Learning to Drop: Robust Graph Neural Network via Topological Denoising (2011.07057v1)

Abstract: Graph Neural Networks (GNNs) have shown to be powerful tools for graph analytics. The key idea is to recursively propagate and aggregate information along edges of the given graph. Despite their success, however, the existing GNNs are usually sensitive to the quality of the input graph. Real-world graphs are often noisy and contain task-irrelevant edges, which may lead to suboptimal generalization performance in the learned GNN models. In this paper, we propose PTDNet, a parameterized topological denoising network, to improve the robustness and generalization performance of GNNs by learning to drop task-irrelevant edges. PTDNet prunes task-irrelevant edges by penalizing the number of edges in the sparsified graph with parameterized networks. To take into consideration of the topology of the entire graph, the nuclear norm regularization is applied to impose the low-rank constraint on the resulting sparsified graph for better generalization. PTDNet can be used as a key component in GNN models to improve their performances on various tasks, such as node classification and link prediction. Experimental studies on both synthetic and benchmark datasets show that PTDNet can improve the performance of GNNs significantly and the performance gain becomes larger for more noisy datasets.

• The paper presents PTDNet, a framework that improves GNN robustness and accuracy by learning to drop noisy edges via topological denoising.
• PTDNet learns to drop noisy edges using parameterized topological denoising, enhancing GNN robustness and accuracy across various models and datasets.
• Experiments show PTDNet improves accuracy and robustness for GNNs on various datasets and models, with greater benefits seen in noisy graphs.

An Analysis of "Learning to Drop: Robust Graph Neural Network via Topological Denoising"

The paper "Learning to Drop: Robust Graph Neural Network via Topological Denoising" by Dongsheng Luo et al. presents a novel methodology for improving the robustness and accuracy of Graph Neural Networks (GNNs) through a denoising framework named PTDNet. This paper addresses the issue that GNNs are susceptible to the quality of input graphs, which often contain task-irrelevant edges, leading to suboptimal model performance. The authors propose a strategy to enhance GNNs by learning to drop such noisy edges using a parameterized topological denoising mechanism.

Core Contributions

The main contribution of the paper is PTDNet, a framework that aims to improve GNN performance by filtering task-irrelevant edges. The architecture of PTDNet is divided into two primary components: the denoising network and general GNNs. The denoising network employs a parameterized approach to evaluate and adjust the importance of each edge, guided by downstream task objectives. This results in a sparsified graph which feeds into GNN layers for better learning outcomes.

Methodological Innovations

1. Parameterized Topological Denoising Network (PTDNet): This component leverages a parameterized method to determine the relevance of edges by incorporating both structural and content information of the nodes connected by an edge. Through this process, PTDNet actively penalizes task-irrelevant edges and adapts to the specific needs of the downstream tasks, unlike traditional methods that might rely on pre-defined rules or random selection.
2. Low-Rank Constraint through Nuclear Norm Regularization: As a part of the denoising process, PTDNet imposes a low-rank constraint on the sparsified graph to encourage robustness and improve generalization. The authors employ nuclear norm relaxation to achieve tractable optimization, which effectively reduces inter-community edges that could potentially introduce noise and dilution of relevant node features.
3. Experimental Validation: The empirical evaluations demonstrate that PTDNet significantly improves the accuracy and robustness of various GNN models, including GCN, GraphSage, and GAT, across multiple real-world and synthetic datasets. Notably, performance gains are more pronounced in graphs with higher noise levels, testifying to the robustness introduced by the denoising process.

Implications and Future Directions

PTDNet introduces a structured approach to selectively prune graph edges, which has meaningful implications for both theoretical advancements and practical applications:

• Theoretical Insight: The paper contributes to a deeper understanding of how noise in graph structures influences GNN performance, and how task-specific graph sparsification can mitigate these effects. The convincing use of low-rank constraints offers a novel angle in controlling the rank of the adjacency matrix for improved learning and generalization.
• Practical Applications: Due to its ability to generalize across different datasets and noise levels, PTDNet can be integrated into existing GNN-based systems to improve their robustness in various tasks like node classification and link prediction. This makes it particularly useful in domains with inherently noisy graph structures such as social networks or biological networks.
• Future Work: The proposed framework opens several avenues for further exploration. Extending PTDNet to other forms of GNN architectures and exploring its adaptability in different domain-specific datasets could yield more tailored approaches to graph learning. Furthermore, exploring the interplay between denoising and interpretability of the learned graph representations could provide additional insights into model design.

In conclusion, PTDNet represents a substantial step forward in addressing noise-related challenges in GNNs, providing a robust, generalizable, and application-agnostic approach to enhance graph learning methodologies. The consideration of both node content and graph topology in the denoising process ensures that this framework is both comprehensive and adaptable, marking a meaningful contribution to the field of graph analytics.