PDO-eConvs

The implementation of the paper "PDO-eConvs: Partial Differential Operator Based Equivariant Convolutions" (ICML2020). Please contact shenzhy@pku.edu.cn if you have any question.

Prerequisites

Tensorflow

Your may refer to https://github.com/Roderickzzc/Pdo-econv-pytorch for an implementation by Pytorch.

Datasets

MNIST-rot-12k can be downloaded from http://www.iro.umontreal.ca/~lisa/icml2007data/mnist_rotation_new.zip, and CIFAR from http://www.cs.toronto.edu/~kriz/cifar.html

Usage

MNIST-rot-12k:

python3 mnist.py

CIFAR10/100

python3 cifar.py --aug True --dataset cifar10

Experimental Results

Error rates on MNIST-rot-12k (without data augmentation).

Network	Test Error (%)	params
CNN	5.03	22k
G-CNN	2.28	25k
PDO-eConv	1.87	26k

Error rates on CIFAR.

Method	G	Depth	C10	C100	params
ResNet	Z^2	26	11.5	31.66	0.37M
HexaConv	p6	26	9.98		0.34M
	p6m	26	8.64		0.34M
PDO-eConv	p6	26	5.65	27.13	0.36M
	p6m	26	5.38	27.00	0.37M
------	------	------	------	------	------
ResNet	Z^2	44	5.61	24.08	2.64M
G-CNN	p4m	44	4.94	23.19	2.62M
ResNet	p8	44	3.68	20.01	2.62M
------	------	------	------	------	------
ResNet	Z^2	1001	4.92	22.71	10.3M
	Z^2	26	4.00	19.25	36.5M
G-CNN	p4m	26	4.17		7.2M
PDO-eConv	p8	26	3.50	18.40	4.6M

Citation

If you found this package useful, please cite

@inproceedings{shen2020pdo,
  title={PDO-eConvs: Partial Differential Operator Based Equivariant Convolutions},
  author={Shen, Zhengyang and He, Lingshen and Lin, Zhouchen and Ma, Jinwen},
  booktitle={International Conference on Machine Learning},
  pages={8697--8706},
  year={2020},
  organization={PMLR}
}