# Fisher-Bures Adversary Graph Convolutional Networks

arXiv: https://arxiv.org/abs/1903.04154 · HTML: https://mlsanity.com/paper/1903.04154/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Mar 2019.

## Built on by (most cited first, 18 of 18)

- [Spectral Feature Augmentation for Graph Contrastive Learning and Beyond](https://mlsanity.com/paper/2212.01026/) (2022)
- [COSTA: Covariance-Preserving Feature Augmentation for Graph Contrastive Learning](https://mlsanity.com/paper/2206.04726/) (2022)
- [Topological Relational Learning on Graphs](https://mlsanity.com/paper/2110.15529/) (2021)
- [Contrastive Laplacian Eigenmaps](https://mlsanity.com/paper/2201.05493/) (2022)
- [Temporal-Viewpoint Transportation Plan for Skeletal Few-shot Action Recognition](https://mlsanity.com/paper/2210.16820/) (2022)
- [Uncertainty-DTW for Time Series and Sequences](https://mlsanity.com/paper/2211.00005/) (2022)
- [Multi-level Second-order Few-shot Learning](https://mlsanity.com/paper/2201.05916/) (2022)
- [Graph-adaptive Rectified Linear Unit for Graph Neural Networks](https://mlsanity.com/paper/2202.06281/) (2022)
- [Meet JEANIE: a Similarity Measure for 3D Skeleton Sequences via Temporal-Viewpoint Alignment](https://mlsanity.com/paper/2402.04599/) (2024)
- [REFINE: Random RangE FInder for Network Embedding](https://mlsanity.com/paper/2108.10703/) (2021)
- [Understanding and Mitigating Hyperbolic Dimensional Collapse in Graph Contrastive Learning](https://mlsanity.com/paper/2310.18209/) (2023)
- [Node Copying: A Random Graph Model for Effective Graph Sampling](https://mlsanity.com/paper/2208.02435/) (2022)
- [Adversarial robustness of VAEs through the lens of local geometry](https://mlsanity.com/paper/2208.03923/) (2022)
- [CHAIN: Enhancing Generalization in Data-Efficient GANs via lipsCHitz continuity constrAIned Normalization](https://mlsanity.com/paper/2404.00521/) (2024)
- [Graph Convolutional Network with Generalized Factorized Bilinear Aggregation](https://mlsanity.com/paper/2107.11666/) (2021)
- [Graph Self-Supervised Learning with Learnable Structural and Positional Encodings](https://mlsanity.com/paper/2502.16233/) (2025)
- [Low-Rank Projections of GCNs Laplacian](https://mlsanity.com/paper/2106.07360/) (2021)
- [Graph Enabled Cross-Domain Knowledge Transfer](https://mlsanity.com/paper/2304.03452/) (2023)

## Abstract (arXiv)

In a graph convolutional network, we assume that the graph G is generated wrt some observation noise. During learning, we make small random perturbations DeltaG of the graph and try to improve generalization. Based on quantum information geometry, DeltaG can be characterized by the eigendecomposition of the graph Laplacian matrix. We try to minimize the loss wrt the perturbed G+DeltaG while making DeltaG to be effective in terms of the Fisher information of the neural network. Our proposed model can consistently improve graph convolutional networks on semi-supervised node classification tasks with reasonable computational overhead. We present three different geometries on the manifold of graphs: the intrinsic geometry measures the information theoretic dynamics of a graph; the extrinsic geometry characterizes how such dynamics can affect externally a graph neural network; the embedding geometry is for measuring node embeddings. These new analytical tools are useful in developing a good understanding of graph neural networks and fostering new techniques.