Graph matching in the setting of federated learning is still an open problem. This paper proposes an unsupervised federated graph matching algorithm, UFGM, for inferring matched node pairs on different graphs across clients while maintaining privacy requirement, by leveraging graphlet theory and trust region optimization. First, the nodes’ graphlet features are captured to generate pseudo matched node pairs on different graphs across clients as pseudo training data for tackling the dilemma of unsupervised graph matching in federated setting and leveraging the strength of supervised graph matching. An approximate graphlet enumeration method is proposed to sample a small number of graphlets and capture nodes’ graphlet features. Theoretical analysis is conducted to demonstrate that the approximate method is able to maintain the quality of graphlet estimation while reducing its expensive cost. Second, we propose a separate trust region algorithm for pseudo supervised federated graph matching while maintaining the privacy constraints. In order to avoid expensive cost of the second-order Hessian computation in the trust region algorithm, we propose two weak quasi-Newton conditions to construct a positive definite scalar matrix as the Hessian approximation with only first-order gradients. We theoretically derive the error introduced by the separate trust region due to the Hessian approximation and conduct the convergence analysis of the approximation method.

The deep learning method is an efficient solution for improving the quality of undersampled magnetic resonance (MR) image reconstruction while reducing lengthy data acquisition. Most deep learning methods neglect the mutual constraints between the real and imaginary components of complex-valued k-space data. In this paper, a new complex-valued convolutional neural network, namely, Dense-U-Dense Net (DUD-Net), is proposed to interpolate the undersampled k-space data and reconstruct MR images. The proposed network comprises dense layers, U-Net, and other dense layers in sequence. The dense layers are used to simulate the mutual constraints between real and imaginary components, and U-Net performs feature sparsity and interpolation estimation for k-space data. Two MRI datasets were used to evaluate the proposed method: brain magnitude-only MR images and knee complex-valued k-space data. Several operations were conducted for data preprocessing. First, the complex-valued MR images were synthesized by phase modulation on magnitude-only images. Second, a radial trajectory based on the golden angle was used for k-space undersampling, whereby a reversible normalization method was proposed to balance the distribution of positive and negative values in k-space data. The optimal performance of DUD-Net was demonstrated based on a quantitative evaluation of inter-method and intra-method comparisons. When compared with other methods, significant improvements were achieved, PSNRs were increased by 10.78 and 5.74dB, whereas RMSEs were decreased by 71.53% and 30.31% for magnitude and phase image, respectively. It is concluded that DUD-Net significantly improves the performance of MR image reconstruction.

Only recently, researchers attempt to provide classification algorithms with provable group fairness guarantees. Most of these algorithms suffer from harassment caused by the requirement that the training and deployment data follow the same distribution. This paper proposes an input-agnostic certified group fairness algorithm, FairSmooth, for improving the fairness of classification models while maintaining the remarkable prediction accuracy. A Gaussian parameter smoothing method is developed to transform base classifiers into their smooth versions. An optimal individual smooth classifier is learnt for each group with only the data regarding the group and an overall smooth classifier for all groups is generated by averaging the parameters of all the individual smooth ones. By leveraging the theory of nonlinear functional analysis, the smooth classifiers are reformulated as output functions of a Nemytskii operator. Theoretical analysis is conducted to derive that the Nemytskii operator is smooth and induces a Frechet differentiable smooth manifold. We theoretically demonstrate that the smooth manifold has a global Lipschitz constant that is independent of the domain of the input data, which derives the input-agnostic certified group fairness.

Recent literatures have shown that knowledge graph (KG) learning models are highly vulnerable to adversarial attacks. However, there is still a paucity of vulnerability analyses of cross-lingual entity alignment under adversarial attacks. This paper proposes an adversarial attack model with two novel attack techniques to perturb the KG structure and degrade the quality of deep cross-lingual entity alignment. First, an entity density maximization method is employed to hide the attacked entities in dense regions in two KGs, such that the derived perturbations are unnoticeable. Second, an attack signal amplification method is developed to reduce the gradient vanishing issues in the process of adversarial attacks for further improving the attack effectiveness.

Recent findings have shown multiple graph learning models, such as graph classification and graph matching, are highly vulnerable to adversarial attacks, i.e. small input perturbations in graph structures and node attributes can cause the model failures. Existing defense techniques often defend specific attacks on particular multiple graph learning tasks. This paper proposes an attack-agnostic graph-adaptive 1-Lipschitz neural network, ERNN, for improving the robustness of deep multiple graph learning while achieving remarkable expressive power. A K_l-Lipschitz Weibull activation function is designed to enforce the gradient norm as K_l at layer l. The nearest matrix orthogonalization and polar decomposition techniques are utilized to constraint the weight norm as 1/K_l and make the norm-constrained weight close to the original weight. The theoretical analysis is conducted to derive lower and upper bounds of feasible K_l under the 1-Lipschitz constraint. The combination of norm-constrained weight and activation function leads to the 1-Lipschitz neural network for expressive and robust multiple graph learning.

Despite achieving remarkable efficiency, traditional network pruning techniques often follow manually-crafted heuristics to generate pruned sparse networks. Such heuristic pruning strategies are hard to guarantee that the pruned networks achieve test accuracy comparable to the original dense ones. Recent works have empirically identified and verified the Lottery Ticket Hypothesis (LTH): a randomly-initialized dense neural network contains an extremely sparse subnetwork, which can be trained to achieve similar accuracy to the former. Due to the lack of theoretical evidence, they often need to run multiple rounds of expensive training and pruning over the original large networks to discover the sparse subnetworks with low accuracy loss. By leveraging dynamical systems theory and inertial manifold theory, this work theoretically verifies the validity of the LTH. We explore the possibility of theoretically lossless pruning as well as one-time pruning, compared with existing neural network pruning and LTH techniques. We reformulate the neural network optimization problem as a gradient dynamical system and reduce this high-dimensional system onto inertial manifolds to obtain a low-dimensional system regarding pruned subnetworks. We demonstrate the precondition and existence of pruned subnetworks and prune the original networks in terms of the gap in their spectrum that make the subnetworks have the smallest dimensions.

Recent studies have shown that graph learning models are highly vulnerable to adversarial attacks, and network alignment methods are no exception. How to enhance the robustness of network alignment against adversarial attacks remains an open research problem. In this paper, we propose a robust network alignment solution, RNA, for offering preemptive protection of existing network alignment algorithms, enhanced with the guidance of effective adversarial attacks. First, we analyze how popular iterative gradient-based adversarial attack techniques suffer from gradient vanishing issues and show a fake sense of attack effectiveness. Based on dynamical isometry theory, an attack signal scaling (ASS) method with established upper bound of feasible signal scaling is introduced to alleviate the gradient vanishing issues for effective adversarial attacks while maintaining the decision boundary of network alignment. Second, we develop an adversarial perturbation elimination (APE) model to neutralize adversarial nodes in vulnerable space to adversarial-free nodes in safe area, by integrating Dirac delta approximation (DDA) techniques and the LSTM models. Our proposed APE method is able to provide proactive protection to existing network alignment algorithms against adversarial attacks. The theoretical analysis demonstrates the existence of an optimal distribution for the APE model to reach a lower bound. Last but not least, extensive evaluation on real datasets presents that RNA is able to offer the preemptive protection to trained network alignment methods against three popular adversarial attack models.

Despite achieving remarkable performance, deep graph learning models, such as node classification and network embedding, suffer from harassment caused by small adversarial perturbations. However, the vulnerability analysis of graph matching under adversarial attacks has not been fully investigated yet. This paper proposes an adversarial attack model with two novel attack techniques to perturb the graph structure and degrade the quality of deep graph matching: (1) a kernel density estimation approach is utilized to estimate and maximize node densities to derive imperceptible perturbations, by pushing attacked nodes to dense regions in two graphs, such that they are indistinguishable from many neighbors; and (2) a meta learning-based projected gradient descent method is developed to well choose attack starting points and to improve the search performance for producing effective perturbations. We evaluate the effectiveness of the attack model on real datasets and validate that the attacks can be transferable to other graph learning models.