Existing adversarial training (AT) methods often suffer from incomplete perturbation, meaning that not all non-robust features are perturbed when generating adversarial examples (AEs). This results in residual correlations between non-robust features and labels, leading to suboptimal learning of robust features. However, achieving complete perturbation—perturbing as many non-robust features as possible, is challenging due to the difficulty in distinguishing robust and non-robust features and the sparsity of labeled data. To address these challenges, we propose a novel approach called Weakly Supervised Contrastive Adversarial Training (WSCAT). WSCAT ensures complete perturbation for improved learning of robust features by disrupting correlations between non-robust features and labels through complete AE generation over partially labeled data, grounded in information theory. Extensive theoretical analysis and comprehensive experiments on widely adopted benchmarks validate the superiority of WSCAT. Our code is available at https://github.com/zhang-lilin/WSCAT.

Graph contrastive learning (GCL) often suffers from false negatives, which degrades the performance on downstream tasks. The existing methods addressing the false negative issue usually rely on human prior knowledge, still leading GCL to suboptimal results. In this paper, we propose a novel Negative Metric Learning (NML) enhanced GCL (NML-GCL). NML-GCL employs a learnable Negative Metric Network (NMN) to build a negative metric space, in which false negatives can be distinguished better from true negatives based on their distance to anchor node. To overcome the lack of explicit supervision signals for NML, we propose a joint training scheme with bi-level optimization objective, which implicitly utilizes the self-supervision signals to iteratively optimize the encoder and the negative metric network. The solid theoretical analysis and the extensive experiments conducted on widely used benchmarks verify the superiority of the proposed method.

Network robustness, which refers to a network’s ability to withstand malicious attacks on its vertices and edges, is critical across various natural and industrial domains. This paper delves into the assessment of network robustness through machine learning-based approaches, with a specific focus on structure-based representations and graph embeddings. The evaluation encompasses both synthetic and real-world networks, and three types of representation paradigms are scrutinized: 1) structure-based representations, including adjacency, incidence, and modularity matrices, 2) graph embeddings, including learning feature representation (LFR), DeepWalk, large-scale information network embedding (LINE), node2vec, structural deep network embedding (SDNE), and struc2vec, and 3) one-dimensional graph embeddings. The findings underscore the preference of convolutional neural networks (CNNs) with structure-based representations, highlighting the efficacy of adjacency and modularity matrices. While graph embeddings showcase versatility, their overall performance is comparatively lower, emphasizing the crucial role of representation complexity. This study contributes valuable insights into robustness evaluation methodologies and underscores the significance of tailored graph representations.

Connectivity robustness and controllability robustness play a crucial role in maintaining the stability of complex network systems. Recently, complex network systems have faced an increasing number of malicious attacks and random failures, emphasizing the vital importance of assessing their performance. The CNN-based predictor serves as a powerful tool for evaluating the robustness of complex networks. However, the excellent performance of CNN-based predictors requires complete network data, which is often not available in real-world networks. In this paper, we investigate the recovery of losing information in networks. The main contributions can be summarized as follows: 1) Explore the impact of information loss in complex networks on CNN-based robustness prediction models. 2) Propose three recovery algorithms for addressing information loss, effectively improving the issue of losing network information. Extensive experiments demonstrate that in the presence of information loss in complex networks, CNN-based predictors exhibit higher prediction errors. However, through the application of recovery algorithms to recover losing information, a significant reduction in prediction errors is achieved.

Despite various measures across different engineering and social systems, network robustness remains crucial for resisting random faults and malicious attacks. In this study, robustness refers to the ability of a network to maintain its functionality after a part of the network has failed. Existing methods assess network robustness using attack simulations, spectral measures, or deep neural networks (DNNs), which return a single metric as a result. Evaluating network robustness is technically challenging, while evaluating a single metric is practically insufficient. This article proposes a multitask analysis system based on the graph isomorphism network (GIN) model, abbreviated as GIN-MAS. First, a destruction-based robustness metric is formulated using the destruction threshold of the examined network. A multitask learning approach is taken to learn the network robustness metrics, including connectivity robustness, controllability robustness, destruction threshold, and the maximum number of connected components. Then, a five-layer GIN is constructed for evaluating the aforementioned four robustness metrics simultaneously. Finally, extensive experimental studies reveal that 1) GIN-MAS outperforms nine other methods, including three state-of-the-art convolutional neural network (CNN)-based robustness evaluators, with lower prediction errors for both known and unknown datasets from various directed and undirected, synthetic, and real-world networks; 2) the multitask learning scheme is not only capable of handling multiple tasks simultaneously but more importantly it enables the parameter and knowledge sharing across tasks, thus preventing overfitting and enhancing the performances; and 3) GIN-MAS performs multitasks significantly faster than other single-task evaluators. The excellent performance of GIN-MAS suggests that more powerful DNNs have great potentials for analyzing more complicated and comprehensive robustness evaluation tasks.

Network robustness refers to the ability of a network to continue its functioning against malicious attacks, which is critical for various natural and industrial networks. Network robustness can be quantitatively measured by a sequence of values that record the remaining functionality after a sequential node- or edge-removal attacks. Robustness evaluations are traditionally determined by attack simulations, which are computationally very time-consuming and sometimes practically infeasible. The convolutional neural network (CNN)-based prediction provides a cost-efficient approach to fast evaluating the network robustness. In this article, the prediction performances of the learning feature representation-based CNN (LFR-CNN) and PATCHY-SAN methods are compared through extensively empirical experiments. Specifically, three distributions of network size in the training data are investigated, including the uniform, Gaussian, and extra distributions. The relationship between the CNN input size and the dimension of the evaluated network is studied. Extensive experimental results reveal that compared to the training data of uniform distribution, the Gaussian and extra distributions can significantly improve both the prediction performance and the generalizability, for both LFR-CNN and PATCHY-SAN, and for various functionality robustness. The extension ability of LFR-CNN is significantly better than PATCHY-SAN, verified by extensive comparisons on predicting the robustness of unseen networks. In general, LFR-CNN outperforms PATCHY-SAN, and thus LFR-CNN is recommended over PATCHY-SAN. However, since both LFR-CNN and PATCHY-SAN have advantages for different scenarios, the optimal settings of the input size of CNN are recommended under different configurations.

Many natural and engineering systems can be modeled and represented in the forms of graph data, and then studied using graph theory and network analysis tools. Graph representation learning aims at generating lower-dimensional representations from higher-dimensional graph data, which is a crucial step that facilitates the follow-up tasks, such as node and graph classifications. In this paper, we present a simple but effective graph representation learning method, namely the pyramid pooling-based local profile (PPLP), which enables local nodal profiles to be transformed into a graph representation, with multi-scale features extracted. PPLP can be either embedded into a graph neural network as the readout layer, or perform independently as a graph embedding algorithm. The resultant representations of PPLP are for graph-level tasks. PPLP is experimentally tested by performing graph classification tasks on ten representative datasets, either as the readout layer of different graph neural networks, or as an independent graph embedding algorithm. Experimental results demonstrate that: 1) when embedded into graph neural networks, PPLP outperforms the widely-used global pooling-based readout methods; 2) as an independent graph embedding algorithm, PPLP performs fairly good, especially on the social network datasets. The investigation confirms PPLP as a simple but promising method for graph-level tasks.

The connectivity and controllability of complex networks play an important role in ensuring the proper functioning of network systems. Robustness of connectivity and controllability is the ability of a network to maintain its basic functions against various malicious attacks. Convolutional neural network (CNN)-based approaches provide an efficient framework to approximate the network robustness, which significantly reduces computation time compared to attack simulations. In this paper, the performance of CNN-based prediction for connectivity and controllability robustness is investigated, when there are noises in the network input representation. Two CNN-based predictors are compared and investigated, 1) convolutional neural network-based robustness predictor (CNN-RP), and 2) spatial pyramid pooling-based convolutional neural network (CNN-SPP). Two aspects of network information noises are considered and investigated, 1) the random node information noises (RNIN), and 2) the random edge information noises (REIN). The following main conclusions are obtained from extensive experimental studies on synthetic networks: 1) CNN-RP is more tolerant than CNN-SPP to network noises, 2) The characteristics of small-world and scale-free networks make them have a favorable anti-noise ability, and 3) RNIN has less impact on CNN-based prediction performance than REIN, RNIN and REIN show opposite effects on prediction performance when the size of the predicted network is out of the training network size range.

Edge rectification is a widely used method to enhance network robustness. However, in some networked systems, edge rectification may be challenging or even infeasible to implement. An edge addition strategy is proposed as an alternative optimization method in this paper. Nested Ring Structure (NRS), whereby each node's edges connect its nearest neighbors along the backbone direction, have exhibited robust controllability against random attacks. Therefore, The Nested Edge Addition (NEA) strategy is proposed, which enhances network controllability by building NRS through edge addition to a given initial network. With a small number of added edges, NEA can rapidly enhance network controllability, allowing the network to be controlled using just one driver node. The more nested edges are added, the stronger the NRS in a network, thus exhibiting better controllability robustness. The effectiveness of NEA is verified by simulations on both synthetic and real-world networks. Extensive experimental results demonstrate that NEA is an efficient strategy for designing network topology and optimizing real-world networks.

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 one 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 for both cases of known and unknown datasets, with significantly lower time-consumption, than its counterparts.

Connectivity and controllability of a complex network are two important issues that guarantee a networked system to function. Robustness of connectivity and controllability guarantees the system to function properly and stably under various malicious attacks. Evaluating network robustness using attack simulations is time consuming, while the convolutional neural network (CNN)-based prediction approach provides a cost-efficient method to approximate the network robustness. In this paper, we investigate the performance of CNN-based approaches for connectivity and controllability robustness prediction, when partial network information is missing, namely the adjacency matrix is incomplete. Extensive experimental studies are carried out. A threshold is explored that if a total amount of more than 7.29% information is lost, the performance of CNN-based prediction will be significantly degenerated for all cases in the experiments. Two scenarios of missing edge representations are compared, 1) a missing edge is marked ‘no edge’ in the input for prediction, and 2) a missing edge is denoted using a special marker of ‘unknown’. Experimental results reveal that the first representation is misleading to the CNN-based predictors.