The Lie Derivative for Learned Equivariance

Installation instructions

Clone submodules and install requirements using

git clone --recurse-submodules https://github.com/ngruver/lie-deriv.git
cd lie-deriv
pip install -r requirements.txt

Layer-wise equivariance experiments

The equivariance of individual models can be calculated using exps_layerwise.py, for example

python exps_layerwise.py \
  --modelname=resnet50 \
  --output_dir=$HOME/lee_results \
  --num_imgs=20 \
  --num_probes=100 \
  --transform=translation

Default models and transforms are available in our wandb sweep configuration

End-to-end equivariance experiments

python exps_e2e.py \
  --modelname=resnet50 \
  --output_dir=$HOME/lee_results \
  --num_datapoints=100

We also include the wandb sweep configuration for our end-to-end equivariance experiments.

Plotting and Visualization

We make our results and plotting code available in a google colab notebook

Citation

If you find our work helpful, please cite it with

@misc{https://doi.org/10.48550/arxiv.2210.02984,
  doi = {10.48550/ARXIV.2210.02984},
  url = {https://arxiv.org/abs/2210.02984},
  author = {Gruver, Nate and Finzi, Marc and Goldblum, Micah and Wilson, Andrew Gordon},
  title = {The Lie Derivative for Measuring Learned Equivariance},
  publisher = {arXiv},
  year = {2022},
  copyright = {Creative Commons Attribution 4.0 International}
}