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Fisher-Bures Adversary Graph Convolutional Networks
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Fisher-Bures Adversary Graph Convolutional Networks

MIT license

This is a reference implementation of the paper Fisher-Bures Adversary Graph Convolutional Network


Based on information geometry, the intrinsic shape of isotropic noise corresponds to the largest eigenvectors of the graph Laplacian. Such noise can bring a small but consistent improvement to generalization. In the paper we discussed three different geometries of a graph that is embedded in a neural network, namely intrinsic geometry (how to define graph distance); extrinsic geometry (how perturbation of the graph affect the neural network); embedding geometry (in the space of all network embeddings). We imported new tools from quantum information geometry into the domain of graph neural networks.


The following table shows the average (20 random splits of train:dev:test data; 10 different random initialisations for each split) testing loss/accuracy, based on a GCN model with one hidden layer, using a unified early stopping criterion. One may refer to for the exact evaluation protocols and hyperparameter settings.

Model Cora Citeseer Pubmed amazon_electronics_computers amazon_electronics_photo
GCN 1.103/80.21 1.394/69.42 0.836/78.33 2.357/37.75 1.998/71.03
FisherGCN 1.084/80.48 1.593/69.61 0.826/78.47 2.354/40.73 1.992/72.34
GCNT 1.076/80.96 1.359/70.28 0.793/79.02 2.269/68.48 1.938/79.4
FisherGCNT 1.045/81.21 1.563/70.47 0.782/79.12 2.262/70.4 1.928/81.12

Notice that the low score of GCN/FisherGCN on amazon_electronics_computer is due to failed runs (stopping too early).


  • Python >=3.6.x
  • Tensorflow >= 1.13

Install dependencies

  pip install -r requirements.txt

to install all dependencies.


We use the same datasets as in [1][2][3]. They are stored in the folder data. Please install git-lfs before closing the repository with the following commands

# ...install git-lfs...
git lfs install
git clone

Run the code

python --model fishergcn


The codes are subject to changes and are not necessarily synchronized with our arxiv report.


The following works are highlighted here because our codes and datasets are largely based on them. See our paper for the complete list of references.

[1] Z. Yang, W. W. Cohen, R. Salakhutdinov, Revisiting Semi-Supervised Learning with Graph Embeddings, ICML, 2016. (Dataset)

[2] T. Kipf, M. Welling, Semi-Supervised Classification with Graph Convolutional Networks, ICLR, 2017. (Dataset)

[3] O. Shchur, M. Mumme, A. Bojchevski, S. Günnemann, Pitfalls of Graph Neural Network Evaluation, Relational Representation Learning Workshop, NIPS 2018. Dataset


If you apply FisherGCN in your work, please cite

  author    = {Ke Sun and Piotr Koniusz and Zhen Wang},
  title     = {Fisher-Bures Adversary Graph Convolutional Network},
  booktitle = {Uncertainty in Artificial Intelligence},
  year      = {2019},
  pages     = {(to appear)},
  note      = {arXiv:1903.04154 [cs.LG]},
  url       = {},
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