Hello reviewer,

We are thankful for your time and consideration and glad that you are actually looking into our supplementary material!

Our algorithm mainly relies on:
1. functional_swd.py: Functions for sliced Wasserstein on the function space L_2([0, 1]).
2. sliced_hierarchical_OT.py: Functions for double-sliced Wasserstein (DSW) based on functional_swd.py.

Our experiments are presented in:
1. 1_L2_Slicing_Example.ipynb: Code that illustates functional_swd on synthetic data, see our supplementary material.
2. 2_PointCloudSet_Comparison.ipynb: Code for our experiments with point clouds.
3. 3_PerceptualPatchComparison.ipynb: Code for our experiments on comparing texture image distributions.
4. 4_MNIST_sOTTD_Adapted.ipynb: Code that computes and saves OTDD, s-OTDD, and ours for MNIST based on [2].
6. 5_FashionMNIST_sOTTD_Adapted.ipynb: Code that computes and saves OTDD, s-OTDD, and ours for FashionMNIST based on [2].
6. 6_CIFAR_sOTDD_Adapted.ipynb: Code that computes and saves OTDD, s-OTDD, and ours for CIFAR10 based on [2].
7. SFTLB_CodeCopy: Our Gromov-Wasserstein experiment, including a condensation of the GitHub repository [1]. 

For our experiments we use additional utility files/folders:
1. point_cloud_utils.py: Reads, processes and subsamples point cloud files.
2. perceptual_patch_utils.py: Generates Perlin noise and contains additional imaging utils.
3. plotting_utils.py: Reads OTDD/s-OTDD/DSW values for MNIST/FashionMNIST/CIFAR10, calulates correlations and plots them.
4. sOTDD folder [missing, copied from [2]]: This is a copy of [2] to calculate sOTDD and OTDD. We modifed one code line to set the `label cost' to zero.

[1]: https://github.com/hainn2803/s-OTDD
[2]: https://github.com/MoePien/slicing_fused_gromov_wasserstein

Additional folders contain our plots.

Thanks, 
The Authors
