Expressive 1-Lipschitz Neural Networks for Robust Multiple Graph Learning against Adversarial Attacks

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 attackagnostic 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 f is designed to enforce the gradient norm ∇ f (x) as K l at layer l. The nearest matrix orthogonalization and polar decomposition techniques are utilized to constraint the weight norm Wl as 1/K l and make Wl close to the original weight W l . 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 f and Wl leads to the 1-Lipschitz neural network for expressive and robust multiple graph learning. Recently, Lipschitz-constrained neural networks are proposed to offer attack-agnostic defense solutions by imposing