Symmetry-Aware Fully-Amortized Optimization with
Scale Equivariant Graph Metanetworks

Bart Kuipers, Freek Byrman, Daniel Uyterlinde, and Alejandro García-Castellanos
University of Amsterdam

This repository builds upon the codebase from the paper:  Scale Equivariant Graph Metanetworks

---

Dataset Setup

To extract the CNN dataset move to the directory data/ and execute:

tar -xvf cifar10.tar.xz
# download cifar10 splits
wget https://github.com/AllanYangZhou/nfn/raw/refs/heads/main/experiments/predict_gen_data_splits/cifar10_split.csv -O data/cifar10/cifar10_split.csv

⚠️ Note: Due to storage limitations, the MLP dataset is not included in this repository. It can be made available upon request.

Configurations

The directory configs/cifar10 contains six YAML configuration files.
Each corresponds to an optimal hyperparameter setting found via grid search.

Example:

configs/
└── cifar10/
    ├── scalegmn_optimizer_cnn_tanh.yml
    ├── scalegmn_optimizer_mlp_tanh.yml
    └── ...

---

Training

To start training, run the following commands:

python -u scalegmn_optimizer_cnn_train.py --conf configs/cifar10/scalegmn_optimizer_cnn_tanh.yml
python -u scalegmn_optimizer_mlp_train.py --conf configs/cifar10/scalegmn_optimizer_mlp_tanh.yml

Evaluation

Once the model is trained, you can evaluate it on the test set using:

python -u scalegmn_optimizer_cnn_test.py --conf configs/cifar10/scalegmn_optimizer_cnn_tanh.yml
python -u scalegmn_optimizer_mlp_test.py --conf configs/cifar10/scalegmn_optimizer_mlp_tanh.yml

Breaking Scale Equivariance

To break the scale equivariance by omitting the canonicalization step simply run the same commands with the --scalegmn_args.<cnn/mlp>_args.break_symmetry flag:

python -u scalegmn_optimizer_cnn_train.py --conf configs/cifar10/scalegmn_optimizer_cnn_tanh.yml --scalegmn_args.cnn_args.break_symmetry
python -u scalegmn_optimizer_mlp_train.py --conf configs/cifar10/scalegmn_optimizer_mlp_tanh.yml --scalegmn_args.mlp_args.break_symmetry

Citation

If you find this work helpful, please cite the original paper:

@misc{kuipers2025symmetryawarefullyamortizedoptimizationscale,
      title={Symmetry-Aware Fully-Amortized Optimization with Scale Equivariant Graph Metanetworks}, 
      author={Bart Kuipers and Freek Byrman and Daniel Uyterlinde and Alejandro García-Castellanos},
      year={2025},
      eprint={2510.08300},
      archivePrefix={arXiv},
      primaryClass={cs.AI},
      url={https://arxiv.org/abs/2510.08300}, 
}