The implementation of the paper "PDO-eConvs: Partial Differential Operator Based Equivariant Convolutions" (ICML2020). Please contact [email protected] if you have any question.
Tensorflow
Your may refer to https://github.com/Roderickzzc/Pdo-econv-pytorch for an implementation by Pytorch.
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
python3 mnist.py
python3 cifar.py --aug True --dataset cifar10
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 |
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}
}