  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.
