Zepeng Zhang

Zepeng Zhang, Ziping Zhao

The graph neural network (GNN) has demonstrated its superior performance in various applications. The working mechanism behind it, however, remains mysterious. GNN models are designed to learn effective representations for graph-structured data, which intrinsically coincides with the principle of graph signal denoising (GSD). Algorithm unrolling, a "learning to optimize" technique, has gained increasing attention due to its prospects in building efficient and interpretable neural network architectures. In this paper, we introduce a class of unrolled networks built based on truncated optimization algorithms (e.g., gradient descent and proximal gradient descent) for GSD problems. They are shown to be tightly connected to many popular GNN models in that the forward propagations in these GNNs are in fact unrolled networks serving specific GSDs. Besides, the training process of a GNN model can be seen as solving a bilevel optimization problem with a GSD problem at the lower level. Such a connection brings a fresh view of GNNs, as we could try to understand their practical capabilities from their GSD counterparts, and it can also motivate designing new GNN models. Based on the algorithm unrolling perspective, an expressive model named UGDGNN, i.e., unrolled gradient descent GNN, is further proposed which inherits appealing theoretical properties. Extensive numerical simulations on seven benchmark datasets demonstrate that UGDGNN can achieve superior or competitive performance over the state-of-the-art models.

Zepeng Zhang, Songtao Lu, Zengfeng Huang et al.

The graph neural network (GNN) models have presented impressive achievements in numerous machine learning tasks. However, many existing GNN models are shown to be vulnerable to adversarial attacks, which creates a stringent need to build robust GNN architectures. In this work, we propose a novel interpretable message passing scheme with adaptive structure (ASMP) to defend against adversarial attacks on graph structure. Layers in ASMP are derived based on optimization steps that minimize an objective function that learns the node feature and the graph structure simultaneously. ASMP is adaptive in the sense that the message passing process in different layers is able to be carried out over dynamically adjusted graphs. Such property allows more fine-grained handling of the noisy (or perturbed) graph structure and hence improves the robustness. Convergence properties of the ASMP scheme are theoretically established. Integrating ASMP with neural networks can lead to a new family of GNN models with adaptive structure (ASGNN). Extensive experiments on semi-supervised node classification tasks demonstrate that the proposed ASGNN outperforms the state-of-the-art GNN architectures in terms of classification performance under various adversarial attacks.

Zepeng Zhang, Olga Fink

Detecting and localizing leakages is a significant challenge for the efficient and sustainable management of water distribution networks (WDN). Leveraging the inherent graph structure of WDNs, recent approaches have used graph-based data-driven methods. However, these methods often learn shortcuts that work well with in-distribution data but fail to generalize to out-of-distribution data. To address this limitation and inspired by the perfect generalization ability of classical algorithms, we propose an algorithm-informed graph neural network (AIGNN). Recognizing that WDNs function as flow networks, incorporating max-flow information can be beneficial for inferring pressures. In the proposed framework, we first train AIGNN to emulate the Ford-Fulkerson algorithm for solving max-flow problems. This algorithmic knowledge is then transferred to address the pressure estimation problem in WDNs. Two AIGNNs are deployed, one to reconstruct pressure based on the current measurements, and another to predict pressure based on previous measurements. Leakages are detected and localized by comparing the outputs of the reconstructor and the predictor. By pretraining AIGNNs to reason like algorithms, they are expected to extract more task-relevant and generalizable features. Experimental results demonstrate that the proposed algorithm-informed approach achieves superior results with better generalization ability compared to GNNs that do not incorporate algorithmic knowledge.