SPP-CNN: An Efficient Framework for Network Robustness Prediction

TL;DR

This work tackles predicting network robustness under attacks without costly attack simulations, introducing SPP-CNN, which inserts a spatial pyramid pooling layer between convolutional and fully-connected layers to handle networks of varying sizes. The model achieves accuracy comparable to or better than state-of-the-art CNN- and GNN-based predictors while significantly reducing run time, and it demonstrates strong generalizability to unseen topologies and real-world networks. By preserving information during size variation and capturing multi-scale features, SPP-CNN offers a practical, scalable tool for rapid robustness estimation in large complex networks. The approach has potential to accelerate optimization and monitoring tasks in real-world systems where resilience is critical.

Abstract

This paper addresses the robustness of a network to sustain its connectivity and controllability against malicious attacks. This kind of network robustness is typically measured by the time-consuming attack simulation, which returns a sequence of values that record the remaining connectivity and controllability after a sequence of node- or edge-removal attacks. For improvement, this paper develops an efficient framework for network robustness prediction, the spatial pyramid pooling convolutional neural network (SPP-CNN). The new framework installs a spatial pyramid pooling layer between the convolutional and fully-connected layers, overcoming the common mismatch issue in the CNN-based prediction approaches and extending its generalizability. Extensive experiments are carried out by comparing SPP-CNN with three state-of-the-art robustness predictors, namely a CNN-based and two graph neural networks-based frameworks. Synthetic and real-world networks, both directed and undirected, are investigated. Experimental results demonstrate that the proposed SPP-CNN achieves better prediction performances and better generalizability to unknown datasets, with significantly lower time-consumption, than its counterparts.

Figures (7)

• Figure 1: General frameworks of CNN-RP, PATCHY-SAN, and LFR-CNN. CNN-RP processes network data as gray-scaled images, while for PATCHY-SAN and LFR-CNN, the LFR module performs the selection, assembly, and normalization (SAN) operations, which compress higher-dimensional (HD) network data to be lower-dimensional (LD) representations.
• Figure 2: CNN structure in CNN-RP. The input is an adjacency matrix; the output is an $N$-vector. Seven feature map (FM) groups are generated with $N_i=\lceil N/2^{(i+1)}\rceil$, for $i=1,2,\ldots,7$. Concatenation layer reshapes the data to be a vector, from FM 7 to FC$_1$. FC$_1$=$512N_7^{2}$ and FC$_2$=$4096$Lou2022TCYB.
• Figure 3: The convolutional neural network structure with a spatial pyramid pooling layer. The detailed structure of convolutional layers are shown in Fig. \ref{['fig:spp_cnn']}.
• Figure 4: CNN structure of SPP-CNN. The spatial pyramid pooling layer is installed between the convolutional layers and fully-connected layers. Hard-sigmoid is installed in the last fully-connected layer, while in other layers ReLU is installed.
• Figure 5: Run time comparison of SPP-CNN, CNN-RP, PATCHY-SAN, LFR-CNN, and attack simulation (SIM): (a) for network size $N_{a}\in[700,1300]$; and (b) for network size $N_{b}\in[300,700]$