# Towards Inductive Robustness: Distilling and Fostering Wave-induced Resonance in Transductive GCNs Against Graph Adversarial Attacks

arXiv: https://arxiv.org/abs/2312.08651 · HTML: https://mlsanity.com/paper/2312.08651/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 35 references that are in the map.
- First posted on arXiv 14 Dec 2023.

## Builds on (most cited first, 16 of 16)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Adversarial Attacks on Neural Networks for Graph Data](https://mlsanity.com/paper/1805.07984/) (2018)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Adversarial Attack on Graph Structured Data](https://mlsanity.com/paper/1806.02371/) (2018)
- [Adversarial Attacks on Graph Neural Networks via Meta Learning](https://mlsanity.com/paper/1902.08412/) (2019)
- [Adversarial Attack and Defense on Graph Data: A Survey](https://mlsanity.com/paper/1812.10528/) (2018)
- [Elastic Graph Neural Networks](https://mlsanity.com/paper/2107.06996/) (2021)
- [Reliable Representations Make A Stronger Defender: Unsupervised Structure Refinement for Robust GNN](https://mlsanity.com/paper/2207.00012/) (2022)
- [Metadata Embeddings for User and Item Cold-start Recommendations](https://mlsanity.com/paper/1507.08439/) (2015)
- [Unsupervised Graph Poisoning Attack via Contrastive Loss Back-propagation](https://mlsanity.com/paper/2201.07986/) (2022)
- [Adversarial Explanations for Understanding Image Classification Decisions and Improved Neural Network Robustness](https://mlsanity.com/paper/1906.02896/) (2019)
- [Node Embedding with Adaptive Similarities for Scalable Learning over Graphs](https://mlsanity.com/paper/1811.10797/) (2018)
- [CatGCN: Graph Convolutional Networks with Categorical Node Features](https://mlsanity.com/paper/2009.05303/) (2020)

## Built on by (most cited first, 2 of 2)

- [When Witnesses Defend: A Witness Graph Topological Layer for Adversarial Graph Learning](https://mlsanity.com/paper/2409.14161/) (2024)
- [A Review of Graph-Powered Data Quality Applications for IoT Monitoring Sensor Networks](https://mlsanity.com/paper/2410.21006/) (2024)

## Abstract (arXiv)

Graph neural networks (GNNs) have recently been shown to be vulnerable to adversarial attacks, where slight perturbations in the graph structure can lead to erroneous predictions. However, current robust models for defending against such attacks inherit the transductive limitations of graph convolutional networks (GCNs). As a result, they are constrained by fixed structures and do not naturally generalize to unseen nodes. Here, we discover that transductive GCNs inherently possess a distillable robustness, achieved through a wave-induced resonance process. Based on this, we foster this resonance to facilitate inductive and robust learning. Specifically, we first prove that the signal formed by GCN-driven message passing (MP) is equivalent to the edge-based Laplacian wave, where, within a wave system, resonance can naturally emerge between the signal and its transmitting medium. This resonance provides inherent resistance to malicious perturbations inflicted on the signal system. We then prove that merely three MP iterations within GCNs can induce signal resonance between nodes and edges, manifesting as a coupling between nodes and their distillable surrounding local subgraph. Consequently, we present Graph Resonance-fostering Network (GRN) to foster this resonance via learning node representations from their distilled resonating subgraphs. By capturing the edge-transmitted signals within this subgraph and integrating them with the node signal, GRN embeds these combined signals into the central node's representation. This node-wise embedding approach allows for generalization to unseen nodes. We validate our theoretical findings with experiments, and demonstrate that GRN generalizes robustness to unseen nodes, whilst maintaining state-of-the-art classification accuracy on perturbed graphs.