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How does Heterophily Impact the Robustness of Graph Neural Networks? Theoretical Connections and Practical Implications

Jiong Zhu, Junchen Jin, Donald Loveland, Michael T. Schaub, and Danai Koutra. 2022. How does Heterophily Impact the Robustness of Graph Neural Networks? Theoretical Connections and Practical Implications. In Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD ’22), August 14–18, 2022, Washington, DC, USA. ACM, New York, NY, USA, 20 pages. https://doi.org/10.1145/3534678.3539418

[Paper + Full Appendix]

Additional Details on Empirical Evaluation

In the full appendix, we include additional details on the setups and results of empirical evaluation, which includes

Implementations and detailed hyperparameters for GNNs and randomized smoothing;
Details on combining heterophilous design with explicit robustness-enhancing mechanisms;
Additional results for evasion attacks (§5.2) and certifiable robustness (§5.3);
Discussions on the comparison between certifiable and empirical robustness.

Requirements

Install a conda virtual environment with requirements
```
conda env create -f HeteroRobustEnv.yml
```
Activate the new environment conda activate torch. The virtual environment is named as torch, and you can change it manually by modifying the first line of HeteroRobustEnv.yml.
```
conda activate torch
```
Verify that the new environment was installed correctly:
```
(torch) conda env list
```
Should you meet any problem, refer to the official conda document.
Additionally, you will need to manually install TensorFlow==2.2 to run H2GCN, CPGNN and GraphSAGE , and make sure that you are running all the code with a CUDA-enabled GPU.

Attack Generation

To generate attacks with Nettack used for benchmark study (§5.2), run the executable file in ./bin/nettack-adj-only.sh:
```
(torch) chmod +x ./bin/nettack-adj-only.sh
(torch) ./bin/nettack-adj-only.sh
```
You can modify the configurations in ./bin/nettack-adj-only.sh.
- Change the random seed SEED
- Change the DATASET you want to attack from [cora, citeseer, fb100, snap-patents-downsampled]
- Change the number of target nodes --random_num <Number_OF_TARGET_NODES>
To generate attacks with Metattack, run this command:
```
(torch) chmod +x ./bin/metattack-adj-only.sh
(torch) ./bin/metattack-adj-only.sh
```
You can modify the configurations in ./bin/metattack-adj-only.sh.
- Change the random seed SEED
- Change the DATASET you want to attack from [cora, citeseer, fb100, snap-patents-downsampled]
- Change the percentage of the edges to be perturbed ptb_ratio. Please enter ptb_ratio as a float between [0, 1].

To generate attacks with Nettack which we studied in §5.1:

python -m HeteroRobust.runner configs/perturbation/nettack-single-perturb.json -p 4

Evaluation

To perform robustness evaluation of the GNN models:

Modify the config files in ./configs/ folder.

For Nettack and Metattack,
- You will need to first generate the perturbations as instructed in last section;
- Please make sure PerturbJobFilters/doc/comment meet with your EXP_NAME in the attack phase (/bin/nettack-adj-only.sh or ./bin/metattack-adj-only.sh);
- Refer to the table below for the detailed arguments for each GNN model;
- For each model, you can switch between poison attack only poison, evasion attack only evasion, and both poison attack and evasion attack poison+evasion;
- Tunable hyperparameters are listed in Vars;
- For Nettack, modify ./configs/adj-only-nettack/nettack-adj-only.json;
- For Metattack, modify ./configs/adj-only-metattack/metattack-adj-only.json.
For Certifiable robustness,
- You do not need to generate perturbations first;
- Sparse smoothing parameters are listed in SessionConfig and TemplateVars;
- Datasets used are listed in datasetName;
- Modify ./configs/adj-only-cert/sparse-smoothing-cert.json.

Run the evaluation

python -m HeteroRobust.runner configs/<CONFIG_TO_RUN> -p <NUMBER_OF_WORKERS>

For example, to evaluate with Nettack with 4 workers, run the following code.

python -m HeteroRobust.runner configs/adj-only-nettack/nettack-adj-only.json -p 4

To evaluate the certifiable robustness with 4 workers, run the following code.

python -m HeteroRobust.runner configs/adj-only-cert/sparse-smoothing-cert.json -p 4

The outputs will be stored in the workspace folder. And you can analyze the results using the jupyter notebooks provided in the results folder. Refer to the Results section for more details.

Below are the model arguments used in experiments of the paper.

GNN	model_name	argument
H2GCN-SVD	`H2GCN`	`--adj_svd_rank {k}` (select the best `{k}` per dataset)
GraphSAGE-SVD	`H2GCN`	`--adj_nhood ['1'] --network_setup I-T1-G-V-C1-M64-R-T2-G-V-C2-MO-R --adj_norm_type rw --adj_svd_rank {k}` (select the best `{k}` per dataset)
H2GCN-MGDC	`H2GCN`	`--network_setup M64-R-T1-GS-V-T2-GS-V-C1-C2-D0.5-MO --adj_norm_type gdc`
GraphSAGE-MGDC	`H2GCN`	`--adj_nhood ['1'] --network_setup I-T1-GS-V-C1-M64-R-T2-GS-V-C2-MO-R --adj_norm_type gdc`
H2GCN	`H2GCN`	(Empty)
GraphSAGE	`H2GCN`	`--adj_nhood ['1'] --network_setup I-T1-G-V-C1-M64-R-T2-G-V-C2-MO-R --adj_norm_type rw`
CPGNN	`CPGNN`	`--network_setup M64-R-MO-E-BP2`
GPR-GNN	`GPRGNN`	`--nhid 64 --alpha {gprgnn_alpha}` (select the best `{gprgnn_alpha}` overall)
FAGCN	`FAGCN`	`--nhid 64 --eps {fagcn_eps} --dropout 0.5` (select the best `{fagcn_eps}` overall)
APPNP	`APPNP`	`--alpha 0.9`
GNNGuard	`GNNGuard`	`--nhid 64 --base_model GCN_fixed`
ProGNN	`ProGNN`	`--nhid 64`
GCN-SVD	`GCNSVD`	`--nhid 64 --svd_solver eye-svd --k {k}` (select the best `{k}` per dataset)
GCN-MGDC	`H2GCN`	`--adj_nhood ['0,1'] --network_setup M64-GS-V-R-D0.5-MO-GS-V --adj_norm_type gdc`
GAT	`GAT`	(Empty)
GCN	`H2GCN`	`--adj_nhood ['0,1'] --network_setup M64-G-V-R-D0.5-MO-G-V`
MLP	`H2GCN`	`--network_setup M64-R-D0.5-MO`

Results

Run the jupyter notebook under ./results/ for analyzing the results.

For Nettack, please run ./results/adj-only-nettack/nettack.ipynb
For Metattack, please run ./results/adj-only-metattack/metattack.ipynb.
For Certifiable robustness, please run ./results/adj-only-cert/cert.ipynb

Refer to the Appendix of the paper for detailed results.

Contact

Please contact Jiong Zhu (jiongzhu@umich.edu) in case you have any questions.

Citation

Please cite our work if you find it is helpful for your research:

@inproceedings{zhu2021graph,
  title={How does Heterophily Impact the Robustness of Graph Neural Networks? Theoretical Connections and Practical Implications},
  author={Zhu, Jiong and Jin, Junchen and Loveland, Donald and Schaub, Michael T and Koutra, Danai},
  booktitle={Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD ’22)},
  year={2022}
}

If you make use of our code in your work, please also cite DeepRobust, upon which our code is built:

@article{li2020deeprobust,
  title={Deeprobust: A pytorch library for adversarial attacks and defenses},
  author={Li, Yaxin and Jin, Wei and Xu, Han and Tang, Jiliang},
  journal={arXiv preprint arXiv:2005.06149},
  year={2020}
}