SchurNet

Equivariant Linear Layers and Wreath Product Groups This repository explores the characterization of equivariant linear layers for representations of permutations and related groups. Instead of traditional parameter-sharing, the approach relies on irreducible representations and Schur’s lemma, providing new insights into existing models like: This repo contains code for the experimental part of the paper "Revisiting Multi-Permutation Equivariance Thourgh The Lens of Irreducible Representations".

Installation

To create a conda environment that is good for all experiments, please run

git clone [email protected]:yonatansverdlov/SchurNet.git
cd SchurNet
conda env create -f dependencies.yml 
conda activate SchurNet

Graph Matching

In this experiment, we highlight the need of all linear equivariant layers. Choose a model_type in Siamese, SchurNet, and DSS. Choose noise_level and run:

cd graph_matching
python train.py --model_type model_type --noise noise_level

Wasserstein Distance Computation

Data

Run the following code:

cd Wasserstein_Distance
python -c "import kagglehub, shutil, os; os.makedirs('./data/samples', exist_ok=True); p=kagglehub.dataset_download('yonatansverdlov/data-for-wasserstein-distance-computation'); [shutil.move(os.path.join(p, f), os.path.join('./data/samples', f)) for f in os.listdir(p)]; shutil.rmtree(p, ignore_errors=True); print('Dataset downloaded directly to: ./data/samples')"

Training

Choose set_name in ncircle3, ncircle6, random, mn_small, mn_large, rna. After downloading the data, please run the following command to start the training process:

python train_wd.py --dataset_name set_name

Deep Weight Space Alignment

Data

Choose data_name to be mnist or cifar10.

MNIST MLP

To run the MLP experiments, first download the data:

cd DWS
mkdir -p data
wget "https://www.dropbox.com/s/sv85hrjswaspok4/mnist_classifiers.zip" -P data
unzip -q data/mnist_classifiers.zip -d data/samples
python utils/data_utils/generate_splits.py --data_name mnist

CIFAR10 MLP

To run the MLP experiments, first download the data:

cd DWS
mkdir -p data
wget -O data/cifar_classifiers.zip "https://www.dropbox.com/scl/fi/lex7rj1147nhq2hsp83r1/cifar10_mlps.zip?rlkey=tiyq14zl70hjbmhq2y9sg14xo&dl=1"
unzip -q data/cifar_classifiers.zip -d data/samples
python utils/data_utils/generate_splits.py --data_name cifar10

Training

For our model with the shared layers run:

python trainer.py --data_name data_name --add_common True

For the baseline of Siamese model, run:

python trainer.py --data_name data_name --add_common False

Citation

@inproceedings{sverdlov2025revisiting,
      title={Revisiting Multi-Permutation Equivariance through the Lens of Irreducible Representations}, 
      author={Yonatan Sverdlov and Ido Springer and Nadav Dym},
      booktitle={International Conference on Learning Representations (ICLR)},
      year={2025},
      eprint={2410.06665},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2410.06665}
}