This code will run in a Python 3.6 or 3.8 environment with all the relevant libraries installed (see requirements.txt). For training the equivariant models (CNSteerableLeNet, DNSteerableLeNet) you will probably want to use a GPU for speed. For the VanillaLeNet, you're better off on a CPU.

The input parameters for each run are contained in the configuration files located in the configs directory. To run a particular experiment use:

python main.py --config configs/config_mb_lenet.txt

An overview of the configuration file format can be found here.

In a Kaggle notebook you can make a local copy of the github repo quickly by running:

!git clone https://github.com/as595/E2CNNRadGal.git

The repo will then appear as a folder in the working directory. To run the code as above you will need to import the e2cnn library and the torchsummary library:

!pip install e2cnn
!pip install torchsummary

!python main.py --config configs/config_mb_lenet.txt

or

%run main.py --config configs/config_mb_lenet.txt

Configuration files are provided for experiments using the MiraBest batched data set. If you use this data set please cite:

• MiraBest : Fiona Porter, Anna M. M. Scaife et al., 2020 Zenodo: 10.5281/zenodo.4288837

This demo uses visualisation code from the E2CNN repo to show that the inference of an E(2)-steerable CNN is invariant under rotation. The left plot shows a radio galaxy image taken from the MiraBest test sample (#25). The middle plot shows the equivariant transformation of a feature space, consisting of one scalar field (color-coded) and one vector field (arrows), after a few layers. The right plot shows the feature space transformed into a comoving reference frame (stabilized view).

For comparison, this is the response of a standard CNN:

Since conventional CNNs are not equivariant under rotations, the response varies randomly with the image orientation. This prevents CNNs from automatically generalizing learned patterns between different reference frames.

The code in this repo makes extensive use of the wonderful e2cnn PyTorch extension library: e2cnn