors focus on three edge‑centric importance scores: (1) Ollivier‑Ricci curvature (ORC), a transport‑based curvature that captures how locally “convex” an edge is; (2) Forman‑Ricci curvature (FRC), a combinatorial curvature that can be computed in linear time with respect to the number of edges; and (3) edge betweenness centrality (EBC), the fraction of all shortest paths that pass through an edge. For each trained model, edges are ranked by the chosen score, and a prescribed percentage (ranging from 30 % to 70 % of edges) is retained while the remainder is removed. Compression ratio is defined as the proportion of retained edges, and theoretical speed‑up is estimated from the reduction in floating‑point operations (FLOPs).

Performance is assessed with six standard classification metrics—accuracy, specificity, sensitivity (recall), ROC‑AUC, precision, and F1‑score—while model complexity is measured by total parameter count and FLOPs. To understand structural consequences of pruning, the authors compute modularity (a measure of community segregation) and global efficiency (a measure of overall information flow) on the resulting graphs.

Experimental results show that all three pruning strategies can dramatically reduce network size with minimal loss of diagnostic performance. For a 50 % compression rate, FRC‑based pruning retains >98 % of the original accuracy across all graph families, while achieving roughly a two‑fold reduction in computation time compared with ORC because FRC is O(|E|) versus the more expensive O(|V|·|E|) cost of ORC. ORC sometimes yields marginally higher accuracy, but its computational overhead makes it less practical for large‑scale or real‑time applications. EBC‑based pruning preserves global flow but tends to degrade accuracy slightly (≈2 % drop) in the high‑dimensional image classification task, indicating that centrality alone does not capture the nuanced importance of edges in these networks.

Structural analysis reveals that pruning with curvature measures (ORC and FRC) maintains higher global efficiency than EBC pruning, while modestly increasing modularity in WS and BA networks. This suggests that the pruned networks become more community‑structured without sacrificing the ability to transmit information efficiently—a desirable property for robust, interpretable models.

The authors conclude that Forman‑Ricci curvature offers a computationally cheap yet effective criterion for edge selection in RWNN pruning, achieving compression ratios and speed‑ups comparable to the more expensive Ollivier‑Ricci curvature while preserving diagnostic performance. They propose future work on dynamic (during‑training) pruning, extension to other medical imaging modalities, and integration of curvature‑enhanced graph convolutions to further exploit geometric information in network design.