Label as Equilibrium: A Performance Booster for Graph Neural Networks on Node Classification

Usage

usage: main.py [-h] [--runs RUNS] [--gpu GPU] [--split SPLIT] [--lr LR]
               [--dropout DROPOUT] [--n-layers N_LAYERS]
               [--weight-decay WEIGHT_DECAY]
               [--early-stop-epochs EARLY_STOP_EPOCHS]
               [--max-epochs MAX_EPOCHS] [--hidden HIDDEN] [--heads HEADS]
               [--alpha ALPHA] [--theta THETA] [--drop-state DROP_STATE]
               [--drop-features DROP_FEATURES] [--input-label INPUT_LABEL]
               [--for-iter FOR_ITER] [--back-iter BACK_ITER] [--inductive]
               [--original-reuse] [--terminate-back] [--cache]
               method dataset

positional arguments:
  method                MLP | SGC | GCN | IGNN | EIGNN | GIN | SAGE | GAT
                        | GCNII | JKNet
  dataset               cora | citeseer | pubmed | flickr | arxiv | yelp |
                        reddit | ...

options:
  -h, --help            show this help message and exit
  --runs RUNS           Default: 1
  --gpu GPU             Default: 0
  --split SPLIT         Ratio of labels for training. Set to 0 to use
                        default split (if any) or 0.6. With an integer x
                        the dataset is splitted like Cora with the
                        training set be composed by x samples per class.
                        Default: 0
  --lr LR               Learning Rate. Default: 0.01
  --dropout DROPOUT     Default: 0
  --n-layers N_LAYERS   Default: 2
  --weight-decay WEIGHT_DECAY
                        Default: 0
  --early-stop-epochs EARLY_STOP_EPOCHS
                        Maximum epochs until stop when accuracy
                        decreasing. Default: 100
  --max-epochs MAX_EPOCHS
                        Maximum epochs. Default: 1000
  --hidden HIDDEN       Dimension of hidden representations and implicit
                        state. Default: 64
  --heads HEADS         Number of attention heads for GAT. Default: 1
  --alpha ALPHA         Hyperparameter for GCNII. Default: 0.5
  --theta THETA         Hyperparameter for GCNII. Default: 1.0
  --drop-state DROP_STATE
                        Ratio of known labels to mask in input. Default: 0
  --drop-features DROP_FEATURES
                        Ratio of node features to mask in input. Default:
                        0
  --input-label INPUT_LABEL
                        Ratio of known labels for input. Default: 0
  --for-iter FOR_ITER   Iterations to produce state in forward-pass.
                        Default: 0
  --back-iter BACK_ITER
                        Iterations to accumulate vjp in backward-pass (0:
                        disabled; -1: adaptive). Default: 0
  --inductive           Enable the inductive setting
  --original-reuse      apply the original version (with label leakage) of
                        label reuse
  --terminate-back      terminate backward pass if the norm of vjp expands
  --cache               accelerate iterations with cache

For example, if you want to run MLP on the Cora dataset with its default split on gpu cuda:3 for 5 runs, execute

python3 main.py MLP cora --split 0 --gpu 3 --runs 5

Reproducibility

Files in scripts/ folder are scripts that reproduce experiments in our article.

• run_weekday runs experiment on the Weekday dataset, producing data for Figure 3 in Section 4.1
• run_chain runs experiment on the Chains dataset, producing data for Figure 4 in Section 4.2
• run_ablation runs experiments on GraphSAGE with LaI, LR, and LaE, producing data for Table 1 in Section 4.3
• run_gnn runs experiments on different homophilic GNNs with LaE, producing data for Table 2 in Section 4.3
• run_hetgnn runs experiments on different heterophilic GNNs with LaE, producing data for Table 3 in Section 4.3
• run_wellpose runs experiments on LR+ and LaE, producing data for Figure C.5 in Appendix C

Datasets

The Chains dataset and the Transitional Chains dataset are generated by code modified from IGNN. The Weekday dataset is generated by code from 3ference. The BGP dataset is from PathNet. The genius dataset is from LINKX. Other datasets used in our paper, including Chameleon, Squirrel, Flickr, Pubmed, Amazon Photo, Coauthor CS, and etc, are retrieved PyG.

Datasets that did not appear in our paper can also be retrieved by our code for further exploration, with the help of PyG, and OGB.

Baselines

We implement all methods except IGNN and EIGNN with PyTorch, PyG, and Scikit-learn, if you want to run one of them, install PyTorch, Scikit-learn, PyG, and OGB first then execute main.py.

To run IGNN and EIGNN, you need to clone this commit of EIGNN (and install its dependencies) then place our main.py into the cloned folder.

Citation

@article{LUO2025107285,
  title = {Label as Equilibrium: A performance booster for Graph Neural Networks on node classification},
  journal = {Neural Networks},
  pages = {107284},
  year = {2025},
  issn = {0893-6080},
  doi = {https://doi.org/10.1016/j.neunet.2025.107284},
  url = {https://www.sciencedirect.com/science/article/pii/S0893608025001637},
  author = {Yi Luo and Guangchun Luo and Guiduo Duan and Aiguo Chen},
  keywords = {Graph Neural Networks, Node classification},
}