Inverse Learning of Symmetries

This repository contains a basic implementation of our NeurIPS 2020 paper Inverse Learning of Symmetries.

Requirements

The code was tested under Python 3.6.5. To run the code, it is necessary to install the following dependencies from the requirements file.

Open a new terminal and create a virtualenv:

mkdir symmetries
cd symmetries
git clone https://github.com/bmda-unibas/InverseLearningOfSymmetries.git
cd ..
virtualenv -p python3 symmetries/paper

Activate the environment:

source symmetries/paper/bin/activate

Install the dependencies:

pip install -r symmetries/InverseLearningOfSymmetries/requirements.txt

Download Kraskov Estimator:

cd symmetries
git clone https://github.com/gregversteeg/NPEET.git
cd NPEET

Install in current virtualenv:

$VIRTUAL_ENV/bin/python setup.py install

Training

To train the artificial experiment in the paper, run this command:

python Main.py --mode train --model STIB --pretrained <path_to_saved_model>

You can decide between to following models:

• VAE
• STIB_WO_REG
• CVAE
• CVIB
• STIB

Evaluation

To evaluate the artificial experiment, run this command:

python Main.py --mode evaluate --model STIB --save_path <path_to_pretrained_model>

You can decide between to following models:

• VAE
• STIB_WO_REG
• CVAE
• CVIB
• STIB

Pre-trained Models

You can find the pretrained models here: Models

Results

Here we report the results of our basic implementation:

Qualitative Results

The left figure depicts the latent space of VAE where the first two dimensions are plotted. In contrast, the middle figure shows the latent space of STIB that was trained without our regulariser. Here, the first invariant dimension Z_0 (x-axis) is plotted against the dimension of Z_1 (y-axis). The right figure illustrates first dimension of the invariant latent space Z_0 (x-axis) plotted against Z_1 (y-axis) after being trained by our method. Horizontal coloured lines in the bottom right panel indicate invariant with respect to the target Y. In remaining panels the stripe structure is broken. Black arrows denote the invariant direction.

Quantitative Results

Model name	X MAE	Y MAE	MI(Z0,Y)
VAE	0.21	0.49	3.89
STIB W/O ADV.	0.01	0.65	3.19
CVAE	0.33	-	2.57
CVIB	0.67	-	2.45
STIB	0.04	0.47	0.25

Reference

If you like our paper and use it for your research, please cite us.

@incollection{Wieser,
title = {Inverse Learning of Symmetries},
author = {Wieser, Mario and Parbhoo, Sonali and Wieczorek, Aleksander and Roth, Volker},
booktitle = {Advances in Neural Information Processing Systems 34},
year = {2020}
}